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

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

Shuo Xiang created SPARK-1542:
---------------------------------

             Summary: 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


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.





--
This message was sent by Atlassian JIRA
(v6.2#6252)