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计算机代写|机器学习代写Machine Learning代考|KIT315 Wrapper Methods

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计算机代写|机器学习代写Machine Learning代考|Wrapper Methods

Unlike filter methods, which do not consider the subsequent learners, wrapper methods directly use the performance of subsequent learners as the evaluation metric for feature subsets. In other words, wrapper methods aim to find the most useful feature subset “tailored” for the given learner.

Generally speaking, wrapper methods are usually better than filter methods in terms of the learner’s final performance since the feature selection is optimized for the given learner. However, wrapper methods are often much more computationally expensive since they train the learner multiple times during the feature selection.

Las Vegas Wrapper (LVW) (Liu and Setiono 1996) is a typical wrapper method. It searches feature subsets using a randomized strategy under the framework of the Las Vegas method, and the subsets are evaluated based on the final classification error. Pseudocode of LVW is given in $\boldsymbol{-}$ Algorithm 11.1.
Line 8 of $\boldsymbol{\square}$ Algorithm $11.1$ estimates the error of learner $\mathfrak{L}$ using cross-validation on the feature subset $A^{\prime}$. If the error of $A^{\prime}$ is smaller than the error of the current feature subset $A^*$, or their errors are comparable but the size of $A^{\prime}$ is smaller, then $A^{\prime}$ is set as the new optimal subset.

It is worth noting that each randomly generated subset is evaluated by training the learner one more time, which is computationally expensive. Hence, LVW introduces a parameter $T$ to limit the number of iterations. However, when the number of original features is large (i.e., $|A|$ is large), LVW may run for a long time if we set $T$ to a large number. In other words, LVW may not produce a solution if there is a constraint on the running time.

计算机代写|机器学习代写Machine Learning代考|Embedded Methods and L1 Regularization

The feature selection process and the learner training process are clearly separated in both filter methods and wrapper methods. By contrast, embedded methods unify the feature selection process and the learner training process into a joint optimization process, that is, the features are automatically selected during the training.

Given a data set $D=\left{\left(\boldsymbol{x}1, y_1\right),\left(\boldsymbol{x}_2, y_2\right), \ldots,\left(\boldsymbol{x}_m, y_m\right)\right}$, where $\boldsymbol{x} \in \mathbb{R}^d$ and $y \in \mathbb{R}$. Taking a simple linear regression model as an example, suppose the squared error is used as the loss function, then the optimization objective is $$\min {\mathbf{w}} \sum_{i=1}^m\left(y_i-\mathbf{w}^{\top} \boldsymbol{x}_i\right)^2$$

Equation (11.5) can easily overfit the data when there is a large number of features but a small number of samples. To alleviate overfitting, we can introduce a regularization term to (11.5). If we use $\mathrm{L}2$ regularization, then we have $$\min {\mathbf{w}} \sum_{i=1}^m\left(y_i-\mathbf{w}^{\top} \boldsymbol{x}_i\right)^2+\lambda|\mathbf{w}|_2^2 .$$

计算机代写|机器学习代写Machine Learning代考|Wrapper Methods

Las Vegas Wrapper (LVW) (Liu and Setiono 1996) 是一种典型的包装方法。它在 Las Vegas 方法的框妿下使用随机策略搜 索特征子集，并根据最终的分类误差对子集进行评估。LVW 的伪代码在一算法 11.1。

计算机代写|机器学习代写Machine Learning代考|Embedded Methods and L1 Regularization

$$\min \mathbf{w} \sum_{i=1}^m\left(y_i-\mathbf{w}^{\top} \boldsymbol{x}i\right)^2$$ 等式 (11.5) 在特征数量较多但样本数量较少的情况下很容易过拟合。为了减斩过拟合，我们可以在 (11.5) 中引入一个正则化 项。如果我们使用L2正则化，那么我们有 $$\min \mathbf{w} \sum{i=1}^m\left(y_i-\mathbf{w}^{\top} \boldsymbol{x}_i\right)^2+\lambda|\mathbf{w}|_2^2$$

MATLAB代写

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