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https://issues.apache.org/jira/browse/SPARK-3181?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=15370871#comment-15370871
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Yanbo Liang commented on SPARK-3181:
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[~dbtsai] [~MechCoder]
There is one problem need to be discussed: The scaling factor {{\sigma}} has to
be estimated as well, and in Eq.(6) {{\sigma}} has to be >= 0. So we can have
two alternatives:
* #1, Use {{\sigma}} directly and L-BFGS-B as the solver. We need to bump up
the dependent breeze version to 0.12 firstly. We can only support L2
regularization as what you did in scikit-learn. However, we can not support L1
or elasticNet regularization, and there is no plan to add OWLQN-B to breeze as
https://github.com/scalanlp/breeze/issues/455 said.
* #2, Replace {{\sigma}} to {{\exp(\alpha)}}, then we can support elasticNet
regularization like what we do in {{LinearRegression}}. But there is no proof
that it will be jointly convex with {{\alpha}} for the huber loss function, we
may fall into the local optimum.
I prefer to opinion #1 which will give the exact solution and looking forward
to hear your thoughts.
> 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: ML, MLlib
> Reporter: Fan Jiang
> Assignee: Yanbo Liang
> Labels: features
> Original Estimate: 0h
> Remaining Estimate: 0h
>
> 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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