Nearest-Neighbor Methods(ESL读书笔记)

最新推荐文章于 2023-10-09 21:11:23 发布

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最新推荐文章于 2023-10-09 21:11:23 发布

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原文链接：http://www.cnblogs.com/donggongdechen/p/10252374.html

本文探讨了近邻方法和核方法在预测分析中的应用。近邻方法通过找到输入空间中与目标点最接近的k个训练样本，然后平均它们的响应来预测输出。而核方法则使用平滑下降到零的权重，更注重目标点附近的样本。此外，文章还提到了高维空间下距离核的调整、局部回归的最小二乘法、基于原始输入的基础扩展模型以及由非线性转换的线性模型组成的投影追求和神经网络模型。

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Nearest-neighbor methods use those observations in the training set T closest in input space to x form Y-hat.

Specifically, the k-nearest neighbor fit for Y-hat is difined as follows: Y(x)=1/kΣy_i,x_ibelong toN_k(x).

where N_k(x) is the neighborhood of x defined by the k closest points x_i in the traing sample.

Closeness implies a metric, which for the moment we assume is Euclidean distance. So, in words, we find the k observations with x_i closest to x in input space, and average their responses.

1.Kernel methods use weights that decrease smoothly to zero with distance from the target point, rather than the effective 0/1 weights used by k-nearest neighbors.

2.In high-dimensional spaces the distance kernels are modified to emphasize some variable more than others.

3.Local regression fits linear models by locally weighted least squares, rather than fitting constants locally.

4.Local models fit to a basis expansion of the original inputs allow arbitrarily complex models.

5.Projection pursuit and neural network models consist of sums of nonlinearly transformed linear models.

转载于:https://www.cnblogs.com/donggongdechen/p/10252374.html