[
https://issues.apache.org/jira/browse/MAHOUT-1273?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13728712#comment-13728712
]
Jason Lee commented on MAHOUT-1273:
-----------------------------------
Hi Ted,
I have done some work on Penalized Linear Regression. I read through the draft
and went over the algorithm described. As described, I think the algorithm is
correct. It uses Mapreduce to compute X'X, X'y, and y'y, then minimizes over
\beta: 1/2 \beta'(X'X) \beta -\beta' X'y +1/2 y'y +\lambda P(\beta), where
P(\beta) is the elastic net penalty function. It requires one pass of Mapreduce
to compute the quantities X'X, X'y, and y'y, and then the algorithm uses the
Pathwise Coordinate Descent Algorithm locally to solve the resulting problem.
This algorithm is extremely suitable when the number of features (p) is around
O(10,000). It only uses one pass of Mapreduce, so the primary computation is
performed locally.
Best,
Jason
> Single Pass Algorithm for Penalized Linear Regression with Cross Validation
> on MapReduce
> ----------------------------------------------------------------------------------------
>
> Key: MAHOUT-1273
> URL: https://issues.apache.org/jira/browse/MAHOUT-1273
> Project: Mahout
> Issue Type: New Feature
> Affects Versions: 0.9
> Reporter: Kun Yang
> Labels: documentation, features, patch, test
> Fix For: 0.9
>
> Attachments: Algorithm and Numeric Stability.pdf, java files.pdf,
> Manual and Example.pdf, Notes.pdf, PenalizedLinear.pdf,
> PenalizedLinearRegression.patch
>
> 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.
> The core algorithm is a modified version of coordinate descent (see J.
> Freedman's paper). They implemented a very efficient R package "glmnet",
> which is the de facto standard of penalized regression.
> I have implemented the primitive version of this algorithm in Alpine Data
> Labs.
--
This message is automatically generated by JIRA.
If you think it was sent incorrectly, please contact your JIRA administrators
For more information on JIRA, see: http://www.atlassian.com/software/jira
