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From Debasish Das <debasish.da...@gmail.com>
Subject Re: Constraint Solver for Spark
Date Wed, 11 Jun 2014 09:20:09 GMT
I got it...ALS formulation is solving the matrix completion problem....

To convert the problem to matrix factorization or take user feedback
(missing entries means the user hate the site ?), we should put 0 to the
missing entries (or may be -1)...in that case we have to use computeYtY and
accumulate over users in each block to generate full gram matrix...and
after that while computing userXy(index) we have to be careful in putting
0/-1 for rest of the features...

Is implicit feedback trying to do something like this ?

Basically I am trying to see if it is possible to cache the gram matrix and
it's cholesky factorization, and then call the QpSolver multiple times with
updated gradient term...I am expecting better runtimes than dposv when
ranks are high...

But seems like that's not possible without a broadcast step which might
kill all the runtime gain...


On Wed, Jun 11, 2014 at 12:21 AM, Xiangrui Meng <mengxr@gmail.com> wrote:

> For explicit feedback, ALS uses only observed ratings for computation.
> So XtXs are not the same. -Xiangrui
>
> On Tue, Jun 10, 2014 at 8:58 PM, Debasish Das <debasish.das83@gmail.com>
> wrote:
> > Sorry last one went out by mistake:
> >
> > Is not for users (0 to numUsers), fullXtX is same ? In the ALS
> formulation
> > this is W^TW or H^TH which should be same for all the users ? Why we are
> > reading userXtX(index) and adding it to fullXtX in the loop over all
> > numUsers ?
> >
> > // Solve the least-squares problem for each user and return the new
> feature
> > vectors
> >
> >     Array.range(0, numUsers).map { index =>
> >
> >       // Compute the full XtX matrix from the lower-triangular part we
> got
> > above
> >
> >       fillFullMatrix(userXtX(index), fullXtX)
> >
> >       // Add regularization
> >
> >       var i = 0
> >
> >       while (i < rank) {
> >
> >         fullXtX.data(i * rank + i) += lambda
> >
> >         i += 1
> >
> >       }
> >
> >       // Solve the resulting matrix, which is symmetric and
> > positive-definite
> >
> >       algo match {
> >
> >         case ALSAlgo.Implicit =>
> > Solve.solvePositive(fullXtX.addi(YtY.get.value),
> > userXy(index)).data
> >
> >         case ALSAlgo.Explicit => Solve.solvePositive(fullXtX, userXy
> > (index)).data
> >
> >       }
> >
> >     }
> >
> >
> > On Tue, Jun 10, 2014 at 8:56 PM, Debasish Das <debasish.das83@gmail.com>
> > wrote:
> >
> >> Hi,
> >>
> >> I am bit confused wiht the code here:
> >>
> >> // Solve the least-squares problem for each user and return the new
> >> feature vectors
> >>
> >>     Array.range(0, numUsers).map { index =>
> >>
> >>       // Compute the full XtX matrix from the lower-triangular part we
> >> got above
> >>
> >>       fillFullMatrix(userXtX(index), fullXtX)
> >>
> >>       // Add regularization
> >>
> >>       var i = 0
> >>
> >>       while (i < rank) {
> >>
> >>         fullXtX.data(i * rank + i) += lambda
> >>
> >>         i += 1
> >>
> >>       }
> >>
> >>       // Solve the resulting matrix, which is symmetric and
> >> positive-definite
> >>
> >>       algo match {
> >>
> >>         case ALSAlgo.Implicit =>
> Solve.solvePositive(fullXtX.addi(YtY.get.value),
> >> userXy(index)).data
> >>
> >>         case ALSAlgo.Explicit => Solve.solvePositive(fullXtX, userXy
> >> (index)).data
> >>
> >>       }
> >>
> >>     }
> >>
> >>
> >> On Fri, Jun 6, 2014 at 10:42 AM, Debasish Das <debasish.das83@gmail.com
> >
> >> wrote:
> >>
> >>> Hi Xiangrui,
> >>>
> >>> It's not the linear constraint, It is quadratic inequality with slack,
> >>> first order taylor approximation of off diagonal cross terms and a
> cyclic
> >>> coordinate descent, which we think will yield orthogonality....It's
> still
> >>> under works...
> >>>
> >>> Also we want to put a L1 constraint as set of linear equations when
> >>> solving for ALS...
> >>>
> >>> I will create the JIRA...as I see it, this will evolve to a generic
> >>> constraint solver for machine learning problems that has a QP
> >>> structure....ALS is one example....another example is kernel SVMs...
> >>>
> >>> I did not know that lgpl solver can be added to the classpath....if it
> >>> can be then definitely we should add these in ALS.scala...
> >>>
> >>> Thanks.
> >>> Deb
> >>>
> >>>
> >>>
> >>> On Thu, Jun 5, 2014 at 11:31 PM, Xiangrui Meng <mengxr@gmail.com>
> wrote:
> >>>
> >>>> I don't quite understand why putting linear constraints can promote
> >>>> orthogonality. For the interfaces, if the subproblem is determined by
> >>>> Y^T Y and Y^T b for each iteration, then the least squares solver, the
> >>>> non-negative least squares solver, or your convex solver is simply a
> >>>> function
> >>>>
> >>>> (A, b) -> x.
> >>>>
> >>>> You can define it as an interface, and make the solver pluggable by
> >>>> adding a setter to ALS. If you want to use your lgpl solver, just
> >>>> include it in the classpath. Creating two separate files still seems
> >>>> unnecessary to me. Could you create a JIRA and we can move our
> >>>> discussion there? Thanks!
> >>>>
> >>>> Best,
> >>>> Xiangrui
> >>>>
> >>>> On Thu, Jun 5, 2014 at 7:20 PM, Debasish Das <
> debasish.das83@gmail.com>
> >>>> wrote:
> >>>> > Hi Xiangrui,
> >>>> >
> >>>> > For orthogonality properties in the factors we need a constraint
> solver
> >>>> > other than the usuals (l1, upper and lower bounds, l2 etc)
> >>>> >
> >>>> > The interface of constraint solver is standard and I can add it
in
> >>>> mllib
> >>>> > optimization....
> >>>> >
> >>>> > But I am not sure how will I call the gpl licensed ipm solver from
> >>>> > mllib....assume the solver interface is as follows:
> >>>> >
> >>>> > Qpsolver (densematrix h, array [double] f, int linearEquality,
int
> >>>> > linearInequality, bool lb, bool ub)
> >>>> >
> >>>> > And then I have functions to update equalities, inequalities, bounds
> >>>> etc
> >>>> > followed by the run which generates the solution....
> >>>> >
> >>>> > For l1 constraints I have to use epigraph formulation which needs
a
> >>>> > variable transformation before the solve....
> >>>> >
> >>>> > I was thinking that for the problems that does not need constraints
> >>>> people
> >>>> > will use ALS.scala and ConstrainedALS.scala will have the
> constrained
> >>>> > formulations....
> >>>> >
> >>>> > I can point you to the code once it is ready and then you can guide
> me
> >>>> how
> >>>> > to refactor it to mllib als ?
> >>>> >
> >>>> > Thanks.
> >>>> > Deb
> >>>> > Hi Deb,
> >>>> >
> >>>> > Why do you want to make those methods public? If you only need
to
> >>>> > replace the solver for subproblems. You can try to make the solver
> >>>> > pluggable. Now it supports least squares and non-negative least
> >>>> > squares. You can define an interface for the subproblem solvers
and
> >>>> > maintain the IPM solver at your own code base, if the only
> information
> >>>> > you need is Y^T Y and Y^T b.
> >>>> >
> >>>> > Btw, just curious, what is the use case for quadratic constraints?
> >>>> >
> >>>> > Best,
> >>>> > Xiangrui
> >>>> >
> >>>> > On Thu, Jun 5, 2014 at 3:38 PM, Debasish Das <
> debasish.das83@gmail.com
> >>>> >
> >>>> > wrote:
> >>>> >> Hi,
> >>>> >>
> >>>> >> We are adding a constrained ALS solver in Spark to solve matrix
> >>>> >> factorization use-cases which needs additional constraints
(bounds,
> >>>> >> equality, inequality, quadratic constraints)
> >>>> >>
> >>>> >> We are using a native version of a primal dual SOCP solver
due to
> its
> >>>> > small
> >>>> >> memory footprint and sparse ccs matrix computation it uses...The
> >>>> solver
> >>>> >> depends on AMD and LDL packages from Timothy Davis for sparse
ccs
> >>>> matrix
> >>>> >> algebra (released under lgpl)...
> >>>> >>
> >>>> >> Due to GPL dependencies, it won't be possible to release the
code
> as
> >>>> > Apache
> >>>> >> license for now...If we get good results on our use-cases,
we will
> >>>> plan to
> >>>> >> write a version in breeze/modify joptimizer for sparse ccs
> >>>> operations...
> >>>> >>
> >>>> >> I derived ConstrainedALS from Spark mllib ALS and I am comparing
> the
> >>>> >> performance with default ALS and non-negative ALS as baseline.
Plan
> >>>> is to
> >>>> >> release the code as GPL license for community review...I have
kept
> the
> >>>> >> package structure as org.apache.spark.mllib.recommendation
> >>>> >>
> >>>> >> There are some private functions defined in ALS, which I would
> like to
> >>>> >> reuse....Is it possible to take the private out from the following
> >>>> >> functions:
> >>>> >>
> >>>> >> 1. makeLinkRDDs
> >>>> >> 2. makeInLinkBlock
> >>>> >> 3. makeOutLinkBlock
> >>>> >> 4. randomFactor
> >>>> >> 5. unblockFactors
> >>>> >>
> >>>> >> I don't want to copy any code.... I can ask for a PR to make
these
> >>>> >> changes...
> >>>> >>
> >>>> >> Thanks.
> >>>> >> Deb
> >>>>
> >>>
> >>>
> >>
>

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