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https://issues.apache.org/jira/browse/SPARK-17201?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=15434073#comment-15434073
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Weichen Xu commented on SPARK-17201:
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yeah, you are right...
I search some proof for this such as this:
http://math.stackexchange.com/questions/209237/why-does-the-standard-bfgs-update-rule-preserve-positive-definiteness
to BFGS, it can be proven that the approximate Hassien will keep psd.
thanks for looking into this problem deeply !
> Investigate numerical instability for MLOR without regularization
> -----------------------------------------------------------------
>
> Key: SPARK-17201
> URL: https://issues.apache.org/jira/browse/SPARK-17201
> Project: Spark
> Issue Type: Sub-task
> Components: ML, MLlib
> Reporter: Seth Hendrickson
>
> As mentioned
> [here|http://ufldl.stanford.edu/wiki/index.php/Softmax_Regression], when no
> regularization is applied in Softmax regression, second order Newton solvers
> may run into numerical instability problems. We should investigate this in
> practice and find a solution, possibly by implementing pivoting when no
> regularization is applied.
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