# 统计代写|统计与机器学习作业代写Statistical and Machine Learning代考|STATS214

## 统计代写|统计与机器学习作业代写Statistical and Machine Learning代考|Ensemble of Trees

Decision trees are particularly good models, easy to implement, fast to train, and easy to interpret, but they are unstable. In some cases, a change in the class label of one case could result in a completely different structure for the tree, even though it has nearly the same accuracy. This can be problematic when deploying decision trees to support business actions. Even though the overall accuracy can remain similar when the final structure of the decision tree changes, the set of rules based on thresholds will be different because they are based on the tree structure. This might impact the business campaign because it is based on that set of rules.

The decision tree’s instability results from the considerable number of univariate splits and fragmentation of the data. At each split, there are typically many splits on the same predictor variable or different predictor variables that give similar performance. For example, suppose age is split at 45 since it is the most significant split with the predictor variable and the target. However, other splits at 38 or 47 might be almost as significant. A slight change in the data can easily result in an effect that can cascade and create a different tree. A change in the input data can result in a split at 38 years old. Even more problematic, the change in the input data can result in another input variable being more significant to the target such as income. Then, instead of splitting the final tree structure will be quite different, and therefore, the set of rules and thresholds will also be different.

Several methods have been used to take advantage of this decision tree instability to create models that are more powerful, especially in terms of generalizing the final predictive model. One of the most popular methods is to create an ensemble of decision trees.

An ensemble model is the combination of multiple models. The combinations can be formed in these Ways:

• voting on the classifications
• using weighted voting, where some models have more weight
• averaging (weighted or unweighted) the predicted values
There are two types of ensemble of trees: random forests and gradient boosting models.

## 统计代写|统计与机器学习作业代写Statistical and Machine Learning代考|Gradient Boosting

Another approach to ensemble of decision trees is gradient boosting. Gradient boosting is a weighted linear combination of individual decision trees. The algorithm starts with an initial decision tree and generates the residuals. In the next step, the target is the residuals from the previous decision tree. At each step, the accuracy of the tree is computed, and successive trees are adjusted to accommodate previous inaccuracies. Therefore, the gradient boosting algorithm fits a sequence of trees based on the residuals from the previous trees. The final model also has the predicted values averaged over the decision trees.
Just like the forest models, the gradient boosting model should have improved predictive accuracy because of variance reduction. It is hoped that the final model has low bias and low variance.
A major difference between random forest and gradient boosting is in the way the ensemble of decision trees is created. In forests, each decision tree is created independently. In gradient boosting, the set of decision trees is created in a sequence. This difference can allow random forest models to be trained faster and gradient boosting models to be more accurate. On the other hand, random forests can better generalize, and gradient boosting models are easier to overfit.

Gradient boosting is based on a slightly different approach than random forests, particularly assigned to the perturb and combine method. Boosting is a machine learning ensemble meta-algorithm for primarily reducing variance. The term boosting refers to a family of algorithms that can convert weak learners (in this case, decision trees with large residuals) into strong learners.

Adaptive resampling and combining methods are examples of boosting. They sequentially perturb the training data based on the results of the previous models. Cases that are incorrectly classified are given more weight in subsequent models. For continuous targets, from the second decision tree in objective function which in this model minimizes the residuals.
The gradient boosting model is shown below.
$$F_M(x)=F_0+\beta_1 T_1(x)+\beta_2 T_1(x)+\cdots+\beta_M T_M(x)$$
where $\mathrm{M}$ is the number of iterations, or decision trees in the gradient boosting model, $\mathrm{F}_0$ is the initial guess, $\beta$ is the weight for each decision tree in the linear combination, and $T$ is the decision tree model in each iteration.

# 统计与机器学习代考

## 统计代写|统计与机器学习作业代写统计和机器学习代考|树的集合

• 对分类进行投票
• 使用加权投票，其中一些模型有更多的权重
• 平均(加权或不加权)预测值
有两种类型的树集合:随机森林和梯度提升模型

## 统计代写|统计与机器学习作业代写统计与机器学习代考|梯度提升

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$$F_M(x)=F_0+\beta_1 T_1(x)+\beta_2 T_1(x)+\cdots+\beta_M T_M(x)$$

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