Github user yanboliang commented on a diff in the pull request:

    https://github.com/apache/spark/pull/19020#discussion_r140439119
  
    --- Diff: 
mllib/src/main/scala/org/apache/spark/ml/optim/aggregator/HuberAggregator.scala 
---
    @@ -0,0 +1,142 @@
    +/*
    + * Licensed to the Apache Software Foundation (ASF) under one or more
    + * contributor license agreements.  See the NOTICE file distributed with
    + * this work for additional information regarding copyright ownership.
    + * The ASF licenses this file to You under the Apache License, Version 2.0
    + * (the "License"); you may not use this file except in compliance with
    + * the License.  You may obtain a copy of the License at
    + *
    + *    http://www.apache.org/licenses/LICENSE-2.0
    + *
    + * Unless required by applicable law or agreed to in writing, software
    + * distributed under the License is distributed on an "AS IS" BASIS,
    + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    + * See the License for the specific language governing permissions and
    + * limitations under the License.
    + */
    +package org.apache.spark.ml.optim.aggregator
    +
    +import org.apache.spark.broadcast.Broadcast
    +import org.apache.spark.ml.feature.Instance
    +import org.apache.spark.ml.linalg.Vector
    +
    +/**
    + * HuberAggregator computes the gradient and loss for a huber loss 
function,
    + * as used in robust regression for samples in sparse or dense vector in 
an online fashion.
    + *
    + * The huber loss function based on:
    + * Art B. Owen (2006), A robust hybrid of lasso and ridge regression.
    + * (http://statweb.stanford.edu/~owen/reports/hhu.pdf)
    + *
    + * Two HuberAggregator can be merged together to have a summary of loss 
and gradient of
    + * the corresponding joint dataset.
    + *
    + * The huber loss function is given by
    + *
    + * <blockquote>
    + *   $$
    + *   \begin{align}
    + *   \min_{w, \sigma}\frac{1}{2n}{\sum_{i=1}^n\left(\sigma +
    + *   H_m\left(\frac{X_{i}w - y_{i}}{\sigma}\right)\sigma\right) + 
\frac{1}{2}\alpha {||w||_2}^2}
    + *   \end{align}
    + *   $$
    + * </blockquote>
    + *
    + * where
    + *
    + * <blockquote>
    + *   $$
    + *   \begin{align}
    + *   H_m(z) = \begin{cases}
    + *            z^2, & \text {if } |z| &lt; \epsilon, \\
    + *            2\epsilon|z| - \epsilon^2, & \text{otherwise}
    + *            \end{cases}
    + *   \end{align}
    + *   $$
    + * </blockquote>
    + *
    + * It is advised to set the parameter $\epsilon$ to 1.35 to achieve 95% 
statistical efficiency.
    --- End diff --
    
    Done.


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