Shuo Xiang created SPARK-1542:
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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.
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