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From "Kun Yang (JIRA)" <j...@apache.org>
Subject [jira] [Commented] (MAHOUT-1273) Single Pass Algorithm for Penalized Linear Regression with Cross Validation on MapReduce
Date Sat, 03 Aug 2013 23:35:48 GMT

    [ https://issues.apache.org/jira/browse/MAHOUT-1273?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=13728698#comment-13728698
] 

Kun Yang commented on MAHOUT-1273:
----------------------------------

Hi Ted,

The value of Y is always fixed which is independent of \beta. Y are just the response and
are read from the data set.
                
> 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.  

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