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<p>在推荐系统中，我们需要根据用户的打分历史，预测出用户在其他没有打分的商品上的打分情况；</p>
<p>而对于用户来说，我们拥有用户的抽象特征，比如用户的注册编号，用户的性别等；</p>
<p>如何将这些抽象的特征和用户的打分喜好关联起来，这就是Matrix Factorization做的事情</p>
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<p>RBF NetWork = Radial Basis Function Network</p>
<p>考虑Gaussian Kernel SVM：$g_{SVM} = sign(\sum_{SV} \alpha_ny_nexp(-\gamma||x-x_n||^2) + b)$</p>
<p>我们可以将Gaussian Kernel SVM理解为，我们将多个以支撑向量为中心的高斯函数线性组合，可以实现在无限多维上进行larger margin的数据分类；</p>
<p>Gaussian Kernel又称为Radial Basis Function Kernel（RBF Kernel） ：</p>
<p>（1）Radial指计算函数值只与新数据点x与高斯函数的中心点$x_n$的距离有关，与其他无关；</p>
<p>（2）Basis Function指通过线性组合的方式，将多个高斯函数组合在一起；</p>
<p>我们设$g_n(x) = y_nexp(-\gamma||x-x_n||^2)$:</p>
<p>$g_{SVM}(x) = sign(\sum_{SV}\alpha_ng_n(x) +b)$</p>
<p>函数表达的意思可以理解为：计算新来数据点和原有支撑向量 之间的距离，距离越近，则支撑向量在最后表决意见时的权重越大</p>
<p>RBF Network：linear aggregation of radial hypotheses</p>
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<p>本文主要整理 CART决策树和TGBDT。</p>
<p>我们可以将bagging，adaboost，decision tree都视为一边学习一边得到模型权重的方式。</p>
<p>对于bagging来说，不同的模型来自数据的bootstrap采样方式；模型权重都是相同的；</p>
<p>对于adaboost来说，不同的模型来自优化带权重的损失函数（weighted error function／下一个模型更关心上一个模型训练错误的样本）；模型权重根据模型本身的误差决定，即随着训练产生的；</p>
<p>decision tree决策树也可以视为一个集成学习的模型，即 树的每一条分支都是conditional的学习方式，</p>
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<p>本文Non-Linear SVM，我们着重总结，在large margin保证SVM 模型不复杂的前提下，我们如何通过feature transform的形式，让原始模型可以处理更复杂的样本</p>
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2019-03-09
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<p>本篇准备整理一下线性模型。线性模型是针对参数w而言是线性的，则我们称这个模型是线性模型。</p>
<p>本篇主要整理 PLA，PLA的变体Pocket Algorithm，Linear Regression和Logistic Regression。</p>
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