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From Phil Steitz <p...@steitz.com>
Subject [math] Correlation and Covariance
Date Sun, 08 Feb 2009 20:52:35 GMT
MATH-114 and MATH-138 propose support for correlation matrices.  I have 
been working on these and would like to propose the following:

Create a new package o.a.c.m.stat.correlation to house intially
    a) Covariance - creates variance-covariance matrix from a matrix 
whose columns represent covariates.  Also includes convenience methods 
that work pairwise on double[] arrays (similar to VectorialCovariance, 
but requiring that the arrays be stored)
    b) PearsonCorrelation - creates Pearson's product-moment correlation 
matrix from either a covariance matrix or a matrix of covariates. Also 
includes methods to return matrices of correlation standard errors and 
p-values (aka significances, i.e. p-value for null hypothesis that the 
coefficient is 0).
    c) SpearmanRankCorrelation - like Pearson's but no covariance matrix 
constructor and using rank correlation. 

To implement c), we need a place for the RankingAlgorithm interface and 
implementations (see MATH-138).   Any suggestions on where to put 
these?  Leaving in correlation may be awkward later on as we do more 
with rank transformations.

I have a) implemented using a fairly stable two-pass algorithm.  I tried 
just using VectorialCovariance, but could not get the accuracy I wanted 
using the one-pass algorithm there.  We should probably at some point 
look at improving the updating formula used there along the lines of 
what we do for Variance, but it is a nice feature of that class that it 
does not require the input vectors to be stored and I would not want to 
see that changed.   For b), similar to the patch in JIRA, I would use 
the R computation from SimpleRegression if working from a matrix, or 
just compute column sigmas and scale directly if working from a 
covariance matrix.

Does this sound good?

If I don't hear any objections, I will commit some code along the lines 
above for us to look at.

Phil


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