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Ensemble Methods in Data Mining by John Elder, Giovanni Seni

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APPENDIX B

Gradient Boosting and Robust Loss Functions

In this appendix we illustrate the process of instatiating the Gradient Boosting algorithm of Table 4.8 to a particular differentiable loss function.

We need to solve:

image

This is done in two steps:

-   Step 1: given c, solve for Tm = T (x; pm):

image

-   Step 2: given Tm, solve for c:

image

Solving Equation (B.2) for robust loss functions L(y,) such as the absolute loss, Huber loss, binomial deviance, etc., ...

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