[jira] [Closed] (SPARK-1542) Add ADMM for solving Lasso (and elastic net) problem

["Shuo Xiang (JIRA)" <ji...@apache.org>]

     [ https://issues.apache.org/jira/browse/SPARK-1542?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]

Shuo Xiang closed SPARK-1542.
-----------------------------

    Resolution: Duplicate

Duplicate with SPARK-1543 by mistake. 

> Add ADMM for solving Lasso (and elastic net) problem
> ----------------------------------------------------
>
>                 Key: SPARK-1542
>                 URL: https://issues.apache.org/jira/browse/SPARK-1542
>             Project: Spark
>          Issue Type: New Feature
>            Reporter: Shuo Xiang
>            Priority: Minor
>              Labels: features
>   Original Estimate: 168h
>  Remaining Estimate: 168h
>
> This PR introduces the Alternating Direction Method of Multipliers (ADMM) for solving Lasso (elastic net, in fact) in mllib. 
> ADMM is capable of solving a class of composite minimization problems in a distributed way. Specifically for Lasso (if only L1-regularization) or elastic-net (both L1- and L2- regularization), it requires solving independent systems of linear equations on each partition and a soft-threholding operation on the driver. Unlike SGD, it is a deterministic algorithm (except for the random partition). Details can be found in the [S. Boyd's paper](http://www.stanford.edu/~boyd/papers/admm_distr_stats.html).
> The linear algebra operations mainly rely on the Breeze library, particularly, it applies `breeze.linalg.cholesky` to perform cholesky decomposition on each partition to solve the linear system.
> I tried to follow the organization of existing Lasso implementation. However, as ADMM is also a good fit for similar optimization problems, e.g., (sparse) logistic regression, it may worth to re-organize and put ADMM into a separate section.



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