Related papers: Computational Explorations of Total Variation Dist…
Total variation distance (TV distance) is a fundamental notion of distance between probability distributions. In this work, we introduce and study the problem of computing the TV distance of two product distributions over the domain…
We study the problem of approximating the total variation distance between two mixtures of product distributions over an $n$-dimensional discrete domain. Given two mixtures $\mathbb{P}$ and $\mathbb{Q}$ with $k_1$ and $k_2$ product…
Total variation distance (TV distance) is an important measure for the difference between two distributions. Recently, there has been progress in approximating the TV distance between product distributions: a deterministic algorithm for a…
Two-sample testing, where we aim to determine whether two distributions are equal or not equal based on samples from each one, is challenging if we cannot place assumptions on the properties of the two distributions. In particular,…
In this paper, we establish a novel connection between total variation (TV) distance estimation and probabilistic inference. In particular, we present an efficient, structure-preserving reduction from relative approximation of TV distance…
We show that computing the total variation distance between two product distributions is $\#\mathsf{P}$-complete. This is in stark contrast with other distance measures such as Kullback-Leibler, Chi-square, and Hellinger, which tensorize…
We give a simple polynomial-time approximation algorithm for the total variation distance between two product distributions.
The total variation distance is a metric of central importance in statistics and probability theory. However, somewhat surprisingly, questions about computing it algorithmically appear not to have been systematically studied until very…
With the proliferation of generative AI and the increasing volume of generative data (also called as synthetic data), assessing the fidelity of generative data has become a critical concern. In this paper, we propose a discriminative…
We consider the problem of estimating Ising models over $n$ variables in Total Variation (TV) distance, given $l$ independent samples from the model. While the statistical complexity of the problem is well-understood [DMR20], identifying…
Spin systems form an important class of undirected graphical models. For two Gibbs distributions $\mu$ and $\nu$ induced by two spin systems on the same graph $G = (V, E)$, we study the problem of approximating the total variation distance…
When two different parties use the same learning rule on their own data, how can we test whether the distributions of the two outcomes are similar? In this paper, we study the similarity of outcomes of learning rules through the lens of the…
We study the relation between the total variation (TV) and Hellinger distances between two Gaussian location mixtures. Our first result establishes a general upper bound: for any two mixing distributions supported on a compact set, the…
Uncertainty propagation in non-linear dynamical systems has become a key problem in various fields including control theory and machine learning. In this work we focus on discrete-time non-linear stochastic dynamical systems. We present a…
Total variation (TV) minimization is one of the most important techniques in modern signal/image processing, and has wide range of applications. While there are numerous recent works on the restoration guarantee of the TV minimization in…
The total variation distance is a core statistical distance between probability measures that satisfies the metric axioms, with value always falling in $[0,1]$. This distance plays a fundamental role in machine learning and signal…
We prove results on the decidability and complexity of computing the total variation distance (equivalently, the $L_1$-distance) of hidden Markov models (equivalently, labelled Markov chains). This distance measures the difference between…
If one seeks to estimate the total variation between two product measures $||P^\otimes_{1:n}-Q^\otimes_{1:n}||$ in terms of their marginal TV sequence $\delta=(||P_1-Q_1||,||P_2-Q_2||,\ldots,||P_n-Q_n||)$, then trivial upper and lower…
Mixtures of high dimensional Gaussian distributions have been studied extensively in statistics and learning theory. While the total variation distance appears naturally in the sample complexity of distribution learning, it is analytically…
We consider the initial situation where a dataset has been over-partitioned into $k$ clusters and seek a domain independent way to merge those initial clusters. We identify the total variation distance (TVD) as suitable for this goal. By…