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https://issues.apache.org/jira/browse/SPARK-17748?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=15536781#comment-15536781
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Seth Hendrickson edited comment on SPARK-17748 at 9/30/16 7:16 PM:
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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.
cc [~srowen] [~yanboliang] [~dbtsai]
was (Author: sethah):
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.
cc [~srowen] [~yanboliang]
> 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.
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