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I am reading Friedman's paper on stochastic gradient boosting - and saw as per below the following set of formulas. Purely from a notation perspective - why do we write $F(x)$ = $F_{m-1}(x)$ outside the brackets in step 3 when we take the gradient?

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Antoine
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Wouter
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1 Answers1

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It's saying: compute the gradient of this expression with respect the variable $F(x)$ , and then substitute the value of $F_{n-1}(x)$ for $F(x)$ into the result.

The "take the derivative with respect to the variable $F(x)$" is a bit awkward conceptually, it may help to introduce a dummy for $F(x)$, like $\zeta = F(x)$, and then take the derivative with respect to $\zeta$.

Matthew Drury
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