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Posted to issues@spark.apache.org by "Joseph K. Bradley (JIRA)" <ji...@apache.org> on 2016/09/06 20:37:20 UTC
[jira] [Commented] (SPARK-17201) Investigate numerical instability
for MLOR without regularization
[ https://issues.apache.org/jira/browse/SPARK-17201?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=15468475#comment-15468475 ]
Joseph K. Bradley commented on SPARK-17201:
-------------------------------------------
Does this actually resolve the issue?
The quotes above from [~sethah]'s post say:
* A positive semidefinite Hessian can cause numerical instability.
* L-BFGS preserves the property of being positive definite across iterations.
However, this is not a proof that L-BFGS will not have numerical stability problems. E.g., it does not preclude issues such as the approximation of the Hessian becoming increasingly poorly conditioned with each iteration.
+1 for rigorous testing!
> 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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