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https://issues.apache.org/jira/browse/SPARK-17824?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Yanbo Liang updated SPARK-17824:
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Description:
Cholesky decomposition is unstable (for near-singular and rank deficient
matrices) and only works on positive definite matrices which can not guaranteed
in all cases, it was often used when matrix A is very large and sparse due to
faster calculation. QR decomposition has better numerical properties than
Cholesky and can works on matrices which are not positive definite. Spark MLlib
{{WeightedLeastSquares}} use Cholesky decomposition to solve normal equation
currently, we should also support or move to QR solver for better stability.
I'm preparing to send a PR.
cc [~dbtsai] [~sethah]
was:
Cholesky decomposition is unstable (for near-singular and rank deficient
matrices), it was often used when matrix A is very large and sparse due to
faster calculation. Cholesky decomposition only works on positive definite
matrices which can not guaranteed in all cases.
QR decomposition has better numerical properties than Cholesky and can works on
matrices which are not positive definite. Spark MLlib {{WeightedLeastSquares}}
use Cholesky decomposition to solve normal equation currently, we should also
support or move to QR solver for better stability. I'm preparing to send a PR.
cc [~dbtsai] [~sethah]
> QR solver for WeightedLeastSquares
> ----------------------------------
>
> Key: SPARK-17824
> URL: https://issues.apache.org/jira/browse/SPARK-17824
> Project: Spark
> Issue Type: New Feature
> Components: ML
> Reporter: Yanbo Liang
> Assignee: Yanbo Liang
>
> Cholesky decomposition is unstable (for near-singular and rank deficient
> matrices) and only works on positive definite matrices which can not
> guaranteed in all cases, it was often used when matrix A is very large and
> sparse due to faster calculation. QR decomposition has better numerical
> properties than Cholesky and can works on matrices which are not positive
> definite. Spark MLlib {{WeightedLeastSquares}} use Cholesky decomposition to
> solve normal equation currently, we should also support or move to QR solver
> for better stability. I'm preparing to send a PR.
> cc [~dbtsai] [~sethah]
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