[jira] [Commented] (SPARK-17748) One-pass algorithm for linear regression with L1 and elastic-net penalties

["Seth Hendrickson (JIRA)" <ji...@apache.org>]

    [ https://issues.apache.org/jira/browse/SPARK-17748?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=15536781#comment-15536781 ] 

Seth Hendrickson commented on SPARK-17748:
------------------------------------------

I am working on this currently. The basic plan is to refactor WLS so that it has a pluggable solver for the normal equations. We can implement a new interface like 

{code:java}
trait NormalEquationSolver {
  def solve(
      bBar: Double,
      bbBar: Double,
      abBar: DenseVector,
      aaBar: DenseVector,
      aBar: DenseVector): NormalEquationSolution
}
class CholeskySolver extends NormalEquationsSolver
class QuasiNewtonSolver extends NormalEquationSolver
{code}

If others have thoughts on the design please comment, otherwise I will continue working on this and submit a PR reasonably soon.

> One-pass algorithm for linear regression with L1 and elastic-net penalties
> --------------------------------------------------------------------------
>
>                 Key: SPARK-17748
>                 URL: https://issues.apache.org/jira/browse/SPARK-17748
>             Project: Spark
>          Issue Type: Bug
>          Components: ML
>            Reporter: Seth Hendrickson
>
> Currently linear regression uses weighted least squares to solve the normal equations locally on the driver when the dimensionality is small (<4096). Weighted least squares uses a Cholesky decomposition to solve the problem with L2 regularization (which has a closed-form solution). We can support L1/elasticnet penalties by solving the equations locally using OWL-QN solver.
> Also note that Cholesky does not handle singular covariance matrices, but L-BFGS and OWL-QN are capable of providing reasonable solutions. This patch can also add support for solving singular covariance matrices by also adding L-BFGS.



--
This message was sent by Atlassian JIRA
(v6.3.4#6332)

---------------------------------------------------------------------
To unsubscribe, e-mail: issues-unsubscribe@spark.apache.org
For additional commands, e-mail: issues-help@spark.apache.org