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Network Maximal Correlation
Name
1606.04789.pdf
Description
Submitted version
Size
1.46 MB
Format
Adobe PDF
Checksum (MD5)
0ae12f214ba3ad9481ff509a97da18ca
Author(s)
Feizi, Soheil
Makhdoumi, Ali
Duffy, Ken
Kellis, Manolis
Medard, Muriel
Date Issued
2017
Journal
IEEE Transactions on Network Science and Engineering
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Version
Original manuscript
Abstract
© 2017 IEEE. We introduce Network Maximal Correlation (NMC) as a multivariate measure of nonlinear association among random variables. NMC is defined via an optimization that infers transformations of variables by maximizing aggregate inner products between transformed variables. For finite discrete and jointly Gaussian random variables, we characterize a solution of the NMC optimization using basis expansion of functions over appropriate basis functions. For finite discrete variables, we propose an algorithm based on alternating conditional expectation to determine NMC. Moreover we propose a distributed algorithm to compute an approximation of NMC for large and dense graphs using graph partitioning. For finite discrete variables, we show that the probability of discrepancy greater than any given level between NMC and NMC computed using empirical distributions decays exponentially fast as the sample size grows. For jointly Gaussian variables, we show that under some conditions the NMC optimization is an instance of the Max-Cut problem. We then illustrate an application of NMC in inference of graphical model for bijective functions of jointly Gaussian variables. Finally, we show NMC's utility in a data application of learning nonlinear dependencies among genes in a cancer dataset.
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
10.1109/TNSE.2017.2716966
