[MAHOUT-1273] Single Pass Algorithm for Penalized Linear Regression with Cross Validation on MapReduce

• Type: New Feature
• Status: Closed
• Priority: Major
• Resolution: Won't Fix
• Affects Version/s: 0.9
• Fix Version/s: 0.10.0
• Labels: documentation features patch test
• Assignee: Unassigned
• Reporter: Kun Yang
• Created: 03/Jul/13 18:47
• Updated: 13/Apr/15 10:22
• Resolved: 09/Mar/14 22:27

Description

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.