Information Theory Measures via Multidimensional Gaussianization
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866912091475017728 |
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| author | Laparra, Valero Johnson, J. Emmanuel Camps-Valls, Gustau Santos-Rodríguez, Raul Malo, Jesus |
| author_facet | Laparra, Valero Johnson, J. Emmanuel Camps-Valls, Gustau Santos-Rodríguez, Raul Malo, Jesus |
| contents | Information theory is an outstanding framework to measure uncertainty, dependence and relevance in data and systems. It has several desirable properties for real world applications: it naturally deals with multivariate data, it can handle heterogeneous data types, and the measures can be interpreted in physical units. However, it has not been adopted by a wider audience because obtaining information from multidimensional data is a challenging problem due to the curse of dimensionality. Here we propose an indirect way of computing information based on a multivariate Gaussianization transform. Our proposal mitigates the difficulty of multivariate density estimation by reducing it to a composition of tractable (marginal) operations and simple linear transformations, which can be interpreted as a particular deep neural network. We introduce specific Gaussianization-based methodologies to estimate total correlation, entropy, mutual information and Kullback-Leibler divergence. We compare them to recent estimators showing the accuracy on synthetic data generated from different multivariate distributions. We made the tools and datasets publicly available to provide a test-bed to analyze future methodologies. Results show that our proposal is superior to previous estimators particularly in high-dimensional scenarios; and that it leads to interesting insights in neuroscience, geoscience, computer vision, and machine learning. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2010_03807 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Information Theory Measures via Multidimensional Gaussianization Laparra, Valero Johnson, J. Emmanuel Camps-Valls, Gustau Santos-Rodríguez, Raul Malo, Jesus Machine Learning Information theory is an outstanding framework to measure uncertainty, dependence and relevance in data and systems. It has several desirable properties for real world applications: it naturally deals with multivariate data, it can handle heterogeneous data types, and the measures can be interpreted in physical units. However, it has not been adopted by a wider audience because obtaining information from multidimensional data is a challenging problem due to the curse of dimensionality. Here we propose an indirect way of computing information based on a multivariate Gaussianization transform. Our proposal mitigates the difficulty of multivariate density estimation by reducing it to a composition of tractable (marginal) operations and simple linear transformations, which can be interpreted as a particular deep neural network. We introduce specific Gaussianization-based methodologies to estimate total correlation, entropy, mutual information and Kullback-Leibler divergence. We compare them to recent estimators showing the accuracy on synthetic data generated from different multivariate distributions. We made the tools and datasets publicly available to provide a test-bed to analyze future methodologies. Results show that our proposal is superior to previous estimators particularly in high-dimensional scenarios; and that it leads to interesting insights in neuroscience, geoscience, computer vision, and machine learning. |
| title | Information Theory Measures via Multidimensional Gaussianization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2010.03807 |