Hi,
Thanks for the feedback.
The algorithm is not solving the normal equation as in the ordinary linear
regression. I did not detail the algorithm to solve the penalized optimization
in the paper. To solve the penalized version, I will use the coordinate descent
which is well documented in other paper (see Freedman's paper, for 1000
variables, it takes ~1min to do cross validation in the R package) and is very
efficient.
As I discussed in the conclusion section, to solve the problem with large
number of predictors, it is still a challenge even though in the single machine
or MPI version, but the proposed algorithm can handle the number of variable at
the order of 5000 and it covers lots of applications.
My plan is to implement a working version first then add some refinements such
as sparse vectors.
Any feedback?
Best
-Kun
----- Original Message -----
From: "Ted Dunning (JIRA)" <j...@apache.org>
To: dev@mahout.apache.org
Sent: Sunday, July 21, 2013 1:10:49 PM
Subject: [jira] [Comment Edited] (MAHOUT-1273) Single Pass Algorithm for
Penalized Linear Regression on MapReduce
[
https://issues.apache.org/jira/browse/MAHOUT-1273?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13714796#comment-13714796
]
Ted Dunning edited comment on MAHOUT-1273 at 7/21/13 8:09 PM:
--------------------------------------------------------------
The algorithm document describes a standard method for solving the normal
equations in a single pass. This works fine with a small number of variables,
but is completely infeasible if we have a very large number of variables as
when the input is very sparse.
At least as important is the fact that the document ignores the problem of
solving the regularized version of the problem. A penalty function, p_lambda(
x ), is mentioned, but the algorithm quoted ignores this penalty and solves the
unpenalized form.
was (Author: tdunning):
The algorithm document describes a standard method for solving the normal
equations in a single pass. This works fine with a small number of variables,
but is completely infeasible if we have a very large number of variables as
when the input is very sparse.
At least as important is the fact that the document ignores the problem of
solving the regularized version of the problem. A penalty function,
p_lambda(x), is mentioned, but the algorithm quoted ignores this penalty and
solves the unpenalized form.
> Single Pass Algorithm for Penalized Linear Regression on MapReduce
> ------------------------------------------------------------------
>
> Key: MAHOUT-1273
> URL: https://issues.apache.org/jira/browse/MAHOUT-1273
> Project: Mahout
> Issue Type: New Feature
> Reporter: Kun Yang
> Attachments: PenalizedLinear.pdf
>
> Original Estimate: 720h
> Remaining Estimate: 720h
>
> Penalized linear regression such as Lasso, Elastic-net are widely used in
> machine learning, but there are no very efficient scalable implementations on
> MapReduce.
> The published distributed algorithms for solving this problem is either
> iterative (which is not good for MapReduce, see Steven Boyd's paper) or
> approximate (what if we need exact solutions, see Paralleled stochastic
> gradient descent); another disadvantage of these algorithms is that they can
> not do cross validation in the training phase, which requires a
> user-specified penalty parameter in advance.
> My ideas can train the model with cross validation in a single pass. They are
> based on some simple observations.
> I have implemented the primitive version of this algorithm in Alpine Data
> Labs. Advanced features such as inner-mapper combiner are employed to reduce
> the network traffic in the shuffle phase.
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