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https://issues.apache.org/jira/browse/SPARK-2426?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14224871#comment-14224871
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Debasish Das commented on SPARK-2426:
-------------------------------------
Actually on MovieLens dataset, I am getting good MAP numbers with EQUALITY
constraint...The formulation is similar to PLSA but not exact:
[~akopich] could you please help review if my understanding is correct here ?
k \in {1...25} (if we running with rank as 25)
Minimize \sum_i \sum_j ( r_ij - w_i*h_j) + lambda(||w_i||^2 + ||h_j||^2)
s.t \sum_k w_ik = 1, w_ik >= 0
\sum_k h_kj = 1, h_kj >= 0
This is not quite the stochastic matrix factorization that this paper
http://www.machinelearning.ru/wiki/images/1/1f/Voron14aist.pdf talks about as
PLSA needs the following constraint (I am reading it more) along with
log-likelihood loss:
For each k \sum_j h_kj = 1
On MovieLens dataset I run the EQUALITY version as follows (rank=50, 5
iterations). More iterations does not improve it further.
./bin/spark-submit --total-executor-cores 4 --executor-memory 4g
--driver-memory 1g --master spark://TUSCA09LMLVT00C.local:7077 --jars
~/.m2/repository/com/github/scopt/scopt_2.10/3.2.0/scopt_2.10-3.2.0.jar --class
org.apache.spark.examples.mllib.MovieLensALS
./examples/target/spark-examples_2.10-1.3.0-SNAPSHOT.jar --rank 50
--numIterations 5 --userConstraint EQUALITY --lambdaUser 0.065
--productConstraint EQUALITY --lambdaProduct 0.065 --kryo
--validateRecommendation hdfs://localhost:8020/sandbox/movielens/
Got 1000209 ratings from 6040 users on 3706 movies.
Training: 800670, test: 199539.
Quadratic minimization userConstraint EQUALITY productConstraint EQUALITY
Test RMSE = 1.6970509086529808.
Test users 6038 MAP 0.09333309533803603
So basically best MAP results come from this formulation. 2X improvement over
default of 4.8%
[~mengxr] [~srowen] it will be great if you guys can review the MAP calculation
https://issues.apache.org/jira/browse/SPARK-4231 and help merge it to mllib. I
am keen to understand if there are bugs in the calculation.
This is a bit surprising to me since I have not finished the PLSA code (I am
working on the bi-concave cost) as the paper points out and that means results
can improve further. Note the degradation in RMSE.
I will do runs with Netflix dataset but on our internal dataset (2M x 20K)
trends look similar.
> Quadratic Minimization for MLlib ALS
> ------------------------------------
>
> Key: SPARK-2426
> URL: https://issues.apache.org/jira/browse/SPARK-2426
> Project: Spark
> Issue Type: New Feature
> Components: MLlib
> Affects Versions: 1.3.0
> Reporter: Debasish Das
> Assignee: Debasish Das
> Original Estimate: 504h
> Remaining Estimate: 504h
>
> Current ALS supports least squares and nonnegative least squares.
> I presented ADMM and IPM based Quadratic Minimization solvers to be used for
> the following ALS problems:
> 1. ALS with bounds
> 2. ALS with L1 regularization
> 3. ALS with Equality constraint and bounds
> Initial runtime comparisons are presented at Spark Summit.
> http://spark-summit.org/2014/talk/quadratic-programing-solver-for-non-negative-matrix-factorization-with-spark
> Based on Xiangrui's feedback I am currently comparing the ADMM based
> Quadratic Minimization solvers with IPM based QpSolvers and the default
> ALS/NNLS. I will keep updating the runtime comparison results.
> For integration the detailed plan is as follows:
> 1. Add QuadraticMinimizer and Proximal algorithms in mllib.optimization
> 2. Integrate QuadraticMinimizer in mllib ALS
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