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## What changes were proposed in this pull request? MLlib ```LinearRegression``` supports _huber_ loss addition to _leastSquares_ loss. The huber loss objective function is:  Refer Eq.(6) and Eq.(8) in [A robust hybrid of lasso and ridge regression](http://statweb.stanford.edu/~owen/reports/hhu.pdf). This objective is jointly convex as a function of (w, σ) ∈ R × (0,∞), we can use L-BFGS-B to solve it. The current implementation is a straight forward porting for Python scikit-learn [```HuberRegressor```](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.HuberRegressor.html). There are some differences: * We use mean loss (```lossSum/weightSum```), but sklearn uses total loss (```lossSum```). * We multiply the loss function and L2 regularization by 1/2. It does not affect the result if we multiply the whole formula by a factor, we just keep consistent with _leastSquares_ loss. So if fitting w/o regularization, MLlib and sklearn produce the same output. If fitting w/ regularization, MLlib should set ```regParam``` divide by the number of instances to match the output of sklearn. ## How was this patch tested? Unit tests. Author: Yanbo Liang <ybliang8@gmail.com> Closes #19020 from yanboliang/spark-3181. |
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