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>
+ * $$
+ * \begin{align}
+ * H_m(z) = \begin{cases}
+ * z^2, & \text {if } |z| < \epsilon, \\
+ * 2\epsilon|z| - \epsilon^2, & \text{otherwise}
+ * \end{cases}
+ * \end{align}
+ * $$
+ * </blockquote>
+ *
+ * It is advised to set the parameter $\epsilon$ to 1.35 to achieve 95%
statistical efficiency.
--- End diff --
Done.
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