RBIG4IT |
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Paper |
"Information Theory Measures via Multidimensional Gaussianization" |
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Abstract |
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. |
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Software |
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Paper Summary |
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Extended results |
Here extra results for the paper are shown. Mainly figures for results on synthetic data that would taken too much space in the original paper. |
Total Correlation |
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Entropy |
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KLD |
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mutual information |
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References |
[RBIG4IT2020]: "Information Theory Measures via Multidimensional Gaussianization". V. Laparra, E. Johnson, G. Camps-Valls, R. Santos-Rodriguez, J. Malo. |
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Copyright & Disclaimer |
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us. |