[ML] Logistic regression loss function for boosted tree training #713
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valeriy42
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Oct 8, 2019
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I've now addressed all your review comments. Can you take another look @valeriy42. |
valeriy42
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Oct 9, 2019
lib/maths/CBoostedTree.cc
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| // We searching for the value x which minimises | ||
| // | ||
| // x^* = argmin_x{ sum_i{(a_i - (p_i + x))^2} + lambda * x^2 } | ||
| // | ||
| // This is convex so there is one minimum where derivative w.r.t. x is zero | ||
| // and x^* = 1 / (n + lambda) sum_i{ a_i - p_i }. Denoting the mean prediction | ||
| // error m = 1/n sum_i{ a_i - p_i } we have x^* = n / (n + lambda) m. | ||
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Good job on explaining what the function does! 👍
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| // This is true if and only if all the predictions were identical. In this | ||
| // case we only need one pass over the data and can compute the optimal |
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| // zero to close to one. In particular, the idea is to minimize the leaf | ||
| // weight on an interval [a, b] where if we add "a" the log-odds for all | ||
| // rows <= -5, i.e. max prediction + a = -5, and if we add "b" the log-odds | ||
| // for all rows >= 5, i.e. min prediction + a = 5. |
Co-Authored-By: Valeriy Khakhutskyy <[email protected]>
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This implements binomial logistic regression for the boosted tree. In particular, this targets cross entropy and builds a forest to predict the class log-odds.
We should also have been including sum square leaf weight penalty in the calculation of the optimum tree leaf values, since the splits are chosen targeting the regularised objective. (Note that the regularisation applies to the log-odds for logistic regression, i.e. we'll shrink the log-odds towards zero and so the predicted probabilities towards 0.5.)
I haven't wired this in yet, since that work depends on #701.