[jira] [Created] (SPARK-3181) Add Robust Regression Algorithm with Huber Estimator

["Fan Jiang (JIRA)" <ji...@apache.org>]

Fan Jiang created SPARK-3181:
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             Summary: Add Robust Regression Algorithm with Huber Estimator
                 Key: SPARK-3181
                 URL: https://issues.apache.org/jira/browse/SPARK-3181
             Project: Spark
          Issue Type: New Feature
          Components: MLlib
    Affects Versions: 1.0.2
            Reporter: Fan Jiang
            Priority: Critical
             Fix For: 1.1.1, 1.2.0


Linear least square estimates assume the error has normal distribution and can behave badly when the errors are heavy-tailed. In practical we get various types of data. We need to include Robust Regression  to employ a fitting criterion that is not as vulnerable as least square.

In 1973, Huber introduced M-estimation for regression which stands for "maximum likelihood type". The method is resistant to outliers in the response variable and has been widely used.

The new feature for MLlib will contain 3 new files
/main/scala/org/apache/spark/mllib/regression/RobustRegression.scala
/test/scala/org/apache/spark/mllib/regression/RobustRegressionSuite.scala
/main/scala/org/apache/spark/examples/mllib/HuberRobustRegression.scala

and one new class HuberRobustGradient in 
/main/scala/org/apache/spark/mllib/optimization/Gradient.scala




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