+
+
+
+[img source](https://stackoverflow.com/questions/51841506/data-standardization-vs-normalization-vs-robust-scaler)
+
+As we can see, Normalization - Standardization and Min-Max method will compress most data to a narrow range, while robust scaler does a better job at keeping the spread of the data, although it cannot **remove** the outlier from the processed result. Remember removing/imputing outliers is another topic in data cleaning and should be done beforehand.
+
+Experience on how to choose feature scaling method:
+
+- if your feature is not Gaussian like, say, has a skewed distribution or has outliers, Normalization - Standardization is not a good choice as it will compress most data to a narrow range.
+- However, we can transform the feature into Gaussian like and then use Normalization - Standardization. Feature transformation will be discussed in section 3.4
+- When performing distance or covariance calculation (algorithm like Clustering, PCA and LDA), it is better to use Normalization - Standardization as it will remove the effect of scales on variance and covariance. Explanation [here](https://blog.csdn.net/zbc1090549839/article/details/44103801).
+- Min-Max scaling has the same drawbacks as Normalization - Standardization, and also new data may not be bounded to [0,1] as they can be out of the original range. Some algorithms, for example some deep learning network prefer input on a 0-1 scale so this is a good choice.
+
+
+
+Below is some additional resource on this topic:
+
+- A comparison of the three methods when facing skewed variables can be found [here](https://scikit-learn.org/stable/auto_examples/preprocessing/plot_all_scaling.html#sphx-glr-auto-examples-preprocessing-plot-all-scaling-py).
+- An in-depth study of feature scaling can be found [here](http://sebastianraschka.com/Articles/2014_about_feature_scaling.html).
+
+
+
+### 3.2 Discretize
+
+**Definition**: Discretization is the process of transforming continuous variables into discrete variables by creating a set of contiguous intervals that spans the range of the variable's values.
+
+#### 3.2.1 Why Discretize Matters
+
+- help to improve model performance by grouping of similar attributes with similar predictive strengths
+- enhance interpretability with grouped values
+- minimize the impact of **extreme values/seldom reversal patterns**
+- prevent overfitting possible with numerical variables
+- allow feature interaction between continuous variables (section 3.5.5)
+
+
+
+#### 3.2.2 How to Handle Discretization
+
+| Method | Definition | Pros | Cons |
+| ----------------------------------- | ------------------------------------------------------------ | ------------------------------------------------------------ | ------------------------------------------------------------ |
+| Equal width binning | divides the scope of possible values into N bins of the same width | / | sensitive to skewed distribution |
+| Equal frequency binning | divides the scope of possible values of the variable into N bins, where each bin carries the same amount of observations | may help boost the algorithm's performance | this arbitrary binning may disrupt the relationship with the target |
+| K-means binning | using k-means to partition values into clusters | / | needs hyper-parameter tuning |
+| Discretization using decision trees | using a decision tree to identify the optimal splitting points that would determine the bins | observations within each bin are more similar to themselves than to those of other bins | 1. may cause over-fitting
2. may not get a good performing tree |
+| ChiMerge[^11] | supervised hierarchical bottom-up (merge) method that locally exploits the chi-square criterion to decide whether two adjacent intervals are similar enough to be merged | robust and make use of a priori knowledge | cannot handle unlabeled data |
+
+In general there's no best choice of discretization method. It really depends on the dataset and the following learning algorithm. Study carefully about your features and context before deciding. You can also try different methods and compare the model performance.
+
+Some literature reviews on feature discretization can be found [here1](https://pdfs.semanticscholar.org/94c3/d92eccbb66f571153f99b7ae6c6167a00923.pdf), [here2](http://robotics.stanford.edu/users/sahami/papers-dir/disc.pdf), [here3](http://axon.cs.byu.edu/papers/ventura.thesis.ps).
+
+
+
+### 3.3 Feature Encoding
+
+#### 3.3.1 Why Feature Encoding Matters
+
+We must transform strings of categorical variables into numbers so that algorithms can handle those values. Even if you see an algorithm can take into categorical inputs, it's most likely that the algorithm incorporate the encoding process within.
+
+#### 3.3.2 How to Handle Feature Encoding
+
+| Method | Definition | Pros | Cons |
+| ------------------------ | ------------------------------------------------------------ | ------------------------------------------------------------ | ------------------------------------------------------------ |
+| One-hot encoding | replace the categorical variable by different boolean variables (0/1) to indicate whether or not certain label is true for that observation | keep all information of that variable | 1. expand feature space dramatically if too many labels in that variable
2. does not add additional value to make the variable more predictive |
+| Ordinal-encoding | replace the labels by some ordinal number if ordinal is meaningful | straightforward | does not add additional value to make the variable more predictive |
+| Count/frequency encoding | replace each label of the categorical variable by the count/frequency within that category | / | 1. may yield same encoding for two different labels (if they appear same times) and lose valuable info.
2. may not add predictive power |
+| Mean encoding | replace the label by the mean of the target for that label. (the target must be 0/1 valued or continuous) | 1. Capture information within the label, therefore rendering more predictive features
2. Create a monotonic relationship between the variable and the target
3. Do not expand the feature space | Prone to cause over-fitting |
+| WOE encoding[^9] | replace the label with Weight of Evidence of each label. WOE is computed from the basic odds ratio: ln( (Proportion of Good Outcomes) / (Proportion of Bad Outcomes)) | 1. Establishes a monotonic relationship to the dependent variable
2. Orders the categories on a "logistic" scale which is natural for logistic regression
3，The transformed variables, can then be compared because they are on the same scale. Therefore, it is possible to determine which one is more predictive. | 1. May incur in loss of information (variation) due to binning to few categories
2. Prone to cause over-fitting |
+| Target encoding[^10] | Similar to mean encoding, but use both posterior probability and prior probability of the target | 1. Capture information within the label, therefore rendering more predictive features
2. Create a monotonic relationship between the variable and the target
3. Do not expand the feature space | Prone to cause over-fitting |
+
+**Note**: if we are using one-hot encoding in linear regression, we should keep k-1 binary variable to avoid multicollinearity. This is true for any algorithms that look at all features at the same time during training. Including SVM, neural network and clustering. Tree-based algorithm, on the other hand, need the entire set of binary variable to select the best split.
+
+An in-detail intro to WOE can be found [here](http://documentation.statsoft.com/StatisticaHelp.aspx?path=WeightofEvidence/WeightofEvidenceWoEIntroductoryOverview).
+
+
+
+### 3.4 Feature Transformation
+
+#### 3.4.1 Why Feature Transformation Matters
+
+##### 3.4.1.1 Linear Assumption
+
+**Regression**
+
+Linear regression is a straightforward approach for predicting a quantitative response Y on the basis of a different predictor variable X1, X2, ... Xn. It assumes that there is a linear relationship between X(s) and Y. Mathematically, we can write this linear relationship as Y ≈ β0 + β1X1 + β2X2 + ... + βnXn.
+
+**Classification**
+
+Similarly, for classification, Logistic Regression assumes a linear relationship between the variables and the log of the odds.
+
+Odds = p / (1 - p), where p is the probability of y = 1
+
+log(odds) = β0 + β1X1 + β2X2 + ... + βnXn
+
+**Why it's important to follow linear assumption**
+
+If the machine learning model assumes a linear dependency between the predictors Xs and the outcome Y, when there is not such a linear relationship, the model will have a poor performance. In such cases, we are better off trying another machine learning model that does not make such assumption.
+
+If there is no linear relationship and we have to use the linear/logistic regression models, mathematical transformation/discretization may help create the relationship, though it cannot guarantee a better result.
+
+##### 3.4.1.2 Variable Distribution
+
+**Linear Regression Assumptions**
+
+Linear Regression has the following assumptions over the predictor variables X:
+
+- Linear relationship with the outcome Y
+
+- Multivariate normality
+- No or little multicollinearity
+- Homoscedasticity
+
+Normality assumption means that every variable X should follow a Gaussian distribution.
+
+Homoscedasticity, also known as homogeneity of variance, describes a situation in which the error term (that is, the “noise” or random disturbance in the relationship between the independent variables (Xs) and the dependent variable (Y)) is the same across all values of the independent variables.
+
+Violations in the assumptions of homoscedasticity and / or normality (assuming a distribution of data is homoscedastic or Gaussian, when in reality it is not) may result in poor model performance.
+
+The remaining machine learning models, including Neural Networks, Support Vector Machines, Tree based methods and PCA do not make any assumption over the distribution of the independent variables. However, in many occasions the model performance may **benefit from a "Gaussian-like" distribution**.
+
+Why may models benefit from a "Gaussian-like" distributions? In variables with a normal distribution, the observations of X available to predict Y vary across a greater range of values, that is, the values of X are "spread" over a greater range.
+
+In the situations above, transformation of the original variable can help give the variable more of a bell-shape of the Gaussian distribution.
+
+#### 3.4.2 How to Handle Feature Transformation
+
+| Method | Definition |
+| --------------------------- | -------------------------------------------------------- |
+| Logarithmic transformation | log(x+1). We use (x+1) instead of x to avoid value of 0 |
+| Reciprocal transformation | 1/x. Warning that x should not be 0. |
+| Square root transformation | x**(1/2) |
+| Exponential transformation | X**(m) |
+| Box-cox transformation[^12] | (X**λ-1)/λ |
+| Quantile transformation | transform features using quantiles information |
+
+**Log transformation** is useful when applied to skewed distributions as they tend to expand the values which fall in the range of lower magnitudes and tend to compress or reduce the values which fall in the range of higher magnitudes, which helps to make the skewed distribution as normal-like as possible. **Square root transformation** does a similar thing in this sense.
+
+**Box-Cox transformation** in sklearn[^13] is another popular function belonging to the power transform family of functions. This function has a pre-requisite that the numeric values to be transformed must be positive (similar to what log transform expects). In case they are negative, shifting using a constant value helps. Mathematically, the Box-Cox transform function can be denoted as follows.
+
+
+
+**Quantile transformation** in sklearn[^14] transforms the features to follow a uniform or a normal distribution. Therefore, for a given feature, this transformation tends to spread out the most frequent values. It also reduces the impact of (marginal) outliers: this is therefore a robust preprocessing scheme. However, this transform is non-linear. It may distort linear correlations between variables measured at the same scale but renders variables measured at different scales more directly comparable.
+
+
+
+We can use **Q-Q plot** to check if the variable is normally distributed (a 45 degree straight line of the values over the theoretical quantiles) after transformation.
+
+Below is an example showing the effect of sklearn's Box-plot/Yeo-johnson/Quantile transform to map data from various distributions to a normal distribution.
+
+
+
+
+
+[img source](https://scikit-learn.org/stable/auto_examples/preprocessing/plot_map_data_to_normal.html#sphx-glr-auto-examples-preprocessing-plot-map-data-to-normal-py)
+
+On “small” datasets (less than a few hundred points), the quantile transformer is prone to overfitting. The use of the power transform is then recommended.
+
+
+
+
+### 3.5 Feature Generation
+
+**Definition**: Creating new features as a combination of existing ones. It's a great way to add domain knowledge to the dataset.
+
+#### 3.5.1 Missing Data Derived Feature
+
+As mentioned in section 2.1, we can create new binary feature denoting whether the observations have missing value on raw feature with value 0/1.
+
+#### 3.5.2 Simple Statistical Derived Feature
+
+Creating new features by performing simple statistical calculations on the raw features, including:
+
+ - count/sum
+ - average/median/mode
+ - max/min/stddev/variance/range/IQR/Coefficient of Variation
+ - time span/interval
+
+Take call log for example, we can create new features like: number of calls, number of call-in/call-out, average calling duration, monthly average calling duration, max calling duration, etc.
+
+#### 3.5.3 Feature Crossing
+
+After having some simple statistical derived features, we can have them crossed together. Common dimensions used for crossing include:
+
+- time
+- region
+- business types
+
+Still take call log for example, we can have crossed features like: number of calls during night times/day times, number of calls under different business types (banks/taxi services/travelling/hospitalities), number of calls during the past 3 months, etc. Many of the statistical calculations mentioned in section 3.5.2 can be used again to create more features.
+
+**Note**: An open-source python framework named **Featuretools** that helps automatically generate such features can be found [here](https://github.com/Featuretools/featuretools).
+
+
+
+Personally I haven't used it in practice. You may try and discover if it can be of industry usage.
+
+#### 3.5.4 Ratios and Proportions
+
+Common techniques. For example, in order to predict future performance of credit card sales of a branch, ratios like credit card sales / sales person or credit card sales / marketing spend would be more powerful than just using absolute number of card sold in the branch.
+
+#### 3.5.5 Cross Products between Categorical Features
+
+Consider a categorical feature A, with two possible values {A1, A2}. Let B be a feature with possibilities {B1, B2}. Then, a feature-cross between A & B would take one of the following values: {(A1, B1), (A1, B2), (A2, B1), (A2, B2)}. You can basically give these ‘combinations’ any names you like. Just remember that every combination denotes a synergy between the information contained by the corresponding values of A and B.
+
+This is an extremely useful technique, when certain features together denote a property better than individually by themselves. Mathematically speaking, you are doing a cross product between all possible values of the categorical features. The concepts is similar to Feature Crossing of section 3.5.3, but this one particularly refers to the crossing between 2 categorical features.
+
+#### 3.5.6 Polynomial Expansion
+
+The cross product can also be applied to numerical features, which results in a new interaction feature between A and B. This can be done easily be sklearn's [PolynomialFeatures](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.PolynomialFeatures.html#sklearn.preprocessing.PolynomialFeatures), which generate a new feature set consisting of all polynomial combinations of the features with degree less than or equal to the specified degree. For example, three raw features {X1, X2, X3} can generate a feature set of {1, X1X2, X1X3, X2X3, X1X2X3} with a degree of 2.
+
+#### 3.5.7 Feature Learning by Trees
+
+In tree-based algorithms, each sample will be assigned to a particular leaf node. The decision path to each node can be seen as a new non-linear feature, and we can create N new binary features where n equals to the total number of leaf nodes in a tree or tree ensembles. The features can then be fed into other algorithms such as logistic regression.
+
+The idea of using tree algorithm to generate new features is first introduced by Facebook in this [paper](http://quinonero.net/Publications/predicting-clicks-facebook.pdf).
+
+The good things about this method is that we can get a complex combinations of several features together, which is informative (as is constructed by the tree's learning algorithm). This saves us much time compared to doing feature crossing manually, and is widely used in CTR (click-through rate) of online advertising industry.
+
+#### 3.5.8 Feature Learning by Deep Networks
+
+As we can see from all above, feature generation by manual takes lots of effort and may not guarantee good returns, particular when we have huge amounts of features to work with. Feature learning with trees can be seen as an early attempt in creating features automatically, and with the deep learning methods come into fashion from around 2016, they also have achieved some success in this area, such as **autoencoders** and **restricted Boltzmann machines**. They have been shown to automatically and in a unsupervised or semi-supervised way, learn abstract representations of features (a compressed form), that in turn have supported state-of-the-art results in domains such as speech recognition, image classification, object recognition and other areas. However, such features have limited interpretability and deep learning require much more data to be able to extract high quality result.
+
+
+
+
+
+## 4. Feature Selection
+
+**Definition**: Feature Selection is the process of selecting a subset of relevant features for use in machine learning model building.
+
+It is not always the truth that the more data, the better the result will be. Including irrelevant features (the ones that are just unhelpful to the prediction) and redundant features (irrelevant in the presence of others) will only make the learning process overwhelmed and easy to cause overfitting.
+
+With feature selection, we can have:
+
+- simplification of models to make them easier to interpret
+- shorter training times and lesser computational cost
+- lesser cost in data collection
+- avoid the curse of dimensionality
+- enhanced generalization by reducing overfitting
+
+We should keep in mind that different feature subsets render optimal performance for different algorithms. So it's not a separate process along with the machine learning model training. Therefore, if we are selecting features for a linear model, it is better to use selection procedures targeted to those models, like importance by regression coefficient or Lasso. And if we are selecting features for trees, it is better to use tree derived importance.
+
+
+
+### 4.1 Filter Method
+
+Filter methods select features based on a performance measure regardless of the ML algorithm later employed.
+
+Univariate filters evaluate and rank a single feature according to a certain criteria, while multivariate filters evaluate the entire feature space. Filter methods are:
+
+- selecting variable regardless of the model
+- less computationally expensive
+- usually give lower prediction performance
+
+As a result, filter methods are suited for a first step quick screen and removal of irrelevant features.
+
+| Method | Definition |
+| ------------------------- | ------------------------------------------------------------ |
+| Variance | removing features that show the same value for the majority/all of the observations (constant/quasi-constant features) |
+| Correlation | remove features that are highly correlated with each other |
+| Chi-Square | Compute chi-squared stats between each non-negative feature and class |
+| Mutual Information Filter | Mutual information measures how much information the presence/absence of a feature contributes to making the correct prediction on Y. |
+| Univariate ROC-AUC or MSE | builds one decision tree per feature, to predict the target, then make predictions and ranks the features according to the machine learning metric (roc-auc or mse) |
+| Information Value (IV) | a byproduct of WOE.
IV = Σ(Proportion of Good Outcomes - Proportion of Bad Outcomes) * WOE |
+
+WOE encoding (see section 3.3.2) and IV often go hand in hand in scorecard development. The two concepts both derived from logistic regression and is kind of standard practice in credit card industry. IV is a popular and widely used measure as there are very convenient rules of thumb for variables selection associated with IV as below:
+
+
+
+However, all these filtering methods fail to consider the interaction between features and may reduce our predict power. Personally I only use variance and correlation to filter some absolutely unnecessary features.
+
+
+
+**Note**: One thing to keep in mind when using chi-square test or univariate selection methods, is that in very big datasets, most of the features will show a small p_value, and therefore look like they are highly predictive. This is in fact an effect of the sample size. So care should be taken when selecting features using these procedures. An ultra tiny p_value does not highlight an ultra-important feature, it rather indicates that the dataset contains too many samples.
+
+**Note**: Correlated features do not necessarily affect model performance (trees, etc), but high dimensionality does and too many features hurt model interpretability. So it's always better to reduce correlated features.
+
+
+
+### 4.2 Wrapper Method
+
+Wrappers use a search strategy to search through the space of possible feature subsets and evaluate each subset by the quality of the performance on a ML algorithm. Practically any combination of search strategy and algorithm can be used as a wrapper. It is featured as:
+
+- use ML models to score the feature subset
+- train a new model on each subset
+- very computationally expensive
+- usually provide the best performing subset for a give ML algorithm, but probably not for another
+- need an arbitrary defined stopping criteria
+
+The most common **search strategy** group is Sequential search, including Forward Selection, Backward Elimination and Exhaustive Search. Randomized search is another popular choice, including Evolutionary computation algorithms such as genetic, and Simulated annealing.
+
+Another key element in wrappers is **stopping criteria**. When to stop the search? In general there're three:
+
+- performance increase
+- performance decrease
+- predefined number of features is reached
+
+
+
+#### 4.2.1 Forward Selection
+
+Step forward feature selection starts by evaluating all features individually and selects the one that generates the best performing algorithm, according to a pre-set evaluation criteria. In the second step, it evaluates all possible combinations of the selected feature and a second feature, and selects the pair that produce the best performing algorithm based on the same pre-set criteria.
+
+The pre-set criteria can be the roc_auc for classification and the r squared for regression for example.
+
+This selection procedure is called greedy, because it evaluates all possible single, double, triple and so on feature combinations. Therefore, it is quite computationally expensive, and sometimes, if feature space is big, even unfeasible.
+
+There is a special package for python that implements this type of feature selection: [mlxtend](https://github.com/rasbt/mlxtend).
+
+#### 4.2.2 Backward Elimination
+
+Step backward feature selection starts by fitting a model using all features. Then it removes one feature. It will remove the one that produces the highest performing algorithm (least statistically significant) for a certain evaluation criteria. In the second step, it will remove a second feature, the one that again produces the best performing algorithm. And it proceeds, removing feature after feature, until a certain criteria is met.
+
+The pre-set criteria can be the roc_auc for classification and the r squared for regression for example.
+
+#### 4.2.3 Exhaustive Feature Selection
+
+In an exhaustive feature selection the best subset of features is selected, over all possible feature subsets, by optimizing a specified performance metric for a certain machine learning algorithm. For example, if the classifier is a logistic regression and the dataset consists of **4** features, the algorithm will evaluate all **15** feature combinations as follows:
+
+- all possible combinations of 1 feature
+- all possible combinations of 2 features
+- all possible combinations of 3 features
+- all the 4 features
+
+and select the one that results in the best performance (e.g., classification accuracy) of the logistic regression classifier.
+
+This exhaustive search is very computationally expensive. In practice for this computational cost, it is rarely used.
+
+#### 4.2.4 Genetic Algorithm
+
+TODO
+
+
+
+### 4.3 Embedded Method
+
+Embedded Method combine the advantages of the filter and wrapper methods. A learning algorithm takes advantage of its own variable selection process and performs feature selection and classification at same time. Common embedded methods include Lasso and various types of tree-based algorithms. It is featured as:
+
+- perform feature selection as part of the model building process
+- consider interactions between features
+- less computationally expensive as it only train the model once, compared to Wrappers
+- usually provide the best performing subset for a give ML algorithm, but probably not for another
+
+
+
+#### 4.3.1 Regularization with Lasso
+
+Regularization consists in adding a penalty to the different parameters of the machine learning model to reduce the freedom of the model. Hence, the model will be less likely to fit the noise of the training data so less likely to be overfitting.
+
+In linear model regularization, the penalty is applied over the coefficients that multiply each of the predictors. For linear models there are in general 3 types of regularization:
+
+- L1 regularization (Lasso)
+- L2 regularization (Ridge)
+- L1/L2 (Elastic net)
+
+From the different types of regularization, **Lasso (L1)** has the property that is able to shrink some of the coefficients to zero. Therefore, that feature can be removed from the model.
+
+Both for linear and logistic regression we can use the Lasso regularization to remove non-important features. Keep in mind that increasing the penalization will increase the number of features removed. Therefore, you will need to keep an eye and monitor that you don't set a penalty too high so that to remove even important features, or too low and then not remove non-important features.
+
+Having said this, if the penalty is too high and important features are removed, you should notice a drop in the performance of the algorithm and then realize that you need to decrease the regularization.
+
+Regularization is a large topic. For for information you can refer to here:
+
+- [Least angle and l1 penalised regression: A review](https://projecteuclid.org/download/pdfview_1/euclid.ssu/1211317636)
+- [Penalised feature selection and classification in bioinformatics](https://www.ncbi.nlm.nih.gov/pubmed/18562478)
+- [Feature selection for classification: A review](https://web.archive.org/web/20160314145552/http://www.public.asu.edu/~jtang20/publication/feature_selection_for_classification.pdf)
+
+- [Machine Learning Explained: Regularization](https://www.r-bloggers.com/machine-learning-explained-regularization/)
+
+
+
+#### 4.3.2 Random Forest Importance
+
+Random forests are one of the most popular machine learning algorithms. They are so successful because they provide in general a good predictive performance, low overfitting and easy interpretability. This interpretability is given by the fact that it is straightforward to derive the importance of each variable on the tree decision. In other words, it is easy to compute how much each variable is contributing to the decision.
+
+Random forest is a bagging algorithm consists a bunch of base estimators (decision trees), each of them built over a random extraction of the observations from the dataset and a random extraction of the features. Not every tree sees all the features or all the observations, and this guarantees that the trees are **de-correlated** and therefore **less prone to over-fitting.**
+
+Each tree is also a sequence of yes-no questions based on a single or combination of features. At each split, the question divides the dataset into 2 buckets, each of them hosting observations that are more similar among themselves and different from the ones in the other bucket. Therefore, the importance of each feature is derived by how "**pure**" each of the buckets is.
+
+For classification, the measure of impurity is either the **Gini impurity** or the **information gain/entropy**. For regression the measure of impurity is **variance**. Therefore, when training a tree, it is possible to compute how much each feature decreases the impurity. The more a feature decreases the impurity, the more important the feature is. In random forests, the impurity decrease from each feature can be averaged across trees to determine the final importance of the variable.
+
+Selecting features by using tree derived feature importance is a very straightforward, fast and generally accurate way of selecting good features for machine learning. In particular, if you are going to build tree methods.
+
+However, correlated features will show in a tree similar and lowered importance, compared to what their importance would be if the tree was built without correlated counterparts.
+
+**Limitation**
+
+- correlated features show similar importance
+
+- correlated features importance is lower than real importance, when tree is build without its correlated counterparts
+
+- high carinal variable tend to show higher importance
+
+
+#### 4.3.3 Gradient Boosted Trees Importance
+
+Similarly to selecting features using Random Forests derived feature importance, we can select features based on the importance derived by gradient boosted trees. And we can do that in one go, or in a recursive manner, depending on how much time we have, how many features are in the dataset, and whether they are correlated or not.
+
+
+
+### 4.4 Feature Shuffling
+
+A popular method of feature selection consists in random shuffling the values of a specific variable and determining how that permutation affects the performance metric of the machine learning algorithm. In other words, the idea is to permute the values of each feature, one at the time, and measure how much the permutation decreases the accuracy, or the roc_auc, or the mse of the machine learning model. If the variables are important, this is, highly predictive, a random permutation of their values will decrease dramatically any of these metrics. Contrarily, non-important / non-predictive variables, should have little to no effect on the model performance metric we are assessing.
+
+
+
+### 4.5 Hybrid Method
+
+#### 4.5.1 Recursive Feature Elimination
+
+This method consists of the following steps:
+
+1. Rank the features according to their importance derived from a machine learning algorithm: it can be tree importance, or LASSO / Ridge, or the linear / logistic regression coefficients.
+2. Remove one feature -the least important- and build a machine learning algorithm utilizing the remaining features.
+
+3. Calculate a performance metric of your choice: roc-auc, mse, rmse, accuracy.
+4. If the metric decreases by more of an arbitrarily set threshold, then that feature is important and should be kept. Otherwise, we can remove that feature.
+5. Repeat steps 2-4 until all features have been removed (and therefore evaluated) and the drop in performance assessed.
+
+The method combines the selection process like wrappers and feature importance derivation from ML models like embedded methods so it's called hybrid.
+
+The difference between this method and the step backwards feature selection lies in that it does not remove all features first in order to determine which one to remove. It removes the least important one, based on the machine learning model derived importance. And then, it makes an assessment as to whether that feature should be removed or not. So it removes each feature only once during selection, whereas step backward feature selection removes all the features at each step of selection.
+
+This method is therefore faster than wrapper methods and generally better than embedded methods. In practice it works extremely well. It does also account for correlations (depending on how stringent you set the arbitrary performance drop threshold). On the downside, the drop in performance assessed to decide whether the feature should be kept or removed, is set arbitrarily. The smaller the drop the more features will be selected, and vice versa.
+
+
+
+**Example: Recursive Feature Elimination with Random Forests Importance**
+
+As we talked about in section 4.3.2, Random Forests assign equal or similar importance to features that are highly correlated. In addition, when features are correlated, the importance assigned is lower than the importance attributed to the feature itself, should the tree be built without the correlated counterparts.
+
+Therefore, instead of eliminating features based on importance **at one time** (from all initial features), we may get a better selection by removing one feature **recursively**, and recalculating the importance on each round.
+
+In this situation, when a feature that is highly correlated to another one is removed, then, the importance of the remaining feature increases. This may lead to a better subset feature space selection. On the downside, building several random forests is quite time consuming, in particular if the dataset contains a high number of features.
+
+#### 4.5.2 Recursive Feature Addition
+
+This method consists of the following steps:
+
+1. Rank the features according to their importance derived from a machine learning algorithm: it can be tree importance, or LASSO / Ridge, or the linear / logistic regression coefficients.
+2. Build a machine learning model with only 1 feature, the most important one, and calculate the model metric for performance.
+
+3. Add one feature -the most important- and build a machine learning algorithm utilizing the added and any feature from previous rounds.
+
+4. Calculate a performance metric of your choice: roc-auc, mse, rmse, accuracy.
+
+5. If the metric increases by more than an arbitrarily set threshold, then that feature is important and should be kept. Otherwise, we can remove that feature.
+
+6. Repeat steps 2-5 until all features have been removed (and therefore evaluated) and the drop in performance assessed.
+
+The difference between this method and the step forward feature selection is similar. It does not look for all features first in order to determine which one to add, so it's faster than wrappers.
+
+
+
+### 4.6 Dimensionality Reduction
+
+- PCA（主成分分析）
+
+- SVD（奇异值分解）
+
+
+
+
+
+## 5. Data Leakage
+
+This section is a remainder to myself as I have had made huge mistakes because of not aware of the problem. Data leakage is when information from outside the training dataset is used to create the model[^15]. The result is that you may be creating overly optimistic models that are practically useless and cannot be used in production. The model shows great result on both your training and testing data but in fact it's not because your model really has a good generalizability but it uses information from the test data.
+
+While it is well known to use cross-validation or at least separate a validation set in training and evaluating the models, people may easily forget to do the same during the feature engineering & selection process. Keep in mind that the test dataset must not be used in any way to make choices about the model, including feature engineering & selection.
+
+
+
+------
+
+**Reference**
+
+[^1]: http://www.simonqueenborough.info/R/basic/missing-data
+[^2]: Rubin, D. B. (1976). Inference and missing data. Biometrika 63(3): 581-592.
+[^3]: D. Hawkins. Identification of Outliers, Chapman and Hall , 1980.
+[^4]: https://www.springer.com/gp/book/9781461463955
+[^5]: https://github.com/yzhao062/pyod
+[^6]: https://docs.oracle.com/cd/E40248_01/epm.1112/cb_statistical/frameset.htm?ch07s02s10s01.html
+[^7]: https://www.academia.edu/5324493/Detecting_outliers_Do_not_use_standard_deviation_around_the_mean_use_absolute_deviation_around_the_median
+[^8]: https://www.purplemath.com/modules/boxwhisk3.htm
+[^9]: http://documentation.statsoft.com/StatisticaHelp.aspx?path=WeightofEvidence/WeightofEvidenceWoEIntroductoryOverview
+[^10]: A Preprocessing Scheme for High-Cardinality Categorical Attributes in Classification and Prediction Problems. https://kaggle2.blob.core.windows.net/forum-message-attachments/225952/7441/high%20cardinality%20categoricals.pdf
+[^11]: https://www.aaai.org/Papers/AAAI/1992/AAAI92-019.pdf
+[^12]: http://onlinestatbook.com/2/transformations/box-cox.html
+[^13]: https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.PowerTransformer.html#sklearn.preprocessing.PowerTransformer
+[^14]: https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.QuantileTransformer.html#sklearn.preprocessing.QuantileTransformer
+[^15]: https://machinelearningmastery.com/data-leakage-machine-learning/
\ No newline at end of file
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..d17e2e4
--- /dev/null
+++ b/README.md
@@ -0,0 +1,204 @@
+# Feature Engineering & Feature Selection
+
+## About
+
+A comprehensive [guide]() for **Feature Engineering** and **Feature Selection**, with implementations and examples in Python.
+
+
+
+## What You'll Learn
+
+Not only a collection of hands-on functions, but also explanation on **Why**, **How** and **When** to adopt **Which** techniques of feature engineering in data mining.
+
+- the nature and risk of data problem we often encounter
+- explanation of the various feature engineering & selection techniques
+- rationale to use it
+- pros & cons of each method
+- code & example
+
+
+
+## Getting Started
+
+This repo is mainly used as a reference for anyone who are doing feature engineering, and most of the modules are implemented through scikit-learn or its communities.
+
+To run the demos or use the customized function, please download the ZIP file from the repo or just copy-paste any part of the code you find helpful. They should all be very easy to understand.
+
+**Required Dependencies**:
+
+- Python 3.5, 3.6 or 3.7
+- numpy>=1.15
+- pandas>=0.23
+- scipy>=1.1.0
+- scikit_learn>=0.20.1
+- seaborn>=0.9.0
+
+
+
+## Table of Contents and Code Examples
+
+Below is a list of methods currently implemented in the repo. The complete guide can be found [here]().
+
+**1. Data Exploration**
+
+ 1.1 Variables
+ 1.2 Variable Identification
+ Check Data Types
+ 1.3 Univariate Analysis
+ Descriptive Analysis
+ Discrete Variable Barplot
+ Discrete Variable Countplot
+ Discrete Variable Boxplot
+ Continuous Variable Distplot
+ 1.4 Bi-variate Analysis
+ Scatter Plot
+ Correlation Plot
+ Heat Map
+
+**2. Feature Cleaning**
+
+ 2.1 Missing Values
+ Missing Value Check
+ Listwise Deletion
+ Mean/Median/Mode Imputation
+ End of distribution Imputation
+ Random Imputation
+ Arbitrary Value Imputation
+ Add a variable to denote NA
+ 2.2 Outliers
+ Detect by Arbitrary Boundary
+ Detect by Mean & Standard Deviation
+ Detect by IQR
+ Detect by MAD
+ Mean/Median/Mode Imputation
+ Discretization
+ Imputation with Arbitrary Value
+ Windsorization
+ Discard Outliers
+ 2.3 Rare Values
+ Mode Imputation
+ Grouping into One New Category
+ 2.4 High Cardinality
+ Grouping Labels with Business Understanding
+ Grouping Labels with Rare Occurrence into One Category
+ Grouping Labels with Decision Tree
+
+**3. Feature Engineering**
+
+ 3.1 Feature Scaling
+ Normalization - Standardization
+ Min-Max Scaling
+ Robust Scaling
+ 3.2 Discretize
+ Equal Width Binning
+ Equal Frequency Binning
+ K-means Binning
+ Discretization by Decision Trees
+ ChiMerge
+ 3.3 Feature Encoding
+ One-hot Encoding
+ Ordinal-Encoding
+ Count/frequency Encoding
+ Mean Encoding
+ WOE Encoding
+ Target Encoding
+ 3.4 Feature Transformation
+ Logarithmic Transformation
+ Reciprocal Transformation
+ Square Root Transformation
+ Exponential Transformation
+ Box-cox Transformation
+ Quantile Transformation
+ 3.5 Feature Generation
+ Missing Data Derived
+ Simple Stats
+ Crossing
+ Ratio & Proportion
+ Cross Product
+ Polynomial
+ Feature Leanring by Tree
+ Feature Leanring by Deep Network
+
+**4. Feature Selection**
+
+ 4.1 Filter Method
+ Variance
+ Correlation
+ Chi-Square
+ Mutual Information Filter
+ Univariate ROC-AUC or MSE
+ Information Value (IV)
+ 4.2 Wrapper Method
+ Forward Selection
+ Backward Elimination
+ Exhaustive Feature Selection
+ Genetic Algorithm
+ 4.3 Embedded Method
+ Lasso (L1)
+ Random Forest Importance
+ Gradient Boosted Trees Importance
+ 4.4 Feature Shuffling
+ Random Shuffling
+ 4.5 Hybrid Method
+ Recursive Feature Selection
+ Recursive Feature Addition
+
+
+
+
+## Motivation
+
+Feature Engineering & Selection is the most essential part of building a useable machine learning project, even though hundreds of cutting-edge machine learning algorithms coming in these days like deep learning and transfer learning. Indeed, like what Prof Domingos, the author of *'The Master Algorithm'* says:
+
+> “At the end of the day, some machine learning projects succeed and some fail. What makes the difference? Easily the most important factor is the features used.”
+>
+> — Prof. Pedro Domingos
+
+
+Data and feature determine the upper limit of a ML project, while models and algorithms are just approaching that limit. However, few materials could be found that systematically introduce the art of feature engineering, and even fewer could explain the rationale behind. This repo aims at teaching you a good guide for Feature Engineering & Selection.
+
+
+
+## Key Links and Resources
+
+- Udemy's Feature Engineering online course
+
+https://www.udemy.com/feature-engineering-for-machine-learning/
+
+- Udemy's Feature Selection online course
+
+https://www.udemy.com/feature-selection-for-machine-learning
+
+- JMLR Special Issue on Variable and Feature Selection
+
+http://jmlr.org/papers/special/feature03.html
+
+- Data Analysis Using Regression and Multilevel/Hierarchical Models, Chapter 25: Missing data
+
+http://www.stat.columbia.edu/~gelman/arm/missing.pdf
+
+- Data mining and the impact of missing data
+
+http://core.ecu.edu/omgt/krosj/IMDSDataMining2003.pdf
+
+- PyOD: A Python Toolkit for Scalable Outlier Detection
+
+https://github.com/yzhao062/pyod
+
+- Weight of Evidence (WoE) Introductory Overview
+
+http://documentation.statsoft.com/StatisticaHelp.aspx?path=WeightofEvidence/WeightofEvidenceWoEIntroductoryOverview
+
+- About Feature Scaling and Normalization
+
+http://sebastianraschka.com/Articles/2014_about_feature_scaling.html
+
+- Feature Generation with RF, GBDT and Xgboost
+
+https://blog.csdn.net/anshuai_aw1/article/details/82983997
+
+- A review of feature selection methods with applications
+
+https://ieeexplore.ieee.org/iel7/7153596/7160221/07160458.pdf
+
+
diff --git a/data/housing.data.txt b/data/housing.data.txt
new file mode 100644
index 0000000..b488787
--- /dev/null
+++ b/data/housing.data.txt
@@ -0,0 +1,506 @@
+ 0.00632 18.00 2.310 0 0.5380 6.5750 65.20 4.0900 1 296.0 15.30 396.90 4.98 24.00
+ 0.02731 0.00 7.070 0 0.4690 6.4210 78.90 4.9671 2 242.0 17.80 396.90 9.14 21.60
+ 0.02729 0.00 7.070 0 0.4690 7.1850 61.10 4.9671 2 242.0 17.80 392.83 4.03 34.70
+ 0.03237 0.00 2.180 0 0.4580 6.9980 45.80 6.0622 3 222.0 18.70 394.63 2.94 33.40
+ 0.06905 0.00 2.180 0 0.4580 7.1470 54.20 6.0622 3 222.0 18.70 396.90 5.33 36.20
+ 0.02985 0.00 2.180 0 0.4580 6.4300 58.70 6.0622 3 222.0 18.70 394.12 5.21 28.70
+ 0.08829 12.50 7.870 0 0.5240 6.0120 66.60 5.5605 5 311.0 15.20 395.60 12.43 22.90
+ 0.14455 12.50 7.870 0 0.5240 6.1720 96.10 5.9505 5 311.0 15.20 396.90 19.15 27.10
+ 0.21124 12.50 7.870 0 0.5240 5.6310 100.00 6.0821 5 311.0 15.20 386.63 29.93 16.50
+ 0.17004 12.50 7.870 0 0.5240 6.0040 85.90 6.5921 5 311.0 15.20 386.71 17.10 18.90
+ 0.22489 12.50 7.870 0 0.5240 6.3770 94.30 6.3467 5 311.0 15.20 392.52 20.45 15.00
+ 0.11747 12.50 7.870 0 0.5240 6.0090 82.90 6.2267 5 311.0 15.20 396.90 13.27 18.90
+ 0.09378 12.50 7.870 0 0.5240 5.8890 39.00 5.4509 5 311.0 15.20 390.50 15.71 21.70
+ 0.62976 0.00 8.140 0 0.5380 5.9490 61.80 4.7075 4 307.0 21.00 396.90 8.26 20.40
+ 0.63796 0.00 8.140 0 0.5380 6.0960 84.50 4.4619 4 307.0 21.00 380.02 10.26 18.20
+ 0.62739 0.00 8.140 0 0.5380 5.8340 56.50 4.4986 4 307.0 21.00 395.62 8.47 19.90
+ 1.05393 0.00 8.140 0 0.5380 5.9350 29.30 4.4986 4 307.0 21.00 386.85 6.58 23.10
+ 0.78420 0.00 8.140 0 0.5380 5.9900 81.70 4.2579 4 307.0 21.00 386.75 14.67 17.50
+ 0.80271 0.00 8.140 0 0.5380 5.4560 36.60 3.7965 4 307.0 21.00 288.99 11.69 20.20
+ 0.72580 0.00 8.140 0 0.5380 5.7270 69.50 3.7965 4 307.0 21.00 390.95 11.28 18.20
+ 1.25179 0.00 8.140 0 0.5380 5.5700 98.10 3.7979 4 307.0 21.00 376.57 21.02 13.60
+ 0.85204 0.00 8.140 0 0.5380 5.9650 89.20 4.0123 4 307.0 21.00 392.53 13.83 19.60
+ 1.23247 0.00 8.140 0 0.5380 6.1420 91.70 3.9769 4 307.0 21.00 396.90 18.72 15.20
+ 0.98843 0.00 8.140 0 0.5380 5.8130 100.00 4.0952 4 307.0 21.00 394.54 19.88 14.50
+ 0.75026 0.00 8.140 0 0.5380 5.9240 94.10 4.3996 4 307.0 21.00 394.33 16.30 15.60
+ 0.84054 0.00 8.140 0 0.5380 5.5990 85.70 4.4546 4 307.0 21.00 303.42 16.51 13.90
+ 0.67191 0.00 8.140 0 0.5380 5.8130 90.30 4.6820 4 307.0 21.00 376.88 14.81 16.60
+ 0.95577 0.00 8.140 0 0.5380 6.0470 88.80 4.4534 4 307.0 21.00 306.38 17.28 14.80
+ 0.77299 0.00 8.140 0 0.5380 6.4950 94.40 4.4547 4 307.0 21.00 387.94 12.80 18.40
+ 1.00245 0.00 8.140 0 0.5380 6.6740 87.30 4.2390 4 307.0 21.00 380.23 11.98 21.00
+ 1.13081 0.00 8.140 0 0.5380 5.7130 94.10 4.2330 4 307.0 21.00 360.17 22.60 12.70
+ 1.35472 0.00 8.140 0 0.5380 6.0720 100.00 4.1750 4 307.0 21.00 376.73 13.04 14.50
+ 1.38799 0.00 8.140 0 0.5380 5.9500 82.00 3.9900 4 307.0 21.00 232.60 27.71 13.20
+ 1.15172 0.00 8.140 0 0.5380 5.7010 95.00 3.7872 4 307.0 21.00 358.77 18.35 13.10
+ 1.61282 0.00 8.140 0 0.5380 6.0960 96.90 3.7598 4 307.0 21.00 248.31 20.34 13.50
+ 0.06417 0.00 5.960 0 0.4990 5.9330 68.20 3.3603 5 279.0 19.20 396.90 9.68 18.90
+ 0.09744 0.00 5.960 0 0.4990 5.8410 61.40 3.3779 5 279.0 19.20 377.56 11.41 20.00
+ 0.08014 0.00 5.960 0 0.4990 5.8500 41.50 3.9342 5 279.0 19.20 396.90 8.77 21.00
+ 0.17505 0.00 5.960 0 0.4990 5.9660 30.20 3.8473 5 279.0 19.20 393.43 10.13 24.70
+ 0.02763 75.00 2.950 0 0.4280 6.5950 21.80 5.4011 3 252.0 18.30 395.63 4.32 30.80
+ 0.03359 75.00 2.950 0 0.4280 7.0240 15.80 5.4011 3 252.0 18.30 395.62 1.98 34.90
+ 0.12744 0.00 6.910 0 0.4480 6.7700 2.90 5.7209 3 233.0 17.90 385.41 4.84 26.60
+ 0.14150 0.00 6.910 0 0.4480 6.1690 6.60 5.7209 3 233.0 17.90 383.37 5.81 25.30
+ 0.15936 0.00 6.910 0 0.4480 6.2110 6.50 5.7209 3 233.0 17.90 394.46 7.44 24.70
+ 0.12269 0.00 6.910 0 0.4480 6.0690 40.00 5.7209 3 233.0 17.90 389.39 9.55 21.20
+ 0.17142 0.00 6.910 0 0.4480 5.6820 33.80 5.1004 3 233.0 17.90 396.90 10.21 19.30
+ 0.18836 0.00 6.910 0 0.4480 5.7860 33.30 5.1004 3 233.0 17.90 396.90 14.15 20.00
+ 0.22927 0.00 6.910 0 0.4480 6.0300 85.50 5.6894 3 233.0 17.90 392.74 18.80 16.60
+ 0.25387 0.00 6.910 0 0.4480 5.3990 95.30 5.8700 3 233.0 17.90 396.90 30.81 14.40
+ 0.21977 0.00 6.910 0 0.4480 5.6020 62.00 6.0877 3 233.0 17.90 396.90 16.20 19.40
+ 0.08873 21.00 5.640 0 0.4390 5.9630 45.70 6.8147 4 243.0 16.80 395.56 13.45 19.70
+ 0.04337 21.00 5.640 0 0.4390 6.1150 63.00 6.8147 4 243.0 16.80 393.97 9.43 20.50
+ 0.05360 21.00 5.640 0 0.4390 6.5110 21.10 6.8147 4 243.0 16.80 396.90 5.28 25.00
+ 0.04981 21.00 5.640 0 0.4390 5.9980 21.40 6.8147 4 243.0 16.80 396.90 8.43 23.40
+ 0.01360 75.00 4.000 0 0.4100 5.8880 47.60 7.3197 3 469.0 21.10 396.90 14.80 18.90
+ 0.01311 90.00 1.220 0 0.4030 7.2490 21.90 8.6966 5 226.0 17.90 395.93 4.81 35.40
+ 0.02055 85.00 0.740 0 0.4100 6.3830 35.70 9.1876 2 313.0 17.30 396.90 5.77 24.70
+ 0.01432 100.00 1.320 0 0.4110 6.8160 40.50 8.3248 5 256.0 15.10 392.90 3.95 31.60
+ 0.15445 25.00 5.130 0 0.4530 6.1450 29.20 7.8148 8 284.0 19.70 390.68 6.86 23.30
+ 0.10328 25.00 5.130 0 0.4530 5.9270 47.20 6.9320 8 284.0 19.70 396.90 9.22 19.60
+ 0.14932 25.00 5.130 0 0.4530 5.7410 66.20 7.2254 8 284.0 19.70 395.11 13.15 18.70
+ 0.17171 25.00 5.130 0 0.4530 5.9660 93.40 6.8185 8 284.0 19.70 378.08 14.44 16.00
+ 0.11027 25.00 5.130 0 0.4530 6.4560 67.80 7.2255 8 284.0 19.70 396.90 6.73 22.20
+ 0.12650 25.00 5.130 0 0.4530 6.7620 43.40 7.9809 8 284.0 19.70 395.58 9.50 25.00
+ 0.01951 17.50 1.380 0 0.4161 7.1040 59.50 9.2229 3 216.0 18.60 393.24 8.05 33.00
+ 0.03584 80.00 3.370 0 0.3980 6.2900 17.80 6.6115 4 337.0 16.10 396.90 4.67 23.50
+ 0.04379 80.00 3.370 0 0.3980 5.7870 31.10 6.6115 4 337.0 16.10 396.90 10.24 19.40
+ 0.05789 12.50 6.070 0 0.4090 5.8780 21.40 6.4980 4 345.0 18.90 396.21 8.10 22.00
+ 0.13554 12.50 6.070 0 0.4090 5.5940 36.80 6.4980 4 345.0 18.90 396.90 13.09 17.40
+ 0.12816 12.50 6.070 0 0.4090 5.8850 33.00 6.4980 4 345.0 18.90 396.90 8.79 20.90
+ 0.08826 0.00 10.810 0 0.4130 6.4170 6.60 5.2873 4 305.0 19.20 383.73 6.72 24.20
+ 0.15876 0.00 10.810 0 0.4130 5.9610 17.50 5.2873 4 305.0 19.20 376.94 9.88 21.70
+ 0.09164 0.00 10.810 0 0.4130 6.0650 7.80 5.2873 4 305.0 19.20 390.91 5.52 22.80
+ 0.19539 0.00 10.810 0 0.4130 6.2450 6.20 5.2873 4 305.0 19.20 377.17 7.54 23.40
+ 0.07896 0.00 12.830 0 0.4370 6.2730 6.00 4.2515 5 398.0 18.70 394.92 6.78 24.10
+ 0.09512 0.00 12.830 0 0.4370 6.2860 45.00 4.5026 5 398.0 18.70 383.23 8.94 21.40
+ 0.10153 0.00 12.830 0 0.4370 6.2790 74.50 4.0522 5 398.0 18.70 373.66 11.97 20.00
+ 0.08707 0.00 12.830 0 0.4370 6.1400 45.80 4.0905 5 398.0 18.70 386.96 10.27 20.80
+ 0.05646 0.00 12.830 0 0.4370 6.2320 53.70 5.0141 5 398.0 18.70 386.40 12.34 21.20
+ 0.08387 0.00 12.830 0 0.4370 5.8740 36.60 4.5026 5 398.0 18.70 396.06 9.10 20.30
+ 0.04113 25.00 4.860 0 0.4260 6.7270 33.50 5.4007 4 281.0 19.00 396.90 5.29 28.00
+ 0.04462 25.00 4.860 0 0.4260 6.6190 70.40 5.4007 4 281.0 19.00 395.63 7.22 23.90
+ 0.03659 25.00 4.860 0 0.4260 6.3020 32.20 5.4007 4 281.0 19.00 396.90 6.72 24.80
+ 0.03551 25.00 4.860 0 0.4260 6.1670 46.70 5.4007 4 281.0 19.00 390.64 7.51 22.90
+ 0.05059 0.00 4.490 0 0.4490 6.3890 48.00 4.7794 3 247.0 18.50 396.90 9.62 23.90
+ 0.05735 0.00 4.490 0 0.4490 6.6300 56.10 4.4377 3 247.0 18.50 392.30 6.53 26.60
+ 0.05188 0.00 4.490 0 0.4490 6.0150 45.10 4.4272 3 247.0 18.50 395.99 12.86 22.50
+ 0.07151 0.00 4.490 0 0.4490 6.1210 56.80 3.7476 3 247.0 18.50 395.15 8.44 22.20
+ 0.05660 0.00 3.410 0 0.4890 7.0070 86.30 3.4217 2 270.0 17.80 396.90 5.50 23.60
+ 0.05302 0.00 3.410 0 0.4890 7.0790 63.10 3.4145 2 270.0 17.80 396.06 5.70 28.70
+ 0.04684 0.00 3.410 0 0.4890 6.4170 66.10 3.0923 2 270.0 17.80 392.18 8.81 22.60
+ 0.03932 0.00 3.410 0 0.4890 6.4050 73.90 3.0921 2 270.0 17.80 393.55 8.20 22.00
+ 0.04203 28.00 15.040 0 0.4640 6.4420 53.60 3.6659 4 270.0 18.20 395.01 8.16 22.90
+ 0.02875 28.00 15.040 0 0.4640 6.2110 28.90 3.6659 4 270.0 18.20 396.33 6.21 25.00
+ 0.04294 28.00 15.040 0 0.4640 6.2490 77.30 3.6150 4 270.0 18.20 396.90 10.59 20.60
+ 0.12204 0.00 2.890 0 0.4450 6.6250 57.80 3.4952 2 276.0 18.00 357.98 6.65 28.40
+ 0.11504 0.00 2.890 0 0.4450 6.1630 69.60 3.4952 2 276.0 18.00 391.83 11.34 21.40
+ 0.12083 0.00 2.890 0 0.4450 8.0690 76.00 3.4952 2 276.0 18.00 396.90 4.21 38.70
+ 0.08187 0.00 2.890 0 0.4450 7.8200 36.90 3.4952 2 276.0 18.00 393.53 3.57 43.80
+ 0.06860 0.00 2.890 0 0.4450 7.4160 62.50 3.4952 2 276.0 18.00 396.90 6.19 33.20
+ 0.14866 0.00 8.560 0 0.5200 6.7270 79.90 2.7778 5 384.0 20.90 394.76 9.42 27.50
+ 0.11432 0.00 8.560 0 0.5200 6.7810 71.30 2.8561 5 384.0 20.90 395.58 7.67 26.50
+ 0.22876 0.00 8.560 0 0.5200 6.4050 85.40 2.7147 5 384.0 20.90 70.80 10.63 18.60
+ 0.21161 0.00 8.560 0 0.5200 6.1370 87.40 2.7147 5 384.0 20.90 394.47 13.44 19.30
+ 0.13960 0.00 8.560 0 0.5200 6.1670 90.00 2.4210 5 384.0 20.90 392.69 12.33 20.10
+ 0.13262 0.00 8.560 0 0.5200 5.8510 96.70 2.1069 5 384.0 20.90 394.05 16.47 19.50
+ 0.17120 0.00 8.560 0 0.5200 5.8360 91.90 2.2110 5 384.0 20.90 395.67 18.66 19.50
+ 0.13117 0.00 8.560 0 0.5200 6.1270 85.20 2.1224 5 384.0 20.90 387.69 14.09 20.40
+ 0.12802 0.00 8.560 0 0.5200 6.4740 97.10 2.4329 5 384.0 20.90 395.24 12.27 19.80
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\ No newline at end of file
diff --git a/data/pima-indians-diabetes.data.csv b/data/pima-indians-diabetes.data.csv
new file mode 100644
index 0000000..9c3e9b8
--- /dev/null
+++ b/data/pima-indians-diabetes.data.csv
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\ No newline at end of file
diff --git a/data/titanic.csv b/data/titanic.csv
new file mode 100644
index 0000000..5cc466e
--- /dev/null
+++ b/data/titanic.csv
@@ -0,0 +1,892 @@
+PassengerId,Survived,Pclass,Name,Sex,Age,SibSp,Parch,Ticket,Fare,Cabin,Embarked
+1,0,3,"Braund, Mr. Owen Harris",male,22,1,0,A/5 21171,7.25,,S
+2,1,1,"Cumings, Mrs. John Bradley (Florence Briggs Thayer)",female,38,1,0,PC 17599,71.2833,C85,C
+3,1,3,"Heikkinen, Miss. Laina",female,26,0,0,STON/O2. 3101282,7.925,,S
+4,1,1,"Futrelle, Mrs. Jacques Heath (Lily May Peel)",female,35,1,0,113803,53.1,C123,S
+5,0,3,"Allen, Mr. William Henry",male,35,0,0,373450,8.05,,S
+6,0,3,"Moran, Mr. James",male,,0,0,330877,8.4583,,Q
+7,0,1,"McCarthy, Mr. Timothy J",male,54,0,0,17463,51.8625,E46,S
+8,0,3,"Palsson, Master. Gosta Leonard",male,2,3,1,349909,21.075,,S
+9,1,3,"Johnson, Mrs. Oscar W (Elisabeth Vilhelmina Berg)",female,27,0,2,347742,11.1333,,S
+10,1,2,"Nasser, Mrs. Nicholas (Adele Achem)",female,14,1,0,237736,30.0708,,C
+11,1,3,"Sandstrom, Miss. Marguerite Rut",female,4,1,1,PP 9549,16.7,G6,S
+12,1,1,"Bonnell, Miss. Elizabeth",female,58,0,0,113783,26.55,C103,S
+13,0,3,"Saundercock, Mr. William Henry",male,20,0,0,A/5. 2151,8.05,,S
+14,0,3,"Andersson, Mr. Anders Johan",male,39,1,5,347082,31.275,,S
+15,0,3,"Vestrom, Miss. Hulda Amanda Adolfina",female,14,0,0,350406,7.8542,,S
+16,1,2,"Hewlett, Mrs. (Mary D Kingcome) ",female,55,0,0,248706,16,,S
+17,0,3,"Rice, Master. Eugene",male,2,4,1,382652,29.125,,Q
+18,1,2,"Williams, Mr. Charles Eugene",male,,0,0,244373,13,,S
+19,0,3,"Vander Planke, Mrs. Julius (Emelia Maria Vandemoortele)",female,31,1,0,345763,18,,S
+20,1,3,"Masselmani, Mrs. Fatima",female,,0,0,2649,7.225,,C
+21,0,2,"Fynney, Mr. Joseph J",male,35,0,0,239865,26,,S
+22,1,2,"Beesley, Mr. Lawrence",male,34,0,0,248698,13,D56,S
+23,1,3,"McGowan, Miss. Anna ""Annie""",female,15,0,0,330923,8.0292,,Q
+24,1,1,"Sloper, Mr. William Thompson",male,28,0,0,113788,35.5,A6,S
+25,0,3,"Palsson, Miss. Torborg Danira",female,8,3,1,349909,21.075,,S
+26,1,3,"Asplund, Mrs. Carl Oscar (Selma Augusta Emilia Johansson)",female,38,1,5,347077,31.3875,,S
+27,0,3,"Emir, Mr. Farred Chehab",male,,0,0,2631,7.225,,C
+28,0,1,"Fortune, Mr. Charles Alexander",male,19,3,2,19950,263,C23 C25 C27,S
+29,1,3,"O'Dwyer, Miss. Ellen ""Nellie""",female,,0,0,330959,7.8792,,Q
+30,0,3,"Todoroff, Mr. Lalio",male,,0,0,349216,7.8958,,S
+31,0,1,"Uruchurtu, Don. Manuel E",male,40,0,0,PC 17601,27.7208,,C
+32,1,1,"Spencer, Mrs. William Augustus (Marie Eugenie)",female,,1,0,PC 17569,146.5208,B78,C
+33,1,3,"Glynn, Miss. Mary Agatha",female,,0,0,335677,7.75,,Q
+34,0,2,"Wheadon, Mr. Edward H",male,66,0,0,C.A. 24579,10.5,,S
+35,0,1,"Meyer, Mr. Edgar Joseph",male,28,1,0,PC 17604,82.1708,,C
+36,0,1,"Holverson, Mr. Alexander Oskar",male,42,1,0,113789,52,,S
+37,1,3,"Mamee, Mr. Hanna",male,,0,0,2677,7.2292,,C
+38,0,3,"Cann, Mr. Ernest Charles",male,21,0,0,A./5. 2152,8.05,,S
+39,0,3,"Vander Planke, Miss. Augusta Maria",female,18,2,0,345764,18,,S
+40,1,3,"Nicola-Yarred, Miss. Jamila",female,14,1,0,2651,11.2417,,C
+41,0,3,"Ahlin, Mrs. Johan (Johanna Persdotter Larsson)",female,40,1,0,7546,9.475,,S
+42,0,2,"Turpin, Mrs. William John Robert (Dorothy Ann Wonnacott)",female,27,1,0,11668,21,,S
+43,0,3,"Kraeff, Mr. Theodor",male,,0,0,349253,7.8958,,C
+44,1,2,"Laroche, Miss. Simonne Marie Anne Andree",female,3,1,2,SC/Paris 2123,41.5792,,C
+45,1,3,"Devaney, Miss. Margaret Delia",female,19,0,0,330958,7.8792,,Q
+46,0,3,"Rogers, Mr. William John",male,,0,0,S.C./A.4. 23567,8.05,,S
+47,0,3,"Lennon, Mr. Denis",male,,1,0,370371,15.5,,Q
+48,1,3,"O'Driscoll, Miss. Bridget",female,,0,0,14311,7.75,,Q
+49,0,3,"Samaan, Mr. Youssef",male,,2,0,2662,21.6792,,C
+50,0,3,"Arnold-Franchi, Mrs. Josef (Josefine Franchi)",female,18,1,0,349237,17.8,,S
+51,0,3,"Panula, Master. Juha Niilo",male,7,4,1,3101295,39.6875,,S
+52,0,3,"Nosworthy, Mr. Richard Cater",male,21,0,0,A/4. 39886,7.8,,S
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+54,1,2,"Faunthorpe, Mrs. Lizzie (Elizabeth Anne Wilkinson)",female,29,1,0,2926,26,,S
+55,0,1,"Ostby, Mr. Engelhart Cornelius",male,65,0,1,113509,61.9792,B30,C
+56,1,1,"Woolner, Mr. Hugh",male,,0,0,19947,35.5,C52,S
+57,1,2,"Rugg, Miss. Emily",female,21,0,0,C.A. 31026,10.5,,S
+58,0,3,"Novel, Mr. Mansouer",male,28.5,0,0,2697,7.2292,,C
+59,1,2,"West, Miss. Constance Mirium",female,5,1,2,C.A. 34651,27.75,,S
+60,0,3,"Goodwin, Master. William Frederick",male,11,5,2,CA 2144,46.9,,S
+61,0,3,"Sirayanian, Mr. Orsen",male,22,0,0,2669,7.2292,,C
+62,1,1,"Icard, Miss. Amelie",female,38,0,0,113572,80,B28,
+63,0,1,"Harris, Mr. Henry Birkhardt",male,45,1,0,36973,83.475,C83,S
+64,0,3,"Skoog, Master. Harald",male,4,3,2,347088,27.9,,S
+65,0,1,"Stewart, Mr. Albert A",male,,0,0,PC 17605,27.7208,,C
+66,1,3,"Moubarek, Master. Gerios",male,,1,1,2661,15.2458,,C
+67,1,2,"Nye, Mrs. (Elizabeth Ramell)",female,29,0,0,C.A. 29395,10.5,F33,S
+68,0,3,"Crease, Mr. Ernest James",male,19,0,0,S.P. 3464,8.1583,,S
+69,1,3,"Andersson, Miss. Erna Alexandra",female,17,4,2,3101281,7.925,,S
+70,0,3,"Kink, Mr. Vincenz",male,26,2,0,315151,8.6625,,S
+71,0,2,"Jenkin, Mr. Stephen Curnow",male,32,0,0,C.A. 33111,10.5,,S
+72,0,3,"Goodwin, Miss. Lillian Amy",female,16,5,2,CA 2144,46.9,,S
+73,0,2,"Hood, Mr. Ambrose Jr",male,21,0,0,S.O.C. 14879,73.5,,S
+74,0,3,"Chronopoulos, Mr. Apostolos",male,26,1,0,2680,14.4542,,C
+75,1,3,"Bing, Mr. Lee",male,32,0,0,1601,56.4958,,S
+76,0,3,"Moen, Mr. Sigurd Hansen",male,25,0,0,348123,7.65,F G73,S
+77,0,3,"Staneff, Mr. Ivan",male,,0,0,349208,7.8958,,S
+78,0,3,"Moutal, Mr. Rahamin Haim",male,,0,0,374746,8.05,,S
+79,1,2,"Caldwell, Master. Alden Gates",male,0.83,0,2,248738,29,,S
+80,1,3,"Dowdell, Miss. Elizabeth",female,30,0,0,364516,12.475,,S
+81,0,3,"Waelens, Mr. Achille",male,22,0,0,345767,9,,S
+82,1,3,"Sheerlinck, Mr. Jan Baptist",male,29,0,0,345779,9.5,,S
+83,1,3,"McDermott, Miss. Brigdet Delia",female,,0,0,330932,7.7875,,Q
+84,0,1,"Carrau, Mr. Francisco M",male,28,0,0,113059,47.1,,S
+85,1,2,"Ilett, Miss. Bertha",female,17,0,0,SO/C 14885,10.5,,S
+86,1,3,"Backstrom, Mrs. Karl Alfred (Maria Mathilda Gustafsson)",female,33,3,0,3101278,15.85,,S
+87,0,3,"Ford, Mr. William Neal",male,16,1,3,W./C. 6608,34.375,,S
+88,0,3,"Slocovski, Mr. Selman Francis",male,,0,0,SOTON/OQ 392086,8.05,,S
+89,1,1,"Fortune, Miss. Mabel Helen",female,23,3,2,19950,263,C23 C25 C27,S
+90,0,3,"Celotti, Mr. Francesco",male,24,0,0,343275,8.05,,S
+91,0,3,"Christmann, Mr. Emil",male,29,0,0,343276,8.05,,S
+92,0,3,"Andreasson, Mr. Paul Edvin",male,20,0,0,347466,7.8542,,S
+93,0,1,"Chaffee, Mr. Herbert Fuller",male,46,1,0,W.E.P. 5734,61.175,E31,S
+94,0,3,"Dean, Mr. Bertram Frank",male,26,1,2,C.A. 2315,20.575,,S
+95,0,3,"Coxon, Mr. Daniel",male,59,0,0,364500,7.25,,S
+96,0,3,"Shorney, Mr. Charles Joseph",male,,0,0,374910,8.05,,S
+97,0,1,"Goldschmidt, Mr. George B",male,71,0,0,PC 17754,34.6542,A5,C
+98,1,1,"Greenfield, Mr. William Bertram",male,23,0,1,PC 17759,63.3583,D10 D12,C
+99,1,2,"Doling, Mrs. John T (Ada Julia Bone)",female,34,0,1,231919,23,,S
+100,0,2,"Kantor, Mr. Sinai",male,34,1,0,244367,26,,S
+101,0,3,"Petranec, Miss. Matilda",female,28,0,0,349245,7.8958,,S
+102,0,3,"Petroff, Mr. Pastcho (""Pentcho"")",male,,0,0,349215,7.8958,,S
+103,0,1,"White, Mr. Richard Frasar",male,21,0,1,35281,77.2875,D26,S
+104,0,3,"Johansson, Mr. Gustaf Joel",male,33,0,0,7540,8.6542,,S
+105,0,3,"Gustafsson, Mr. Anders Vilhelm",male,37,2,0,3101276,7.925,,S
+106,0,3,"Mionoff, Mr. Stoytcho",male,28,0,0,349207,7.8958,,S
+107,1,3,"Salkjelsvik, Miss. Anna Kristine",female,21,0,0,343120,7.65,,S
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+771,0,3,"Lievens, Mr. Rene Aime",male,24,0,0,345781,9.5,,S
+772,0,3,"Jensen, Mr. Niels Peder",male,48,0,0,350047,7.8542,,S
+773,0,2,"Mack, Mrs. (Mary)",female,57,0,0,S.O./P.P. 3,10.5,E77,S
+774,0,3,"Elias, Mr. Dibo",male,,0,0,2674,7.225,,C
+775,1,2,"Hocking, Mrs. Elizabeth (Eliza Needs)",female,54,1,3,29105,23,,S
+776,0,3,"Myhrman, Mr. Pehr Fabian Oliver Malkolm",male,18,0,0,347078,7.75,,S
+777,0,3,"Tobin, Mr. Roger",male,,0,0,383121,7.75,F38,Q
+778,1,3,"Emanuel, Miss. Virginia Ethel",female,5,0,0,364516,12.475,,S
+779,0,3,"Kilgannon, Mr. Thomas J",male,,0,0,36865,7.7375,,Q
+780,1,1,"Robert, Mrs. Edward Scott (Elisabeth Walton McMillan)",female,43,0,1,24160,211.3375,B3,S
+781,1,3,"Ayoub, Miss. Banoura",female,13,0,0,2687,7.2292,,C
+782,1,1,"Dick, Mrs. Albert Adrian (Vera Gillespie)",female,17,1,0,17474,57,B20,S
+783,0,1,"Long, Mr. Milton Clyde",male,29,0,0,113501,30,D6,S
+784,0,3,"Johnston, Mr. Andrew G",male,,1,2,W./C. 6607,23.45,,S
+785,0,3,"Ali, Mr. William",male,25,0,0,SOTON/O.Q. 3101312,7.05,,S
+786,0,3,"Harmer, Mr. Abraham (David Lishin)",male,25,0,0,374887,7.25,,S
+787,1,3,"Sjoblom, Miss. Anna Sofia",female,18,0,0,3101265,7.4958,,S
+788,0,3,"Rice, Master. George Hugh",male,8,4,1,382652,29.125,,Q
+789,1,3,"Dean, Master. Bertram Vere",male,1,1,2,C.A. 2315,20.575,,S
+790,0,1,"Guggenheim, Mr. Benjamin",male,46,0,0,PC 17593,79.2,B82 B84,C
+791,0,3,"Keane, Mr. Andrew ""Andy""",male,,0,0,12460,7.75,,Q
+792,0,2,"Gaskell, Mr. Alfred",male,16,0,0,239865,26,,S
+793,0,3,"Sage, Miss. Stella Anna",female,,8,2,CA. 2343,69.55,,S
+794,0,1,"Hoyt, Mr. William Fisher",male,,0,0,PC 17600,30.6958,,C
+795,0,3,"Dantcheff, Mr. Ristiu",male,25,0,0,349203,7.8958,,S
+796,0,2,"Otter, Mr. Richard",male,39,0,0,28213,13,,S
+797,1,1,"Leader, Dr. Alice (Farnham)",female,49,0,0,17465,25.9292,D17,S
+798,1,3,"Osman, Mrs. Mara",female,31,0,0,349244,8.6833,,S
+799,0,3,"Ibrahim Shawah, Mr. Yousseff",male,30,0,0,2685,7.2292,,C
+800,0,3,"Van Impe, Mrs. Jean Baptiste (Rosalie Paula Govaert)",female,30,1,1,345773,24.15,,S
+801,0,2,"Ponesell, Mr. Martin",male,34,0,0,250647,13,,S
+802,1,2,"Collyer, Mrs. Harvey (Charlotte Annie Tate)",female,31,1,1,C.A. 31921,26.25,,S
+803,1,1,"Carter, Master. William Thornton II",male,11,1,2,113760,120,B96 B98,S
+804,1,3,"Thomas, Master. Assad Alexander",male,0.42,0,1,2625,8.5167,,C
+805,1,3,"Hedman, Mr. Oskar Arvid",male,27,0,0,347089,6.975,,S
+806,0,3,"Johansson, Mr. Karl Johan",male,31,0,0,347063,7.775,,S
+807,0,1,"Andrews, Mr. Thomas Jr",male,39,0,0,112050,0,A36,S
+808,0,3,"Pettersson, Miss. Ellen Natalia",female,18,0,0,347087,7.775,,S
+809,0,2,"Meyer, Mr. August",male,39,0,0,248723,13,,S
+810,1,1,"Chambers, Mrs. Norman Campbell (Bertha Griggs)",female,33,1,0,113806,53.1,E8,S
+811,0,3,"Alexander, Mr. William",male,26,0,0,3474,7.8875,,S
+812,0,3,"Lester, Mr. James",male,39,0,0,A/4 48871,24.15,,S
+813,0,2,"Slemen, Mr. Richard James",male,35,0,0,28206,10.5,,S
+814,0,3,"Andersson, Miss. Ebba Iris Alfrida",female,6,4,2,347082,31.275,,S
+815,0,3,"Tomlin, Mr. Ernest Portage",male,30.5,0,0,364499,8.05,,S
+816,0,1,"Fry, Mr. Richard",male,,0,0,112058,0,B102,S
+817,0,3,"Heininen, Miss. Wendla Maria",female,23,0,0,STON/O2. 3101290,7.925,,S
+818,0,2,"Mallet, Mr. Albert",male,31,1,1,S.C./PARIS 2079,37.0042,,C
+819,0,3,"Holm, Mr. John Fredrik Alexander",male,43,0,0,C 7075,6.45,,S
+820,0,3,"Skoog, Master. Karl Thorsten",male,10,3,2,347088,27.9,,S
+821,1,1,"Hays, Mrs. Charles Melville (Clara Jennings Gregg)",female,52,1,1,12749,93.5,B69,S
+822,1,3,"Lulic, Mr. Nikola",male,27,0,0,315098,8.6625,,S
+823,0,1,"Reuchlin, Jonkheer. John George",male,38,0,0,19972,0,,S
+824,1,3,"Moor, Mrs. (Beila)",female,27,0,1,392096,12.475,E121,S
+825,0,3,"Panula, Master. Urho Abraham",male,2,4,1,3101295,39.6875,,S
+826,0,3,"Flynn, Mr. John",male,,0,0,368323,6.95,,Q
+827,0,3,"Lam, Mr. Len",male,,0,0,1601,56.4958,,S
+828,1,2,"Mallet, Master. Andre",male,1,0,2,S.C./PARIS 2079,37.0042,,C
+829,1,3,"McCormack, Mr. Thomas Joseph",male,,0,0,367228,7.75,,Q
+830,1,1,"Stone, Mrs. George Nelson (Martha Evelyn)",female,62,0,0,113572,80,B28,
+831,1,3,"Yasbeck, Mrs. Antoni (Selini Alexander)",female,15,1,0,2659,14.4542,,C
+832,1,2,"Richards, Master. George Sibley",male,0.83,1,1,29106,18.75,,S
+833,0,3,"Saad, Mr. Amin",male,,0,0,2671,7.2292,,C
+834,0,3,"Augustsson, Mr. Albert",male,23,0,0,347468,7.8542,,S
+835,0,3,"Allum, Mr. Owen George",male,18,0,0,2223,8.3,,S
+836,1,1,"Compton, Miss. Sara Rebecca",female,39,1,1,PC 17756,83.1583,E49,C
+837,0,3,"Pasic, Mr. Jakob",male,21,0,0,315097,8.6625,,S
+838,0,3,"Sirota, Mr. Maurice",male,,0,0,392092,8.05,,S
+839,1,3,"Chip, Mr. Chang",male,32,0,0,1601,56.4958,,S
+840,1,1,"Marechal, Mr. Pierre",male,,0,0,11774,29.7,C47,C
+841,0,3,"Alhomaki, Mr. Ilmari Rudolf",male,20,0,0,SOTON/O2 3101287,7.925,,S
+842,0,2,"Mudd, Mr. Thomas Charles",male,16,0,0,S.O./P.P. 3,10.5,,S
+843,1,1,"Serepeca, Miss. Augusta",female,30,0,0,113798,31,,C
+844,0,3,"Lemberopolous, Mr. Peter L",male,34.5,0,0,2683,6.4375,,C
+845,0,3,"Culumovic, Mr. Jeso",male,17,0,0,315090,8.6625,,S
+846,0,3,"Abbing, Mr. Anthony",male,42,0,0,C.A. 5547,7.55,,S
+847,0,3,"Sage, Mr. Douglas Bullen",male,,8,2,CA. 2343,69.55,,S
+848,0,3,"Markoff, Mr. Marin",male,35,0,0,349213,7.8958,,C
+849,0,2,"Harper, Rev. John",male,28,0,1,248727,33,,S
+850,1,1,"Goldenberg, Mrs. Samuel L (Edwiga Grabowska)",female,,1,0,17453,89.1042,C92,C
+851,0,3,"Andersson, Master. Sigvard Harald Elias",male,4,4,2,347082,31.275,,S
+852,0,3,"Svensson, Mr. Johan",male,74,0,0,347060,7.775,,S
+853,0,3,"Boulos, Miss. Nourelain",female,9,1,1,2678,15.2458,,C
+854,1,1,"Lines, Miss. Mary Conover",female,16,0,1,PC 17592,39.4,D28,S
+855,0,2,"Carter, Mrs. Ernest Courtenay (Lilian Hughes)",female,44,1,0,244252,26,,S
+856,1,3,"Aks, Mrs. Sam (Leah Rosen)",female,18,0,1,392091,9.35,,S
+857,1,1,"Wick, Mrs. George Dennick (Mary Hitchcock)",female,45,1,1,36928,164.8667,,S
+858,1,1,"Daly, Mr. Peter Denis ",male,51,0,0,113055,26.55,E17,S
+859,1,3,"Baclini, Mrs. Solomon (Latifa Qurban)",female,24,0,3,2666,19.2583,,C
+860,0,3,"Razi, Mr. Raihed",male,,0,0,2629,7.2292,,C
+861,0,3,"Hansen, Mr. Claus Peter",male,41,2,0,350026,14.1083,,S
+862,0,2,"Giles, Mr. Frederick Edward",male,21,1,0,28134,11.5,,S
+863,1,1,"Swift, Mrs. Frederick Joel (Margaret Welles Barron)",female,48,0,0,17466,25.9292,D17,S
+864,0,3,"Sage, Miss. Dorothy Edith ""Dolly""",female,,8,2,CA. 2343,69.55,,S
+865,0,2,"Gill, Mr. John William",male,24,0,0,233866,13,,S
+866,1,2,"Bystrom, Mrs. (Karolina)",female,42,0,0,236852,13,,S
+867,1,2,"Duran y More, Miss. Asuncion",female,27,1,0,SC/PARIS 2149,13.8583,,C
+868,0,1,"Roebling, Mr. Washington Augustus II",male,31,0,0,PC 17590,50.4958,A24,S
+869,0,3,"van Melkebeke, Mr. Philemon",male,,0,0,345777,9.5,,S
+870,1,3,"Johnson, Master. Harold Theodor",male,4,1,1,347742,11.1333,,S
+871,0,3,"Balkic, Mr. Cerin",male,26,0,0,349248,7.8958,,S
+872,1,1,"Beckwith, Mrs. Richard Leonard (Sallie Monypeny)",female,47,1,1,11751,52.5542,D35,S
+873,0,1,"Carlsson, Mr. Frans Olof",male,33,0,0,695,5,B51 B53 B55,S
+874,0,3,"Vander Cruyssen, Mr. Victor",male,47,0,0,345765,9,,S
+875,1,2,"Abelson, Mrs. Samuel (Hannah Wizosky)",female,28,1,0,P/PP 3381,24,,C
+876,1,3,"Najib, Miss. Adele Kiamie ""Jane""",female,15,0,0,2667,7.225,,C
+877,0,3,"Gustafsson, Mr. Alfred Ossian",male,20,0,0,7534,9.8458,,S
+878,0,3,"Petroff, Mr. Nedelio",male,19,0,0,349212,7.8958,,S
+879,0,3,"Laleff, Mr. Kristo",male,,0,0,349217,7.8958,,S
+880,1,1,"Potter, Mrs. Thomas Jr (Lily Alexenia Wilson)",female,56,0,1,11767,83.1583,C50,C
+881,1,2,"Shelley, Mrs. William (Imanita Parrish Hall)",female,25,0,1,230433,26,,S
+882,0,3,"Markun, Mr. Johann",male,33,0,0,349257,7.8958,,S
+883,0,3,"Dahlberg, Miss. Gerda Ulrika",female,22,0,0,7552,10.5167,,S
+884,0,2,"Banfield, Mr. Frederick James",male,28,0,0,C.A./SOTON 34068,10.5,,S
+885,0,3,"Sutehall, Mr. Henry Jr",male,25,0,0,SOTON/OQ 392076,7.05,,S
+886,0,3,"Rice, Mrs. William (Margaret Norton)",female,39,0,5,382652,29.125,,Q
+887,0,2,"Montvila, Rev. Juozas",male,27,0,0,211536,13,,S
+888,1,1,"Graham, Miss. Margaret Edith",female,19,0,0,112053,30,B42,S
+889,0,3,"Johnston, Miss. Catherine Helen ""Carrie""",female,,1,2,W./C. 6607,23.45,,S
+890,1,1,"Behr, Mr. Karl Howell",male,26,0,0,111369,30,C148,C
+891,0,3,"Dooley, Mr. Patrick",male,32,0,0,370376,7.75,,Q
diff --git a/data_exploration/explore.py b/data_exploration/explore.py
new file mode 100644
index 0000000..81fac64
--- /dev/null
+++ b/data_exploration/explore.py
@@ -0,0 +1,207 @@
+#import pandas as pd
+import numpy as np
+import seaborn as sns
+import matplotlib.pyplot as plt
+import os
+plt.style.use('seaborn-colorblind')
+
+# 2018.11.07 Created by Eamon.Zhang
+
+
+def get_dtypes(data,drop_col=[]):
+ """Return the dtypes for each column of a pandas Dataframe
+
+ Parameters
+ ----------
+ data : pandas Dataframe
+
+ drop_col : columns to omit in a list
+
+ Returns
+ -------
+ str_var_list, num_var_list, all_var_list
+
+ """
+
+ name_of_col = list(data.columns)
+ num_var_list = []
+ str_var_list = []
+ all_var_list = []
+
+ str_var_list = name_of_col.copy()
+ for var in name_of_col:
+ # check if column belongs to numeric type
+ if (data[var].dtypes in (np.int, np.int64, np.uint, np.int32, np.float,
+ np.float64, np.float32, np.double)):
+ str_var_list.remove(var)
+ num_var_list.append(var)
+ # drop the omit column from list
+ for var in drop_col:
+ if var in str_var_list:
+ str_var_list.remove(var)
+ if var in num_var_list:
+ num_var_list.remove(var)
+
+ all_var_list.extend(str_var_list)
+ all_var_list.extend(num_var_list)
+ return str_var_list, num_var_list, all_var_list
+
+
+def describe(data,output_path=None):
+ """output the general description of a pandas Dataframe
+ into a csv file
+
+ """
+
+ result = data.describe(include='all')
+ if output_path is not None:
+ output = os.path.join(output_path,'describe.csv')
+ result.to_csv(output)
+ print('result saved at:', str(output))
+ return result
+
+
+def discrete_var_barplot(x,y,data,output_path=None):
+ """draw the barplot of a discrete variable x against y(target variable).
+ By default the bar shows the mean value of y.
+
+ Parameters
+ ----------
+
+
+ Returns
+ -------
+ figure save as PNG
+ """
+
+ plt.figure(figsize=(15,10))
+ sns.barplot(x=x,y=y,data=data)
+ if output_path is not None:
+ output = os.path.join(output_path,'Barplot_'+str(x)+'_'+str(y)+'.png')
+ plt.savefig(output)
+ print('Image saved at', str(output))
+
+
+def discrete_var_countplot(x,data,output_path=None):
+ """draw the countplot of a discrete variable x.
+
+ Parameters
+ ----------
+
+
+ Returns
+ -------
+ figure save as PNG
+ """
+
+ plt.figure(figsize=(15,10))
+ sns.countplot(x=x,data=data)
+ if output_path is not None:
+ output = os.path.join(output_path,'Countplot_'+str(x)+'.png')
+ plt.savefig(output)
+ print('Image saved at',str(output))
+
+
+def discrete_var_boxplot(x,y,data,output_path=None):
+ """draw the boxplot of a discrete variable x against y.
+
+ Parameters
+ ----------
+
+
+ Returns
+ -------
+ figure save as PNG
+ """
+
+ plt.figure(figsize=(15,10))
+ sns.boxplot(x=x,y=y,data=data)
+ if output_path is not None:
+ output = os.path.join(output_path,'Boxplot_'+str(x)+'_'+str(y)+'.png')
+ plt.savefig(output)
+ print('Image saved at',str(output))
+
+
+def continuous_var_distplot(x,output_path=None,bins=None):
+ """draw the distplot of a continuous variable x.
+
+ Parameters
+ ----------
+
+
+ Returns
+ -------
+ figure save as PNG
+ """
+
+ plt.figure(figsize=(15,10))
+ sns.distplot(a=x,kde=False,bins=bins)
+ if output_path is not None:
+ output=os.path.join(output_path,'Distplot_'+str(x.name)+'.png')
+ plt.savefig(output)
+ print('Image saved at',str(output))
+
+
+# 2018.11.28 Created by Eamon.Zhang
+
+def scatter_plot(x,y,data,output_path=None):
+ """draw the scatter-plot of two variables.
+
+ Parameters
+ ----------
+
+
+ Returns
+ -------
+ figure save as PNG
+ """
+
+ plt.figure(figsize=(15,10))
+ sns.scatterplot(x=x,y=y,data=data)
+ if output_path is not None:
+ output = os.path.join(output_path,'Scatter_plot_'+str(x.name)+'_'+str(y.name)+'.png')
+ plt.savefig(output)
+ print('Image saved at',str(output))
+
+
+def correlation_plot(data,output_path=None):
+ """draw the correlation plot between variables.
+
+ Parameters
+ ----------
+
+
+ Returns
+ -------
+ figure save as PNG
+ """
+
+ corrmat = data.corr()
+ fig, ax = plt.subplots()
+ fig.set_size_inches(11,11)
+ sns.heatmap(corrmat,cmap="YlGnBu",linewidths=.5,annot=True)
+ if output_path is not None:
+ output = os.path.join(output_path,'Corr_plot'+'.png')
+ plt.savefig(output)
+ print('Image saved at',str(output))
+
+
+def heatmap(data,output_path=None,fmt='d'):
+ """draw the heatmap between 2 variables.
+
+ Parameters
+ ----------
+
+
+ Returns
+ -------
+ figure save as PNG
+ """
+
+ fig, ax = plt.subplots()
+ fig.set_size_inches(11,11)
+ sns.heatmap(data,cmap="YlGnBu",linewidths=.5,annot=True,fmt=fmt)
+ if output_path is not None:
+ output = os.path.join(output_path,'Heatmap'+'.png')
+ plt.savefig(output)
+ print('Image saved at',str(output))
\ No newline at end of file
diff --git a/feature_cleaning/missing_data.py b/feature_cleaning/missing_data.py
new file mode 100644
index 0000000..f948de9
--- /dev/null
+++ b/feature_cleaning/missing_data.py
@@ -0,0 +1,122 @@
+import pandas as pd
+import numpy as np
+from warnings import warn
+
+# 2018.11.07 Created by Eamon.Zhang
+
+
+def check_missing(data,output_path=None):
+ """
+ check the total number & percentage of missing values
+ per variable of a pandas Dataframe
+ """
+
+ result = pd.concat([data.isnull().sum(),data.isnull().mean()],axis=1)
+ result = result.rename(index=str,columns={0:'total missing',1:'proportion'})
+ if output_path is not None:
+ result.to_csv(output_path+'missing.csv')
+ print('result saved at', output_path, 'missing.csv')
+ return result
+
+
+def drop_missing(data,axis=0):
+ """
+ Listwise deletion:
+ excluding all cases (listwise) that have missing values
+
+ Parameters
+ ----------
+ axis: drop cases(0)/columns(1),default 0
+
+ Returns
+ -------
+ Pandas dataframe with missing cases/columns dropped
+ """
+
+ data_copy = data.copy(deep=True)
+ data_copy = data_copy.dropna(axis=axis,inplace=False)
+ return data_copy
+
+
+def add_var_denote_NA(data,NA_col=[]):
+ """
+ creating an additional variable indicating whether the data
+ was missing for that observation (1) or not (0).
+ """
+
+ data_copy = data.copy(deep=True)
+ for i in NA_col:
+ if data_copy[i].isnull().sum()>0:
+ data_copy[i+'_is_NA'] = np.where(data_copy[i].isnull(),1,0)
+ else:
+ warn("Column %s has no missing cases" % i)
+
+ return data_copy
+
+
+def impute_NA_with_arbitrary(data,impute_value,NA_col=[]):
+ """
+ replacing NA with arbitrary values.
+ """
+
+ data_copy = data.copy(deep=True)
+ for i in NA_col:
+ if data_copy[i].isnull().sum()>0:
+ data_copy[i+'_'+str(impute_value)] = data_copy[i].fillna(impute_value)
+ else:
+ warn("Column %s has no missing cases" % i)
+ return data_copy
+
+
+def impute_NA_with_avg(data,strategy='mean',NA_col=[]):
+ """
+ replacing the NA with mean/median/most frequent values of that variable.
+ Note it should only be performed over training set and then propagated to test set.
+ """
+
+ data_copy = data.copy(deep=True)
+ for i in NA_col:
+ if data_copy[i].isnull().sum()>0:
+ if strategy=='mean':
+ data_copy[i+'_impute_mean'] = data_copy[i].fillna(data[i].mean())
+ elif strategy=='median':
+ data_copy[i+'_impute_median'] = data_copy[i].fillna(data[i].median())
+ elif strategy=='mode':
+ data_copy[i+'_impute_mode'] = data_copy[i].fillna(data[i].mode()[0])
+ else:
+ warn("Column %s has no missing" % i)
+ return data_copy
+
+
+def impute_NA_with_end_of_distribution(data,NA_col=[]):
+ """
+ replacing the NA by values that are at the far end of the distribution of that variable
+ calculated by mean + 3*std
+ """
+
+ data_copy = data.copy(deep=True)
+ for i in NA_col:
+ if data_copy[i].isnull().sum()>0:
+ data_copy[i+'_impute_end_of_distri'] = data_copy[i].fillna(data[i].mean()+3*data[i].std())
+ else:
+ warn("Column %s has no missing" % i)
+ return data_copy
+
+
+def impute_NA_with_random(data,NA_col=[],random_state=0):
+ """
+ replacing the NA with random sampling from the pool of available observations of the variable
+ """
+
+ data_copy = data.copy(deep=True)
+ for i in NA_col:
+ if data_copy[i].isnull().sum()>0:
+ data_copy[i+'_random'] = data_copy[i]
+ # extract the random sample to fill the na
+ random_sample = data_copy[i].dropna().sample(data_copy[i].isnull().sum(), random_state=random_state)
+ random_sample.index = data_copy[data_copy[i].isnull()].index
+ data_copy.loc[data_copy[i].isnull(), str(i)+'_random'] = random_sample
+ else:
+ warn("Column %s has no missing" % i)
+ return data_copy
+
\ No newline at end of file
diff --git a/feature_cleaning/outlier.py b/feature_cleaning/outlier.py
new file mode 100644
index 0000000..64b0d53
--- /dev/null
+++ b/feature_cleaning/outlier.py
@@ -0,0 +1,138 @@
+import pandas as pd
+import numpy as np
+# from warnings import warn
+
+# 2018.11.07 Created by Eamon.Zhang
+
+def outlier_detect_arbitrary(data,col,upper_fence,lower_fence):
+ '''
+ identify outliers based on arbitrary boundaries passed to the function.
+ '''
+
+ para = (upper_fence, lower_fence)
+ tmp = pd.concat([data[col]>upper_fence,data[col]
Upper_fence,data[col]Upper_fence,data[col] threshold
+ print('Num of outlier detected:',outlier_index.value_counts()[1])
+ print('Proportion of outlier detected',outlier_index.value_counts()[1]/len(outlier_index))
+ return outlier_index
+
+
+# 2018.11.10 outlier treatment
+def impute_outlier_with_arbitrary(data,outlier_index,value,col=[]):
+ """
+ impute outliers with arbitrary value
+ """
+
+ data_copy = data.copy(deep=True)
+ for i in col:
+ data_copy.loc[outlier_index,i] = value
+ return data_copy
+
+
+def windsorization(data,col,para,strategy='both'):
+ """
+ top-coding & bottom coding (capping the maximum of a distribution at an arbitrarily set value,vice versa)
+ """
+
+ data_copy = data.copy(deep=True)
+ if strategy == 'both':
+ data_copy.loc[data_copy[col]>para[0],col] = para[0]
+ data_copy.loc[data_copy[col]para[0],col] = para[0]
+ elif strategy == 'bottom':
+ data_copy.loc[data_copy[col]= threshold].index else k)
+ for k in temp_df.index}
+
+ mapping = pd.Series(mapping)
+ mapping_out.append({'col': col, 'mapping': mapping, 'data_type': X[col].dtype}, )
+
+ return X, mapping_out
+
+
+
+#==============================================================================
+# def rare_imputation(X_train, X_test, variable):
+#
+# # find the most frequent category
+# frequent_cat = X_train.groupby(variable)[variable].count().sort_values().tail(1).index.values[0]
+#
+# # find rare labels
+# temp = X_train.groupby([variable])[variable].count()/np.float(len(X_train))
+# rare_cat = [x for x in temp.loc[temp<0.05].index.values]
+#
+# # create new variables, with Rare labels imputed
+#
+# # by the most frequent category
+# X_train[variable+'_freq_imp'] = np.where(X_train[variable].isin(rare_cat), frequent_cat, X_train[variable])
+# X_test[variable+'_freq_imp'] = np.where(X_test[variable].isin(rare_cat), frequent_cat, X_test[variable])
+#
+# # by adding a new label 'Rare'
+# X_train[variable+'_rare_imp'] = np.where(X_train[variable].isin(rare_cat), 'Rare', X_train[variable])
+# X_test[variable+'_rare_imp'] = np.where(X_test[variable].isin(rare_cat), 'Rare', X_test[variable])
+#==============================================================================
+
+# 2018.11.26 created by Eamon.Zhang
+class ModeImputation():
+ """
+ Replacing the rare label by most frequent label
+
+ Parameters
+ ----------
+
+ """
+
+ def __init__(self, mapping=None, cols=None, threshold=0.01):
+ self.cols = cols
+ self.mapping = mapping
+ self._dim = None
+ self.threshold = threshold
+
+
+ def fit(self, X, y=None, **kwargs):
+ """Fit encoder according to X and y.
+ Parameters
+ ----------
+ X : array-like, shape = [n_samples, n_features]
+ Training vectors, where n_samples is the number of samples
+ and n_features is the number of features.
+ y : array-like, shape = [n_samples]
+ Target values.
+ Returns
+ -------
+ self : encoder
+ Returns self.
+ """
+
+ self._dim = X.shape[1]
+
+ _, categories = self.impute_with_mode(
+ X,
+ mapping=self.mapping,
+ cols=self.cols,
+ threshold=self.threshold
+ )
+ self.mapping = categories
+ return self
+
+
+ def transform(self, X):
+ """Perform the transformation to new categorical data.
+ Will use the mapping (if available) and the column list to encode the
+ data.
+ Parameters
+ ----------
+ X : array-like, shape = [n_samples, n_features]
+ Returns
+ -------
+ X : Transformed values with encoding applied.
+ """
+
+ if self._dim is None:
+ raise ValueError('Must train encoder before it can be used to transform data.')
+
+ # make sure that it is the right size
+ if X.shape[1] != self._dim:
+ raise ValueError('Unexpected input dimension %d, expected %d' % (X.shape[1], self._dim,))
+
+ X, _ = self.impute_with_mode(
+ X,
+ mapping=self.mapping,
+ cols=self.cols,
+ threshold=self.threshold
+ )
+
+ return X
+
+
+ def impute_with_mode(self, X_in, threshold, mapping=None, cols=None):
+ """
+ Grouping the observations that show rare labels into a unique category ('rare')
+
+ """
+
+ X = X_in.copy(deep=True)
+
+# if cols is None:
+# cols = X.columns.values
+
+ if mapping is not None: # transform
+ mapping_out = mapping
+ for i in mapping:
+ column = i.get('col') # get the column name
+ X[column] = X[column].map(i['mapping'])
+
+# try:
+# X[column] = X[column].astype(int)
+# except ValueError as e:
+# X[column] = X[column].astype(float)
+ else: # fit
+ mapping_out = []
+ for col in cols:
+# if util.is_category(X[col].dtype):
+# categories = X[col].cat.categories
+# else:
+ temp_df = pd.Series(X[col].value_counts()/len(X))
+ median = X[col].mode()[0]
+ mapping = { k: (median if k not in temp_df[temp_df >= threshold].index else k)
+ for k in temp_df.index}
+
+ mapping = pd.Series(mapping)
+ mapping_out.append({'col': col, 'mapping': mapping, 'data_type': X[col].dtype}, )
+
+ return X, mapping_out
diff --git a/feature_engineering/discretization.py b/feature_engineering/discretization.py
new file mode 100644
index 0000000..fc04561
--- /dev/null
+++ b/feature_engineering/discretization.py
@@ -0,0 +1,329 @@
+import pandas as pd
+from sklearn.tree import DecisionTreeClassifier
+from sklearn.model_selection import cross_val_score
+import numpy as np
+
+# from warnings import warn
+
+# 2018.11.17 Created by Eamon.Zhang
+# ChiMerge method modeified from https://github.com/tatsumiw/ChiMerge/blob/master/ChiMerge.py
+# TODO: add more constraits to the discretized result.
+class ChiMerge():
+ """
+ supervised discretization using the ChiMerge method.
+
+
+ Parameters
+ ----------
+ confidenceVal: number
+ default=3.841, correspond to p=0.05 dof=1
+ num_of_bins: int
+ number of bins after discretize
+ col: str
+ the column to be performed
+
+ """
+
+ def __init__(self, col=None, bins=None, confidenceVal=3.841, num_of_bins=10):
+ self.col = col
+ self._dim = None
+ self.confidenceVal = confidenceVal
+ self.bins = bins
+ self.num_of_bins = num_of_bins
+
+
+ def fit(self, X, y, **kwargs):
+ """Fit encoder according to X and y.
+ Parameters
+ ----------
+ X : array-like, shape = [n_samples, n_features]
+ Training vectors, where n_samples is the number of samples
+ and n_features is the number of features.
+ y : array-like, shape = [n_samples]
+ Target values.
+ Returns
+ -------
+ self : encoder
+ Returns self.
+ """
+
+ self._dim = X.shape[1]
+
+ _, bins = self.chimerge(
+ X_in=X,
+ y=y,
+ confidenceVal=self.confidenceVal,
+ col=self.col,
+ num_of_bins=self.num_of_bins
+ )
+ self.bins = bins
+ return self
+
+
+ def transform(self, X):
+ """Perform the transformation to new data.
+ Will use the tree model and the column list to discretize the
+ column.
+ Parameters
+ ----------
+ X : array-like, shape = [n_samples, n_features]
+ Returns
+ -------
+ X : new dataframe with discretized new column.
+ """
+
+ if self._dim is None:
+ raise ValueError('Must train encoder before it can be used to transform data.')
+
+ # make sure that it is the right size
+ if X.shape[1] != self._dim:
+ raise ValueError('Unexpected input dimension %d, expected %d' % (X.shape[1], self._dim,))
+
+ X, _ = self.chimerge(
+ X_in=X,
+ col=self.col,
+ bins=self.bins
+ )
+
+ return X
+
+ def chimerge(self, X_in, y=None, confidenceVal=None, num_of_bins=None, col=None, bins=None):
+ """
+ discretize a variable using ChiMerge
+
+ """
+
+ X = X_in.copy(deep=True)
+
+ if bins is not None: # transform
+ try:
+ X[col+'_chimerge'] = pd.cut(X[col],bins=bins,include_lowest=True)
+ except Exception as e:
+ print(e)
+
+ else: # fit
+ try:
+ # create an array which save the num of 0/1 samples of the column to be chimerge
+ total_num = X.groupby([col])[y].count()
+ total_num = pd.DataFrame({'total_num': total_num})
+ positive_class = X.groupby([col])[y].sum()
+ positive_class = pd.DataFrame({'positive_class': positive_class})
+ regroup = pd.merge(total_num, positive_class, left_index=True, right_index=True,how='inner')
+ regroup.reset_index(inplace=True)
+ regroup['negative_class'] = regroup['total_num'] - regroup['positive_class']
+ regroup = regroup.drop('total_num', axis=1)
+ np_regroup = np.array(regroup)
+ # merge interval that have 0 pos/neg samples
+ i = 0
+ while (i <= np_regroup.shape[0] - 2):
+ if ((np_regroup[i, 1] == 0 and np_regroup[i + 1, 1] == 0) or ( np_regroup[i, 2] == 0 and np_regroup[i + 1, 2] == 0)):
+ np_regroup[i, 1] = np_regroup[i, 1] + np_regroup[i + 1, 1] # pos
+ np_regroup[i, 2] = np_regroup[i, 2] + np_regroup[i + 1, 2] # neg
+ np_regroup[i, 0] = np_regroup[i + 1, 0]
+ np_regroup = np.delete(np_regroup, i + 1, 0)
+ i = i - 1
+ i = i + 1
+ # calculate chi for neighboring intervals
+ # ∑[(yA-yB)²/yB]
+ chi_table = np.array([])
+ for i in np.arange(np_regroup.shape[0] - 1):
+ chi = (np_regroup[i, 1] * np_regroup[i + 1, 2] - np_regroup[i, 2] * np_regroup[i + 1, 1]) ** 2 \
+ * (np_regroup[i, 1] + np_regroup[i, 2] + np_regroup[i + 1, 1] + np_regroup[i + 1, 2]) / \
+ ((np_regroup[i, 1] + np_regroup[i, 2]) * (np_regroup[i + 1, 1] + np_regroup[i + 1, 2]) * (
+ np_regroup[i, 1] + np_regroup[i + 1, 1]) * (np_regroup[i, 2] + np_regroup[i + 1, 2]))
+ chi_table = np.append(chi_table, chi)
+ # merge intervals that have closing chi
+ while (1):
+ if (len(chi_table) <= (num_of_bins - 1) and min(chi_table) >= confidenceVal):
+ break
+ chi_min_index = np.argwhere(chi_table == min(chi_table))[0]
+ np_regroup[chi_min_index, 1] = np_regroup[chi_min_index, 1] + np_regroup[chi_min_index + 1, 1]
+ np_regroup[chi_min_index, 2] = np_regroup[chi_min_index, 2] + np_regroup[chi_min_index + 1, 2]
+ np_regroup[chi_min_index, 0] = np_regroup[chi_min_index + 1, 0]
+ np_regroup = np.delete(np_regroup, chi_min_index + 1, 0)
+
+ if (chi_min_index == np_regroup.shape[0] - 1):
+ chi_table[chi_min_index - 1] = (np_regroup[chi_min_index - 1, 1] * np_regroup[chi_min_index, 2] - np_regroup[chi_min_index - 1, 2] * np_regroup[chi_min_index, 1]) ** 2 \
+ * (np_regroup[chi_min_index - 1, 1] + np_regroup[chi_min_index - 1, 2] + np_regroup[chi_min_index, 1] + np_regroup[chi_min_index, 2]) / \
+ ((np_regroup[chi_min_index - 1, 1] + np_regroup[chi_min_index - 1, 2]) * (np_regroup[chi_min_index, 1] + np_regroup[chi_min_index, 2]) * (np_regroup[chi_min_index - 1, 1] + np_regroup[chi_min_index, 1]) * (np_regroup[chi_min_index - 1, 2] + np_regroup[chi_min_index, 2]))
+ chi_table = np.delete(chi_table, chi_min_index, axis=0)
+
+ else:
+ chi_table[chi_min_index - 1] = (np_regroup[chi_min_index - 1, 1] * np_regroup[chi_min_index, 2] - np_regroup[chi_min_index - 1, 2] * np_regroup[chi_min_index, 1]) ** 2 \
+ * (np_regroup[chi_min_index - 1, 1] + np_regroup[chi_min_index - 1, 2] + np_regroup[chi_min_index, 1] + np_regroup[chi_min_index, 2]) / \
+ ((np_regroup[chi_min_index - 1, 1] + np_regroup[chi_min_index - 1, 2]) * (np_regroup[chi_min_index, 1] + np_regroup[chi_min_index, 2]) * (np_regroup[chi_min_index - 1, 1] + np_regroup[chi_min_index, 1]) * (np_regroup[chi_min_index - 1, 2] + np_regroup[chi_min_index, 2]))
+ chi_table[chi_min_index] = (np_regroup[chi_min_index, 1] * np_regroup[chi_min_index + 1, 2] - np_regroup[chi_min_index, 2] * np_regroup[chi_min_index + 1, 1]) ** 2 \
+ * (np_regroup[chi_min_index, 1] + np_regroup[chi_min_index, 2] + np_regroup[chi_min_index + 1, 1] + np_regroup[chi_min_index + 1, 2]) / \
+ ((np_regroup[chi_min_index, 1] + np_regroup[chi_min_index, 2]) * (np_regroup[chi_min_index + 1, 1] + np_regroup[chi_min_index + 1, 2]) * (np_regroup[chi_min_index, 1] + np_regroup[chi_min_index + 1, 1]) * (np_regroup[chi_min_index, 2] + np_regroup[chi_min_index + 1, 2]))
+ chi_table = np.delete(chi_table, chi_min_index + 1, axis=0)
+ result_data = pd.DataFrame()
+ result_data['variable'] = [col] * np_regroup.shape[0]
+ bins = []
+ tmp = []
+ for i in np.arange(np_regroup.shape[0]):
+ if i == 0:
+ y = '-inf' + ',' + str(np_regroup[i, 0])
+ #x = np_regroup[i, 0]
+ #list_temp.append(x)
+ elif i == np_regroup.shape[0] - 1:
+ y = str(np_regroup[i - 1, 0]) + '+'
+ #x = 100000000.
+ #list_temp.append(x)
+ else:
+ y = str(np_regroup[i - 1, 0]) + ',' + str(np_regroup[i, 0])
+ #x = np_regroup[i, 0]
+ #list_temp.append(x)
+ bins.append(np_regroup[i - 1, 0])
+ tmp.append(y)
+
+ #list_temp.append(df[variable].max()+0.1)
+ bins.append(X[col].min()-0.1)
+
+ result_data['interval'] = tmp
+ result_data['flag_0'] = np_regroup[:, 2]
+ result_data['flag_1'] = np_regroup[:, 1]
+ bins.sort(reverse=False)
+ print('Interval for variable %s' % col)
+ print(result_data)
+
+ except Exception as e:
+ print(e)
+
+ return X, bins
+
+
+
+
+# 2018.11.15 Created by Eamon.Zhang
+class DiscretizeByDecisionTree():
+ """
+ Discretisation with Decision Trees consists of using a decision tree
+ to identify the optimal splitting points that would determine the bins
+ or contiguous intervals:
+
+ 1.train a decision tree of limited depth (2, 3 or 4) using the variable
+ we want to discretise to predict the target.
+ 2.the original variable values are then replaced by the
+ probability returned by the tree.
+
+ Parameters
+ ----------
+ col: str
+ column to discretise
+ max_depth: int or list of int
+ max depth of the tree. Can be an int or a list of int we want the tree model to search
+ for the optimal depth.
+
+ """
+
+ def __init__(self, col=None, max_depth=None, tree_model=None):
+ self.col = col
+ self._dim = None
+ self.max_depth = max_depth
+ self.tree_model = tree_model
+
+
+ def fit(self, X, y, **kwargs):
+ """Fit encoder according to X and y.
+ Parameters
+ ----------
+ X : array-like, shape = [n_samples, n_features]
+ Training vectors, where n_samples is the number of samples
+ and n_features is the number of features.
+ y : array-like, shape = [n_samples]
+ Target values.
+ Returns
+ -------
+ self : encoder
+ Returns self.
+ """
+
+ self._dim = X.shape[1]
+
+ _, tree = self.discretize(
+ X_in=X,
+ y=y,
+ max_depth=self.max_depth,
+ col=self.col,
+ tree_model=self.tree_model
+ )
+ self.tree_model = tree
+ return self
+
+ def transform(self, X):
+ """Perform the transformation to new categorical data.
+ Will use the tree model and the column list to discretize the
+ column.
+ Parameters
+ ----------
+ X : array-like, shape = [n_samples, n_features]
+ Returns
+ -------
+ X : new dataframe with discretized new column.
+ """
+
+ if self._dim is None:
+ raise ValueError('Must train encoder before it can be used to transform data.')
+
+ # make sure that it is the right size
+ if X.shape[1] != self._dim:
+ raise ValueError('Unexpected input dimension %d, expected %d' % (X.shape[1], self._dim,))
+
+ X, _ = self.discretize(
+ X_in=X,
+ col=self.col,
+ tree_model=self.tree_model
+ )
+
+ return X
+
+
+ def discretize(self, X_in, y=None, max_depth=None, tree_model=None, col=None):
+ """
+ discretize a variable using DecisionTreeClassifier
+
+ """
+
+ X = X_in.copy(deep=True)
+
+ if tree_model is not None: # transform
+ X[col+'_tree_discret'] = tree_model.predict_proba(X[col].to_frame())[:,1]
+
+ else: # fit
+ if isinstance(max_depth,int):
+ tree_model = DecisionTreeClassifier(max_depth=max_depth)
+ tree_model.fit(X[col].to_frame(), y)
+ # X[col+'_tree_discret'] = tree_model.predict_proba(X[col].to_frame())[:,1]
+ #print(x.tree_discret.unique())
+# bins = pd.concat( [X.groupby([col+'_tree_discret'])[col].min(),
+# X.groupby([col+'_tree_discret'])[col].max()], axis=1)
+# print('bins:')
+# print(bins)
+
+ elif len(max_depth)>1:
+ score_ls = [] # here I will store the roc auc
+ score_std_ls = [] # here I will store the standard deviation of the roc_auc
+ for tree_depth in max_depth:
+ tree_model = DecisionTreeClassifier(max_depth=tree_depth)
+ scores = cross_val_score(tree_model, X[col].to_frame(), y, cv=3, scoring='roc_auc')
+ score_ls.append(np.mean(scores))
+ score_std_ls.append(np.std(scores))
+ temp = pd.concat([pd.Series(max_depth), pd.Series(score_ls), pd.Series(score_std_ls)], axis=1)
+ temp.columns = ['depth', 'roc_auc_mean', 'roc_auc_std']
+ print('result ROC-AUC for each depth')
+ print(temp)
+ max_roc = temp.roc_auc_mean.max()
+ optimal_depth=temp[temp.roc_auc_mean==max_roc]['depth'].values
+ print('optimal_depth:',optimal_depth)
+ tree_model = DecisionTreeClassifier(max_depth=optimal_depth)
+ tree_model.fit(X[col].to_frame(), y)
+# bins = pd.concat( [X.groupby([col+'_tree_discret'])[col].min(),
+# X.groupby([col+'_tree_discret'])[col].max()], axis=1)
+# print('bins:')
+# print(bins)
+ else:
+ raise ValueError('max_depth of a tree must be an integer or a list')
+
+ return X, tree_model
+
+
diff --git a/feature_engineering/encoding.py b/feature_engineering/encoding.py
new file mode 100644
index 0000000..c524076
--- /dev/null
+++ b/feature_engineering/encoding.py
@@ -0,0 +1,109 @@
+import pandas as pd
+
+# 2018.11.28 Created by Eamon.Zhang
+
+class MeanEncoding():
+ """
+ replacing the label by the mean of the target for that label.
+
+ Parameters
+ ----------
+
+ """
+
+ def __init__(self, mapping=None, cols=None):
+ self.cols = cols
+ self.mapping = mapping
+ self._dim = None
+ # self.threshold = threshold
+
+
+ def fit(self, X, y=None, **kwargs):
+ """Fit encoder according to X and y.
+ Parameters
+ ----------
+ X : array-like, shape = [n_samples, n_features]
+ Training vectors, where n_samples is the number of samples
+ and n_features is the number of features.
+ y : array-like, shape = [n_samples]
+ Target values.
+ Returns
+ -------
+ self : encoder
+ Returns self.
+ """
+
+ self._dim = X.shape[1]
+
+ _, categories = self.mean_encoding(
+ X,
+ y,
+ mapping=self.mapping,
+ cols=self.cols
+ # threshold=self.threshold
+ )
+ self.mapping = categories
+ return self
+
+
+ def transform(self, X):
+ """Perform the transformation to new categorical data.
+ Will use the mapping (if available) and the column list to encode the
+ data.
+ Parameters
+ ----------
+ X : array-like, shape = [n_samples, n_features]
+ Returns
+ -------
+ X : Transformed values with encoding applied.
+ """
+
+ if self._dim is None:
+ raise ValueError('Must train encoder before it can be used to transform data.')
+
+ # make sure that it is the right size
+ if X.shape[1] != self._dim:
+ raise ValueError('Unexpected input dimension %d, expected %d' % (X.shape[1], self._dim,))
+
+ X, _ = self.mean_encoding(
+ X,
+ mapping=self.mapping,
+ cols=self.cols
+ # threshold=self.threshold
+ )
+
+ return X
+
+
+ def mean_encoding(self, X_in, y=None, mapping=None, cols=None):
+ """
+ Grouping the observations that show rare labels into a unique category ('rare')
+
+ """
+
+ X = X_in.copy(deep=True)
+
+# if cols is None:
+# cols = X.columns.values
+
+ if mapping is not None: # transform
+ mapping_out = mapping
+ for i in mapping:
+ column = i.get('col') # get the column name
+ X[column] = X[column].map(i['mapping'])
+
+# try:
+# X[column] = X[column].astype(int)
+# except ValueError as e:
+# X[column] = X[column].astype(float)
+ else: # fit
+ mapping_out = []
+ for col in cols:
+# if util.is_category(X[col].dtype):
+# categories = X[col].cat.categories
+# else:
+ mapping = X[y.name].groupby(X[col]).mean().to_dict()
+ mapping = pd.Series(mapping)
+ mapping_out.append({'col': col, 'mapping': mapping, 'data_type': X[col].dtype}, )
+
+ return X, mapping_out
\ No newline at end of file
diff --git a/feature_engineering/transformation.py b/feature_engineering/transformation.py
new file mode 100644
index 0000000..f8aed9c
--- /dev/null
+++ b/feature_engineering/transformation.py
@@ -0,0 +1,73 @@
+import pandas as pd
+import numpy as np
+import matplotlib.pyplot as plt
+import scipy.stats as stats
+import pylab
+# from warnings import warn
+
+# 2018.11.26 Created by Eamon.Zhang
+def diagnostic_plots(df, variable):
+ # function to plot a histogram and a Q-Q plot
+ # side by side, for a certain variable
+
+ plt.figure(figsize=(15,6))
+ plt.subplot(1, 2, 1)
+ df[variable].hist()
+
+ plt.subplot(1, 2, 2)
+ stats.probplot(df[variable], dist="norm", plot=pylab)
+
+ plt.show()
+
+
+def log_transform(data,cols=[]):
+ """
+ Logarithmic transformation
+ """
+
+ data_copy = data.copy(deep=True)
+ for i in cols:
+ data_copy[i+'_log'] = np.log(data_copy[i]+1)
+ print('Variable ' + i +' Q-Q plot')
+ diagnostic_plots(data_copy,str(i+'_log'))
+ return data_copy
+
+
+def reciprocal_transform(data,cols=[]):
+ """
+ Reciprocal transformation
+ """
+
+ data_copy = data.copy(deep=True)
+ for i in cols:
+ data_copy[i+'_reciprocal'] = 1/(data_copy[i])
+ print('Variable ' + i +' Q-Q plot')
+ diagnostic_plots(data_copy,str(i+'_reciprocal'))
+ return data_copy
+
+
+def square_root_transform(data,cols=[]):
+ """
+ square root transformation
+ """
+
+ data_copy = data.copy(deep=True)
+ for i in cols:
+ data_copy[i+'_square_root'] = (data_copy[i])**(0.5)
+ print('Variable ' + i +' Q-Q plot')
+ diagnostic_plots(data_copy,str(i+'_square_root'))
+ return data_copy
+
+
+def exp_transform(data,coef,cols=[]):
+ """
+ exp transformation
+ """
+
+ data_copy = data.copy(deep=True)
+ for i in cols:
+ data_copy[i+'_exp'] = (data_copy[i])**coef
+ print('Variable ' + i +' Q-Q plot')
+ diagnostic_plots(data_copy,str(i+'_exp'))
+ return data_copy
+
diff --git a/feature_selection/embedded_method.py b/feature_selection/embedded_method.py
new file mode 100644
index 0000000..3e4c803
--- /dev/null
+++ b/feature_selection/embedded_method.py
@@ -0,0 +1,76 @@
+#import pandas as pd
+import numpy as np
+
+import matplotlib.pyplot as plt
+#import seaborn as sns
+#from sklearn.model_selection import train_test_split
+
+from sklearn.ensemble import RandomForestClassifier, GradientBoostingClassifier #RandomForestRegressor
+#from sklearn.feature_selection import SelectFromModel
+
+# 2018.11.27 Created by Eamon.Zhang
+
+def rf_importance(X_train,y_train,max_depth=10,class_weight=None,top_n=15,n_estimators=50,random_state=0):
+
+ model = RandomForestClassifier(n_estimators=n_estimators,max_depth=max_depth,
+ random_state=random_state,class_weight=class_weight,
+ n_jobs=-1)
+ model.fit(X_train, y_train)
+ importances = model.feature_importances_
+ indices = np.argsort(importances)[::-1]
+ feat_labels = X_train.columns
+ std = np.std([tree.feature_importances_ for tree in model.estimators_],
+ axis=0) # inter-trees variability.
+ print("Feature ranking:")
+# l1,l2,l3,l4 = [],[],[],[]
+ for f in range(X_train.shape[1]):
+ print("%d. feature no:%d feature name:%s (%f)" % (f + 1, indices[f], feat_labels[indices[f]], importances[indices[f]]))
+# l1.append(f+1)
+# l2.append(indices[f])
+# l3.append(feat_labels[indices[f]])
+# l4.append(importances[indices[f]])
+ #feature_rank = pd.Dataframe(zip(l1,l2,l3,l4),columns=['id','indice','feature','importances'])
+
+ # plotting
+ indices = indices[0:top_n]
+ plt.figure()
+ plt.title("Feature importances top %d" % top_n)
+ plt.bar(range(top_n), importances[indices],
+ color="r", yerr=std[indices], align="center")
+ plt.xticks(range(top_n), indices)
+ plt.xlim([-1,top_n])
+ plt.show()
+
+ return model
+
+
+def gbt_importance(X_train,y_train,max_depth=10,top_n=15,n_estimators=50,random_state=0):
+
+ model = GradientBoostingClassifier(n_estimators=n_estimators,max_depth=max_depth,
+ random_state=random_state)
+ model.fit(X_train, y_train)
+ importances = model.feature_importances_
+ indices = np.argsort(importances)[::-1]
+ feat_labels = X_train.columns
+ std = np.std([tree[0].feature_importances_ for tree in model.estimators_],
+ axis=0) # inter-trees variability.
+ print("Feature ranking:")
+# l1,l2,l3,l4 = [],[],[],[]
+ for f in range(X_train.shape[1]):
+ print("%d. feature no:%d feature name:%s (%f)" % (f + 1, indices[f], feat_labels[indices[f]], importances[indices[f]]))
+# l1.append(f+1)
+# l2.append(indices[f])
+# l3.append(feat_labels[indices[f]])
+# l4.append(importances[indices[f]])
+# feature_rank = pd.Dataframe(zip(l1,l2,l3,l4),columns=['id','indice','feature','importances'])
+ # plotting
+ indices = indices[0:top_n]
+ plt.figure()
+ plt.title("Feature importances top %d" % top_n)
+ plt.bar(range(top_n), importances[indices],
+ color="r", yerr=std[indices], align="center")
+ plt.xticks(range(top_n), indices)
+ plt.xlim([-1,top_n])
+ plt.show()
+
+ return model
\ No newline at end of file
diff --git a/feature_selection/feature_shuffle.py b/feature_selection/feature_shuffle.py
new file mode 100644
index 0000000..c39e103
--- /dev/null
+++ b/feature_selection/feature_shuffle.py
@@ -0,0 +1,43 @@
+import pandas as pd
+#import numpy as np
+
+
+from sklearn.ensemble import RandomForestClassifier #, RandomForestRegressor
+from sklearn.metrics import roc_auc_score #, mean_squared_error
+
+# 2018.11.28 Created by Eamon.Zhang
+
+
+def feature_shuffle_rf(X_train,y_train,max_depth=None,class_weight=None,top_n=15,n_estimators=50,random_state=0):
+
+ model = RandomForestClassifier(n_estimators=n_estimators,max_depth=max_depth,
+ random_state=random_state,class_weight=class_weight,
+ n_jobs=-1)
+ model.fit(X_train, y_train)
+ train_auc = roc_auc_score(y_train, (model.predict_proba(X_train))[:, 1])
+ feature_dict = {}
+
+ # selection logic
+ for feature in X_train.columns:
+ X_train_c = X_train.copy().reset_index(drop=True)
+ y_train_c = y_train.copy().reset_index(drop=True)
+
+ # shuffle individual feature
+ X_train_c[feature] = X_train_c[feature].sample(frac=1,random_state=random_state).reset_index(
+ drop=True)
+ #print(X_train_c.isnull().sum())
+ # make prediction with shuffled feature and calculate roc-auc
+ shuff_auc = roc_auc_score(y_train_c,
+ (model.predict_proba(X_train_c))[:, 1])
+ #print(shuff_auc)
+ # save the drop in roc-auc
+ feature_dict[feature] = (train_auc - shuff_auc)
+ #print(feature_dict)
+
+ auc_drop = pd.Series(feature_dict).reset_index()
+ auc_drop.columns = ['feature', 'auc_drop']
+ auc_drop.sort_values(by=['auc_drop'], ascending=False, inplace=True)
+ selected_features = auc_drop[auc_drop.auc_drop>0]['feature']
+
+ return auc_drop, selected_features
+
diff --git a/feature_selection/filter_method.py b/feature_selection/filter_method.py
new file mode 100644
index 0000000..473176d
--- /dev/null
+++ b/feature_selection/filter_method.py
@@ -0,0 +1,156 @@
+import pandas as pd
+import numpy as np
+#from sklearn.feature_selection import VarianceThreshold
+from sklearn.feature_selection import mutual_info_classif,chi2
+from sklearn.feature_selection import SelectKBest, SelectPercentile
+from sklearn.tree import DecisionTreeClassifier, DecisionTreeRegressor
+from sklearn.metrics import roc_auc_score, mean_squared_error
+
+# 2018.11.17 Created by Eamon.Zhang
+
+def constant_feature_detect(data,threshold=0.98):
+ """ detect features that show the same value for the
+ majority/all of the observations (constant/quasi-constant features)
+
+ Parameters
+ ----------
+ data : pd.Dataframe
+ threshold : threshold to identify the variable as constant
+
+ Returns
+ -------
+ list of variables names
+ """
+
+ data_copy = data.copy(deep=True)
+ quasi_constant_feature = []
+ for feature in data_copy.columns:
+ predominant = (data_copy[feature].value_counts() / np.float(
+ len(data_copy))).sort_values(ascending=False).values[0]
+ if predominant >= threshold:
+ quasi_constant_feature.append(feature)
+ print(len(quasi_constant_feature),' variables are found to be almost constant')
+ return quasi_constant_feature
+
+
+def corr_feature_detect(data,threshold=0.8):
+ """ detect highly-correlated features of a Dataframe
+ Parameters
+ ----------
+ data : pd.Dataframe
+ threshold : threshold to identify the variable correlated
+
+ Returns
+ -------
+ pairs of correlated variables
+ """
+
+ corrmat = data.corr()
+ corrmat = corrmat.abs().unstack() # absolute value of corr coef
+ corrmat = corrmat.sort_values(ascending=False)
+ corrmat = corrmat[corrmat >= threshold]
+ corrmat = corrmat[corrmat < 1] # remove the digonal
+ corrmat = pd.DataFrame(corrmat).reset_index()
+ corrmat.columns = ['feature1', 'feature2', 'corr']
+
+ grouped_feature_ls = []
+ correlated_groups = []
+
+ for feature in corrmat.feature1.unique():
+ if feature not in grouped_feature_ls:
+
+ # find all features correlated to a single feature
+ correlated_block = corrmat[corrmat.feature1 == feature]
+ grouped_feature_ls = grouped_feature_ls + list(
+ correlated_block.feature2.unique()) + [feature]
+
+ # append the block of features to the list
+ correlated_groups.append(correlated_block)
+ return correlated_groups
+
+
+def mutual_info(X,y,select_k=10):
+
+# mi = mutual_info_classif(X,y)
+# mi = pd.Series(mi)
+# mi.index = X.columns
+# mi.sort_values(ascending=False)
+
+ if select_k >= 1:
+ sel_ = SelectKBest(mutual_info_classif, k=select_k).fit(X,y)
+ col = X.columns[sel_.get_support()]
+
+ elif 0 < select_k < 1:
+ sel_ = SelectPercentile(mutual_info_classif, percentile=select_k*100).fit(X,y)
+ col = X.columns[sel_.get_support()]
+
+ else:
+ raise ValueError("select_k must be a positive number")
+
+ return col
+
+
+# 2018.11.27 edit Chi-square test
+def chi_square_test(X,y,select_k=10):
+
+ """
+ Compute chi-squared stats between each non-negative feature and class.
+ This score should be used to evaluate categorical variables in a classification task
+ """
+ if select_k >= 1:
+ sel_ = SelectKBest(chi2, k=select_k).fit(X,y)
+ col = X.columns[sel_.get_support()]
+ elif 0 < select_k < 1:
+ sel_ = SelectPercentile(chi2, percentile=select_k*100).fit(X,y)
+ col = X.columns[sel_.get_support()]
+ else:
+ raise ValueError("select_k must be a positive number")
+
+ return col
+
+
+def univariate_roc_auc(X_train,y_train,X_test,y_test,threshold):
+
+ """
+ First, it builds one decision tree per feature, to predict the target
+ Second, it makes predictions using the decision tree and the mentioned feature
+ Third, it ranks the features according to the machine learning metric (roc-auc or mse)
+ It selects the highest ranked features
+
+ """
+ roc_values = []
+ for feature in X_train.columns:
+ clf = DecisionTreeClassifier()
+ clf.fit(X_train[feature].to_frame(), y_train)
+ y_scored = clf.predict_proba(X_test[feature].to_frame())
+ roc_values.append(roc_auc_score(y_test, y_scored[:, 1]))
+ roc_values = pd.Series(roc_values)
+ roc_values.index = X_train.columns
+ print(roc_values.sort_values(ascending=False))
+ print(len(roc_values[roc_values > threshold]),'out of the %s featues are kept'% len(X_train.columns))
+ keep_col = roc_values[roc_values > threshold]
+ return keep_col
+
+
+def univariate_mse(X_train,y_train,X_test,y_test,threshold):
+
+ """
+ First, it builds one decision tree per feature, to predict the target
+ Second, it makes predictions using the decision tree and the mentioned feature
+ Third, it ranks the features according to the machine learning metric (roc-auc or mse)
+ It selects the highest ranked features
+
+ """
+ mse_values = []
+ for feature in X_train.columns:
+ clf = DecisionTreeRegressor()
+ clf.fit(X_train[feature].to_frame(), y_train)
+ y_scored = clf.predict(X_test[feature].to_frame())
+ mse_values.append(mean_squared_error(y_test, y_scored))
+ mse_values = pd.Series(mse_values)
+ mse_values.index = X_train.columns
+ print(mse_values.sort_values(ascending=False))
+ print(len(mse_values[mse_values > threshold]),'out of the %s featues are kept'% len(X_train.columns))
+ keep_col = mse_values[mse_values > threshold]
+ return keep_col
+
\ No newline at end of file
diff --git a/feature_selection/hybrid.py b/feature_selection/hybrid.py
new file mode 100644
index 0000000..4ff73b7
--- /dev/null
+++ b/feature_selection/hybrid.py
@@ -0,0 +1,128 @@
+#import pandas as pd
+#import numpy as np
+
+from sklearn.ensemble import RandomForestClassifier #, RandomForestRegressor
+from sklearn.metrics import roc_auc_score #, mean_squared_error
+
+# 2018.12.02 Created by Eamon.Zhang
+
+
+def recursive_feature_elimination_rf(X_train,y_train,X_test,y_test,
+ tol=0.001,max_depth=None,
+ class_weight=None,
+ top_n=15,n_estimators=50,random_state=0):
+
+
+ features_to_remove = []
+ count = 1
+ # initial model using all the features
+ model_all_features = RandomForestClassifier(n_estimators=n_estimators,max_depth=max_depth,
+ random_state=random_state,class_weight=class_weight,
+ n_jobs=-1)
+ model_all_features.fit(X_train, y_train)
+ y_pred_test = model_all_features.predict_proba(X_test)[:, 1]
+ auc_score_all = roc_auc_score(y_test, y_pred_test)
+
+ for feature in X_train.columns:
+ print()
+ print('testing feature: ', feature, ' which is feature ', count,
+ ' out of ', len(X_train.columns))
+ count += 1
+ model = RandomForestClassifier(n_estimators=n_estimators,max_depth=max_depth,
+ random_state=random_state,class_weight=class_weight,
+ n_jobs=-1)
+
+ # fit model with all variables minus the removed features
+ # and the feature to be evaluated
+ model.fit(X_train.drop(features_to_remove + [feature], axis=1), y_train)
+ y_pred_test = model.predict_proba(
+ X_test.drop(features_to_remove + [feature], axis=1))[:, 1]
+ auc_score_int = roc_auc_score(y_test, y_pred_test)
+ print('New Test ROC AUC={}'.format((auc_score_int)))
+
+ # print the original roc-auc with all the features
+ print('All features Test ROC AUC={}'.format((auc_score_all)))
+
+ # determine the drop in the roc-auc
+ diff_auc = auc_score_all - auc_score_int
+
+ # compare the drop in roc-auc with the tolerance
+ if diff_auc >= tol:
+ print('Drop in ROC AUC={}'.format(diff_auc))
+ print('keep: ', feature)
+
+ else:
+ print('Drop in ROC AUC={}'.format(diff_auc))
+ print('remove: ', feature)
+
+ # if the drop in the roc is small and we remove the
+ # feature, we need to set the new roc to the one based on
+ # the remaining features
+ auc_score_all = auc_score_int
+
+ # and append the feature to remove to the list
+ features_to_remove.append(feature)
+ print('DONE!!')
+ print('total features to remove: ', len(features_to_remove))
+ features_to_keep = [x for x in X_train.columns if x not in features_to_remove]
+ print('total features to keep: ', len(features_to_keep))
+
+ return features_to_keep
+
+
+def recursive_feature_addition_rf(X_train,y_train,X_test,y_test,
+ tol=0.001,max_depth=None,
+ class_weight=None,
+ top_n=15,n_estimators=50,random_state=0):
+
+
+ features_to_keep = [X_train.columns[0]]
+ count = 1
+ # initial model using only one feature
+ model_one_feature = RandomForestClassifier(n_estimators=n_estimators,max_depth=max_depth,
+ random_state=random_state,class_weight=class_weight,
+ n_jobs=-1)
+ model_one_feature.fit(X_train[[X_train.columns[0]]], y_train)
+ y_pred_test = model_one_feature.predict_proba(X_test[[X_train.columns[0]]])[:, 1]
+ auc_score_all = roc_auc_score(y_test, y_pred_test)
+
+ for feature in X_train.columns[1:]:
+ print()
+ print('testing feature: ', feature, ' which is feature ', count,
+ ' out of ', len(X_train.columns))
+ count += 1
+ model = RandomForestClassifier(n_estimators=n_estimators,max_depth=max_depth,
+ random_state=random_state,class_weight=class_weight,
+ n_jobs=-1)
+
+ # fit model with the selected features
+ # and the feature to be evaluated
+ model.fit(X_train[features_to_keep + [feature]], y_train)
+ y_pred_test = model.predict_proba(
+ X_test[features_to_keep + [feature]])[:, 1]
+ auc_score_int = roc_auc_score(y_test, y_pred_test)
+ print('New Test ROC AUC={}'.format((auc_score_int)))
+
+ # print the original roc-auc with all the features
+ print('All features Test ROC AUC={}'.format((auc_score_all)))
+
+ # determine the drop in the roc-auc
+ diff_auc = auc_score_int - auc_score_all
+
+ # compare the drop in roc-auc with the tolerance
+ if diff_auc >= tol:
+ # if the increase in the roc is bigger than the threshold
+ # we keep the feature and re-adjust the roc-auc to the new value
+ # considering the added feature
+ print('Increase in ROC AUC={}'.format(diff_auc))
+ print('keep: ', feature)
+ auc_score_all = auc_score_int
+ features_to_keep.append(feature)
+ else:
+ print('Increase in ROC AUC={}'.format(diff_auc))
+ print('remove: ', feature)
+
+ print('DONE!!')
+ print('total features to keep: ', len(features_to_keep))
+
+ return features_to_keep
\ No newline at end of file
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