Network Maximal Correlation
© 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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Institute of Electrical and Electronics Engineers (IEEE)
2021
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| Online Access: | https://hdl.handle.net/1721.1/135743 |
| _version_ | 1811096237738295296 |
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| author | Feizi, Soheil Makhdoumi, Ali Duffy, Ken Kellis, Manolis Medard, Muriel |
| author_facet | Feizi, Soheil Makhdoumi, Ali Duffy, Ken Kellis, Manolis Medard, Muriel |
| author_sort | Feizi, Soheil |
| collection | MIT |
| description | © 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. |
| first_indexed | 2024-09-23T16:40:46Z |
| format | Article |
| id | mit-1721.1/135743 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:40:46Z |
| publishDate | 2021 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1357432022-03-30T14:32:48Z Network Maximal Correlation Feizi, Soheil Makhdoumi, Ali Duffy, Ken Kellis, Manolis Medard, Muriel © 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. 2021-10-27T20:29:05Z 2021-10-27T20:29:05Z 2017 2019-06-07T13:38:25Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/135743 en 10.1109/TNSE.2017.2716966 IEEE Transactions on Network Science and Engineering Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Feizi, Soheil Makhdoumi, Ali Duffy, Ken Kellis, Manolis Medard, Muriel Network Maximal Correlation |
| title | Network Maximal Correlation |
| title_full | Network Maximal Correlation |
| title_fullStr | Network Maximal Correlation |
| title_full_unstemmed | Network Maximal Correlation |
| title_short | Network Maximal Correlation |
| title_sort | network maximal correlation |
| url | https://hdl.handle.net/1721.1/135743 |
| work_keys_str_mv | AT feizisoheil networkmaximalcorrelation AT makhdoumiali networkmaximalcorrelation AT duffyken networkmaximalcorrelation AT kellismanolis networkmaximalcorrelation AT medardmuriel networkmaximalcorrelation |