Computational Explorations of Total Variation Distance

Fuente: arXiv
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Bibliographic Details
Main Authors: Bhattacharyya, Arnab, Gayen, Sutanu, Meel, Kuldeep S., Myrisiotis, Dimitrios, Pavan, A., Vinodchandran, N. V.
Format: Preprint
Published: 2024
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author Bhattacharyya, Arnab
Gayen, Sutanu
Meel, Kuldeep S.
Myrisiotis, Dimitrios
Pavan, A.
Vinodchandran, N. V.
author_facet Bhattacharyya, Arnab
Gayen, Sutanu
Meel, Kuldeep S.
Myrisiotis, Dimitrios
Pavan, A.
Vinodchandran, N. V.
contents We investigate some previously unexplored (or underexplored) computational aspects of total variation (TV) distance. First, we give a simple deterministic polynomial-time algorithm for checking equivalence between mixtures of product distributions, over arbitrary alphabets. This corresponds to a special case, whereby the TV distance between the two distributions is zero. Second, we prove that unless $\mathsf{NP} \subseteq \mathsf{RP}$, it is impossible to efficiently estimate the TV distance between arbitrary Ising models, even in a bounded-error randomized setting.
format Preprint
id arxiv_https___arxiv_org_abs_2412_10370
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Computational Explorations of Total Variation Distance
Bhattacharyya, Arnab
Gayen, Sutanu
Meel, Kuldeep S.
Myrisiotis, Dimitrios
Pavan, A.
Vinodchandran, N. V.
Data Structures and Algorithms
Computational Complexity
We investigate some previously unexplored (or underexplored) computational aspects of total variation (TV) distance. First, we give a simple deterministic polynomial-time algorithm for checking equivalence between mixtures of product distributions, over arbitrary alphabets. This corresponds to a special case, whereby the TV distance between the two distributions is zero. Second, we prove that unless $\mathsf{NP} \subseteq \mathsf{RP}$, it is impossible to efficiently estimate the TV distance between arbitrary Ising models, even in a bounded-error randomized setting.
title Computational Explorations of Total Variation Distance
topic Data Structures and Algorithms
Computational Complexity
url https://arxiv.org/abs/2412.10370