ENH - Add Pinball datafit
#134
Conversation
…into pdcd-ws-skglm
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The benchmarks results on L1- Quantile regression problem for the following setups:
@lorentzenchr, your feedback is valuable 🙏 |
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| The datafit reads:: | ||
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| quantile * max(y - Xw, 0) + (1 - quantile) * max(Xw - y, 0) |
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nitpick: the real value does not involve np.max, it is np.maximum(...). sum().
Maybe rewrite as a sum and use _i to denote sample indices ? check how sklearn does it
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I looked up scikit-learn source code, but they don't specify the expression.
I am more with the usage of sum and _ to indicate samples.
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| The datafit reads:: | ||
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| sum_i quantile * max(y_i - Xw_i, 0) + (1 - quantile) * max(Xw_i - y_i, 0) |
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The naming "quantile" is unfortunate. It should be "quantile level", i.e. the quantile at level 50% is the median. The "quantile" in the formula is not the quantile, but Xw_i is an estimation of the quantile.
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thanks @lorentzenchr for the insightful remark, we'll change that
Provided that we now have a solver that handles non-smooth datafits #131
This adds a Pinball datafit that can be used to fit a
QuantileRegressorand hence as a by-product fit a LAD-Lasso (
quantile=0.5)closes #133