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  • Projection Pursuit Regression----读书笔记

    The central idea is to extract linear combinations of the inputs as derived features, and then model the target as a nonlinear function of these features. Assume we have an input vector X with p components, and a target Y. Let ωm, m=1,2,...,M, be unit p-vectors of unknown parameters. The projection pursuit regression(PPR) model has the form f(X)=ΣgmmTX). This is an additive model, but in the derived features VmmTX rather than the inputs themselves. The functions gm are unspecified and are estimated along with directions ωm using some flexible smoothing method. The scalar variable VmmTX is the projection of X onto the unit vector ωm, and we seek ωm so that the model fits well, hence the name "projection pursuit." As a result, the PPR model is most usefull for prediction, and not very usefull for producing an understandable model for the data. How do we fit a PPR model, given training data (xi, yi), i=1,2,...,N? We seek the approximate minimizers of the error function

    Σi=1N [yim=1MgmmTxi)]2.

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  • 原文地址:https://www.cnblogs.com/donggongdechen/p/11529082.html
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