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I am looking at "Additive logistic regression a statistical view of boosting" paper (https://web.stanford.edu/~hastie/Papers/AdditiveLogisticRegression/alr.pdf)

In page 346, the authors introduce a definition for a weighted expectation. I do not understand the motivation behind this definition and how it is used to get to this result.

It introduces this concept to minimize the following expression:

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Can someone explain the idea behind this please?

Thank you

Aggamarcel
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