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https://issues.apache.org/jira/browse/SPARK-3181?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=17148452#comment-17148452
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zhengruifeng commented on SPARK-3181:
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I am working on blockify+gemv/gemm for better performance, and found that the
huber regression' s solution varies significantly when blockSize is changed.
Suggested by [~weichenxu123], I tested the stability by [shuffling the input
dataset|https://issues.apache.org/jira/browse/SPARK-32060?focusedCommentId=17148412&page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel#comment-17148412],
and found that:
the solution of LInearSVC and LinearRegression(SquaredError) looks stable when
input is shuffled; while the solution of LinearRegression(huber) varies
significantly;
I also tested scikit-learn's {{HuberRegressor which also use LBFGSB}} as the
solver, its solutions seem stable. So I guess there maybe something wrong in
{{BreezeLBFGSB}}. Maybe using 'Replace {{\sigma}} to {{\exp(\alpha)' or
'Pseudo-Huber loss' is an alternative.}}
> 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
> Affects Versions: 2.2.0
> Reporter: Fan Jiang
> Assignee: Yanbo Liang
> Priority: Major
> Labels: features
> Fix For: 2.3.0
>
> 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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