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| Paper: | SPTM-P12.3 |
| Session: | Estimation |
| Time: | Friday, May 21, 13:00 - 15:00 |
| Presentation: |
Poster |
| Topic: |
Signal Processing Theory and Methods: Detection, Estimation, and Class. Thry & Apps. |
| Title: |
ORTHOGONAL DECOMPOSITIONS OF MULTIVARIATE STATISTICAL DEPENDENCE MEASURES |
| Authors: |
Ilan Goodman; Rice University | | |
| | Don H. Johnson; Rice University | | |
| Abstract: |
We describe two multivariate statistical dependence measures which can be orthogonally decomposed to separate the effects of pairwise, triplewise, and higher order interactions between the random variables. These decompositions provide a convenient method of analyzing statistical dependencies between large groups of random variables, within which smaller ''sub-groups'' may exhibit dependencies separately from the rest of the variables. The first dependence measure is a generalization of Pearson's phi-squared, and we decompose it using an orthonormal series expansion of joint probability density functions. The second measure is based on the Kullback-Leibler distance, and we decompose it using information geometry. Applications of these techniques include analysis of neural population recordings and multi-modal sensor fusion. We discuss in detail the simple example of three jointly defined binary random variables. |
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