Network Maximal Correlation 
Feizi, Soheil; Makhdoumi, Ali; Duffy, Ken R.; Kellis, Manolis; Medard, Muriel



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 MaxCut 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.

Keyword(s):

Maximum correlation problem; alternating conditional expectation (ACE); HermiteChebyshev polynomials; Gaussian graphical models; gene networks 
Publication Date:

2017 
Type:

Journal article 
PeerReviewed:

Yes 
Institution:

Maynooth University 
Citation(s):

Feizi, Soheil and Makhdoumi, Ali and Duffy, Ken R. and Kellis, Manolis and Medard, Muriel (2017) Network Maximal Correlation. IEEE Transactions on Network Science and Engineering, 4 (4). pp. 229247. ISSN 23274697 
Publisher(s):

IEEE 
File Format(s):

other 
Related Link(s):

http://eprints.maynoothuniversity.ie/10167/1/KDNetwork2017.pdf 
First Indexed:
20181102 06:00:06 Last Updated:
20181102 06:00:06 