Discovering Potential Correlations via Hypercontractivity
Discovering a correlation from one variable to another variable is of fundamental scientific and practical interest. While existing correlation measures are suitable for discovering average correlation, they fail to discover hidden or potential correlations. To bridge this gap, (i) we postulate a se...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-11-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/19/11/586 |
| _version_ | 1818001558333292544 |
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| author | Hyeji Kim Weihao Gao Sreeram Kannan Sewoong Oh Pramod Viswanath |
| author_facet | Hyeji Kim Weihao Gao Sreeram Kannan Sewoong Oh Pramod Viswanath |
| author_sort | Hyeji Kim |
| collection | DOAJ |
| description | Discovering a correlation from one variable to another variable is of fundamental scientific and practical interest. While existing correlation measures are suitable for discovering average correlation, they fail to discover hidden or potential correlations. To bridge this gap, (i) we postulate a set of natural axioms that we expect a measure of potential correlation to satisfy; (ii) we show that the rate of information bottleneck, i.e., the hypercontractivity coefficient, satisfies all the proposed axioms; (iii) we provide a novel estimator to estimate the hypercontractivity coefficient from samples; and (iv) we provide numerical experiments demonstrating that this proposed estimator discovers potential correlations among various indicators of WHO datasets, is robust in discovering gene interactions from gene expression time series data, and is statistically more powerful than the estimators for other correlation measures in binary hypothesis testing of canonical examples of potential correlations. |
| first_indexed | 2024-04-14T03:34:47Z |
| format | Article |
| id | doaj.art-876e25d9a97540f0afb599c61973a8b9 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T03:34:47Z |
| publishDate | 2017-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-876e25d9a97540f0afb599c61973a8b92022-12-22T02:14:48ZengMDPI AGEntropy1099-43002017-11-01191158610.3390/e19110586e19110586Discovering Potential Correlations via HypercontractivityHyeji Kim0Weihao Gao1Sreeram Kannan2Sewoong Oh3Pramod Viswanath4Coordinated Science Lab, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USACoordinated Science Lab, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USADepartment of Electrical Engineering, University of Washington, Seattle, WA 98195, USACoordinated Science Lab, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USACoordinated Science Lab, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USADiscovering a correlation from one variable to another variable is of fundamental scientific and practical interest. While existing correlation measures are suitable for discovering average correlation, they fail to discover hidden or potential correlations. To bridge this gap, (i) we postulate a set of natural axioms that we expect a measure of potential correlation to satisfy; (ii) we show that the rate of information bottleneck, i.e., the hypercontractivity coefficient, satisfies all the proposed axioms; (iii) we provide a novel estimator to estimate the hypercontractivity coefficient from samples; and (iv) we provide numerical experiments demonstrating that this proposed estimator discovers potential correlations among various indicators of WHO datasets, is robust in discovering gene interactions from gene expression time series data, and is statistically more powerful than the estimators for other correlation measures in binary hypothesis testing of canonical examples of potential correlations.https://www.mdpi.com/1099-4300/19/11/586correlation analysispotential correlationinformation bottleneckhypercontractivity |
| spellingShingle | Hyeji Kim Weihao Gao Sreeram Kannan Sewoong Oh Pramod Viswanath Discovering Potential Correlations via Hypercontractivity Entropy correlation analysis potential correlation information bottleneck hypercontractivity |
| title | Discovering Potential Correlations via Hypercontractivity |
| title_full | Discovering Potential Correlations via Hypercontractivity |
| title_fullStr | Discovering Potential Correlations via Hypercontractivity |
| title_full_unstemmed | Discovering Potential Correlations via Hypercontractivity |
| title_short | Discovering Potential Correlations via Hypercontractivity |
| title_sort | discovering potential correlations via hypercontractivity |
| topic | correlation analysis potential correlation information bottleneck hypercontractivity |
| url | https://www.mdpi.com/1099-4300/19/11/586 |
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