Joint Probability Estimation Using Tensor Decomposition and Dictionaries Article Swipe

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Shaan Ul Haque , Ajit Rajwade , Karthik S. Gurumoorthy · YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2203.01667

In this work, we study non-parametric estimation of joint probabilities of a given set of discrete and continuous random variables from their (empirically estimated) 2D marginals, under the assumption that the joint probability could be decomposed and approximated by a mixture of product densities/mass functions. The problem of estimating the joint probability density function (PDF) using semi-parametric techniques such as Gaussian Mixture Models (GMMs) is widely studied. However such techniques yield poor results when the underlying densities are mixtures of various other families of distributions such as Laplacian or generalized Gaussian, uniform, Cauchy, etc. Further, GMMs are not the best choice to estimate joint distributions which are hybrid in nature, i.e., some random variables are discrete while others are continuous. We present a novel approach for estimating the PDF using ideas from dictionary representations in signal processing coupled with low rank tensor decompositions. To the best our knowledge, this is the first work on estimating joint PDFs employing dictionaries alongside tensor decompositions. We create a dictionary of various families of distributions by inspecting the data, and use it to approximate each decomposed factor of the product in the mixture. Our approach can naturally handle hybrid $N$-dimensional distributions. We test our approach on a variety of synthetic and real datasets to demonstrate its effectiveness in terms of better classification rates and lower error rates, when compared to state of the art estimators.

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preprint

Language

en

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http://arxiv.org/abs/2203.01667

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https://arxiv.org/pdf/2203.01667

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https://openalex.org/W4226024986

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https://openalex.org/W4226024986

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DOI

https://doi.org/10.48550/arxiv.2203.01667

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Title

Joint Probability Estimation Using Tensor Decomposition and Dictionaries

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Type

preprint

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en

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2022

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2022-03-03

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Shaan Ul Haque, Ajit Rajwade, Karthik S. Gurumoorthy

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https://arxiv.org/abs/2203.01667

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https://arxiv.org/pdf/2203.01667

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green

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https://arxiv.org/pdf/2203.01667

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Concepts

Joint probability distribution, Mathematics, Estimator, Mixture model, Probability density function, Cauchy distribution, Gaussian, Parametric statistics, Random variable, Applied mathematics, Rank (graph theory), Probability distribution, Probability mass function, Algorithm, Statistics, Combinatorics, Quantum mechanics, Physics

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Cited by

1

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2023: 1

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10

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