fastMI: a fast and consistent copula-based estimator of mutual information
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866912234350837760 |
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| author | Purkayastha, Soumik Song, Peter X. K. |
| author_facet | Purkayastha, Soumik Song, Peter X. K. |
| contents | As a fundamental concept in information theory, mutual information ($MI$) has been commonly applied to quantify association between random vectors. Most existing nonparametric estimators of $MI$ have unstable statistical performance since they involve parameter tuning. We develop a consistent and powerful estimator, called fastMI, that does not incur any parameter tuning. Based on a copula formulation, fastMI estimates $MI$ by leveraging Fast Fourier transform-based estimation of the underlying density. Extensive simulation studies reveal that fastMI outperforms state-of-the-art estimators with improved estimation accuracy and reduced run time for large data sets. fastMI provides a powerful test for independence that exhibits satisfactory type I error control. Anticipating that it will be a powerful tool in estimating mutual information in a broad range of data, we develop an R package fastMI for broader dissemination. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2212_10268 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | fastMI: a fast and consistent copula-based estimator of mutual information Purkayastha, Soumik Song, Peter X. K. Applications Computation Methodology 62H12 As a fundamental concept in information theory, mutual information ($MI$) has been commonly applied to quantify association between random vectors. Most existing nonparametric estimators of $MI$ have unstable statistical performance since they involve parameter tuning. We develop a consistent and powerful estimator, called fastMI, that does not incur any parameter tuning. Based on a copula formulation, fastMI estimates $MI$ by leveraging Fast Fourier transform-based estimation of the underlying density. Extensive simulation studies reveal that fastMI outperforms state-of-the-art estimators with improved estimation accuracy and reduced run time for large data sets. fastMI provides a powerful test for independence that exhibits satisfactory type I error control. Anticipating that it will be a powerful tool in estimating mutual information in a broad range of data, we develop an R package fastMI for broader dissemination. |
| title | fastMI: a fast and consistent copula-based estimator of mutual information |
| topic | Applications Computation Methodology 62H12 |
| url | https://arxiv.org/abs/2212.10268 |