Cross Mutual Information
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915401866149888 |
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| author | Gohil, Chetan Cliff, Oliver M Shine, James M. Fulcher, Ben D. Lizier, Joseph T. |
| author_facet | Gohil, Chetan Cliff, Oliver M Shine, James M. Fulcher, Ben D. Lizier, Joseph T. |
| contents | Mutual information (MI) is a useful information-theoretic measure to quantify the statistical dependence between two random variables: $X$ and $Y$. Often, we are interested in understanding how the dependence between $X$ and $Y$ in one set of samples compares to another. Although the dependence between $X$ and $Y$ in each set of samples can be measured separately using MI, these estimates cannot be compared directly if they are based on samples from a non-stationary distribution. Here, we propose an alternative measure for characterising how the dependence between $X$ and $Y$ as defined by one set of samples is expressed in another, \textit{cross mutual information}. We present a comprehensive set of simulation studies sampling data with $X$-$Y$ dependencies to explore this measure. Finally, we discuss how this relates to measures of model fit in linear regression, and some future applications in neuroimaging data analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_15372 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cross Mutual Information Gohil, Chetan Cliff, Oliver M Shine, James M. Fulcher, Ben D. Lizier, Joseph T. Information Theory Mutual information (MI) is a useful information-theoretic measure to quantify the statistical dependence between two random variables: $X$ and $Y$. Often, we are interested in understanding how the dependence between $X$ and $Y$ in one set of samples compares to another. Although the dependence between $X$ and $Y$ in each set of samples can be measured separately using MI, these estimates cannot be compared directly if they are based on samples from a non-stationary distribution. Here, we propose an alternative measure for characterising how the dependence between $X$ and $Y$ as defined by one set of samples is expressed in another, \textit{cross mutual information}. We present a comprehensive set of simulation studies sampling data with $X$-$Y$ dependencies to explore this measure. Finally, we discuss how this relates to measures of model fit in linear regression, and some future applications in neuroimaging data analysis. |
| title | Cross Mutual Information |
| topic | Information Theory |
| url | https://arxiv.org/abs/2507.15372 |