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| Original file line number | Diff line number | Diff line change |
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| import numpy as np | ||
| import matplotlib.pyplot as plt | ||
| from tqdm import tqdm | ||
| from utils import generate_linear_regression_data, split_data | ||
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| class MSE: | ||
| def __call__(self, y_true, y_pred): | ||
| return np.sum((y_true - y_pred) ** 2) / y_true.size | ||
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| def grad(self, y_true, y_pred): | ||
| return -2 * (y_true - y_pred) / y_true.size | ||
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| class SGDRegressor: | ||
| def __init__ (self, n_iterations = 100, lr = 0.0001): | ||
| self.n_iterations = n_iterations | ||
| self.lr = lr | ||
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| self.weight = None | ||
| self.bias = None | ||
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| self.loss = MSE() | ||
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| def init_weights(self, n_features): | ||
| if self.weight is None or self.bias is None: | ||
| # self.weight = np.random.uniform(-1, 1, (1, n_features)) if self.weight is None else self.weight | ||
| # self.weight = np.random.normal(0, pow(n_features, -0.5), (1, n_features)) if self.weight is None else self.weight | ||
| # self.weight = np.random.normal(0, 1, (1, n_features)) if self.weight is None else self.weight | ||
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| # Xavier initialization | ||
| stdv = 1 / np.sqrt(n_features) | ||
| self.weight = np.random.uniform(-stdv ,stdv, (1, n_features)) if self.weight is None else self.weight | ||
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| self.bias = np.zeros((1, 1)) if self.bias is None else self.bias | ||
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| def fit(self, X, y): | ||
| n_samples, n_features = X.shape | ||
| self.init_weights(n_features) | ||
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| losses = [] | ||
| tqdm_range = tqdm(range(self.n_iterations), total = self.n_iterations) | ||
| for i in range(self.n_iterations): | ||
| tqdm_range.update(1) | ||
| for x_true, y_true in zip(X, y): | ||
| y_true = y_true[:, np.newaxis] | ||
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| y_pred = np.matmul(x_true, self.weight) + self.bias | ||
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| loss = self.loss(y_true, y_pred) | ||
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| grad = self.loss.grad(y_true, y_pred) | ||
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| self.weight -= self.lr * np.matmul(grad.T, x_true) | ||
| self.bias -= self.lr * np.sum(grad) | ||
| losses.append(loss) | ||
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| tqdm_range.set_description(f'epoch: {i + 1}/{self.n_iterations}, loss: {loss:.7f}') | ||
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| return losses | ||
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| def predict(self, X): | ||
| y_pred = np.matmul(X, self.weight) + self.bias | ||
| return y_pred | ||
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| class OrdinaryLeastSquares: | ||
| def __init__(self) -> None: | ||
| self.b = None | ||
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| def add_bias(self, X): | ||
| return np.concatenate((X, np.ones((X.shape[0], 1))), axis = 1) | ||
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| def fit(self, X, y): | ||
| X = self.add_bias(X) | ||
| #b* = (X^T * X)^-1 * X^T * y | ||
| self.b = (np.linalg.matrix_power(X.transpose().dot(X), -1)).dot(X.transpose()).dot(y) | ||
| return self.b | ||
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| def predict(self, X): | ||
| X = self.add_bias(X) | ||
| return X.dot(self.b) | ||
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| if __name__ == '__main__': | ||
| X_train, y_train, true_coefs = generate_linear_regression_data(300) | ||
| X_train, X_test, y_train, y_test = split_data(X_train, y_train, ratio = 0.25) | ||
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| plt.title("Linear Regression") | ||
| plt.xlabel("X") | ||
| plt.ylabel("Y") | ||
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| plt.scatter(X_test, y_test, color ='g', s=10, label='Ground truth') | ||
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| model = SGDRegressor(n_iterations=1000) | ||
| losses = model.fit(X_train, y_train) | ||
| y_pred = model.predict(X_test) | ||
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| plt.plot(X_test, y_pred, 'red', label='Gradient descent') | ||
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| model = OrdinaryLeastSquares() | ||
| model.fit(X_train, y_train) | ||
| y_pred = model.predict(X_test) | ||
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| plt.plot(X_test, y_pred, 'orange', label='Ordinary least squares') | ||
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| y_true = np.dot(X_test, true_coefs) | ||
| plt.plot(X_test, y_true, 'blue', label='True coefficients') | ||
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| plt.legend(loc=2) | ||
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| plt.grid(True, linestyle='-', color='0.75') | ||
| plt.show() |
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