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https://issues.apache.org/jira/browse/SPARK-6323?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14361005#comment-14361005
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Debasish Das edited comment on SPARK-6323 at 3/13/15 7:48 PM:
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There are some other interesting cases for large rank non-convex function but
we will come to it once fixing PLSA using factorization but yes in all the
formulation things break up like ALS and that's why we can distribute the solve
to spark workers...If the objective function does not break like neural net
(which is the natural extension for ALS) then we need parameter server type
ideas for solver...
was (Author: debasish83):
There are some other interesting cases for large rank non-convex function but
we will come to it once fixing PLSA using factorization...
> Large rank matrix factorization with Nonlinear loss and constraints
> -------------------------------------------------------------------
>
> Key: SPARK-6323
> URL: https://issues.apache.org/jira/browse/SPARK-6323
> Project: Spark
> Issue Type: New Feature
> Components: ML, MLlib
> Affects Versions: 1.4.0
> Reporter: Debasish Das
> Fix For: 1.4.0
>
> Original Estimate: 672h
> Remaining Estimate: 672h
>
> Currently ml.recommendation.ALS is optimized for gram matrix generation which
> scales to modest ranks. The problems that we can solve are in the normal
> equation/quadratic form: 0.5x'Hx + c'x + g(z)
> g(z) can be one of the constraints from Breeze proximal library:
> https://github.com/scalanlp/breeze/blob/master/math/src/main/scala/breeze/optimize/proximal/Proximal.scala
> In this PR we will re-use ml.recommendation.ALS design and come up with
> ml.recommendation.ALM (Alternating Minimization). Thanks to [~mengxr] recent
> changes, it's straightforward to do it now !
> ALM will be capable of solving the following problems: min f ( x ) + g ( z )
> 1. Loss function f ( x ) can be LeastSquareLoss, LoglikelihoodLoss and
> HingeLoss. Most likely we will re-use the Gradient interfaces already defined
> and implement LoglikelihoodLoss
> 2. Constraints g ( z ) supported are same as above except that we don't
> support affine + bounds yet Aeq x = beq , lb <= x <= ub yet. Most likely we
> don't need that for ML applications
> 3. For solver we will use breeze.optimize.proximal.NonlinearMinimizer which
> in turn uses projection based solver (SPG) or proximal solvers (ADMM) based
> on convergence speed.
> https://github.com/scalanlp/breeze/blob/master/math/src/main/scala/breeze/optimize/proximal/NonlinearMinimizer.scala
> 4. The factors will be SparseVector so that we keep shuffle size in check.
> For example we will run with 10K ranks but we will force factors to be
> 100-sparse.
> This is closely related to Sparse LDA
> https://issues.apache.org/jira/browse/SPARK-5564 with the difference that we
> are not using graph representation here.
> As we do scaling experiments, we will understand which flow is more suited as
> ratings get denser (my understanding is that since we already scaled ALS to 2
> billion ratings and we will keep sparsity in check, the same 2 billion flow
> will scale to 10K ranks as well)...
> This JIRA is intended to extend the capabilities of ml recommendation to
> generalized loss function.
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