Related papers: A homogenization principle for total variation
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 total variation distance under two information-erasing maps on inhomogeneous Bernoulli product measures: summation and homogenization. While summation is a Markov kernel and hence satisfies the usual data processing inequality,…
Let $X_1,X_2,\ldots$ be a sequence of i.i.d. random variables, with mean zero and variance one. Let $W_n=(X_1+\ldots+X_n)/\sqrt{n}$. An old and celebrated result of Prohorov asserts that $W_n$ converges in total variation to the standard…
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…
We study the total variation distance (TV) between two $n$-fold Bernoulli product measures parametrized by $\vec p=(p_1,\ldots,p_n)$ and $\vec q=(q_1,\ldots,q_n)$, respectively, in the \emph{tiny} and \emph{small} regimes. In the tiny…
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…
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…
Consider a discrete time Markov chain with rather general state space which has an invariant probability measure $\mu$. There are several sufficient conditions in the literature which guarantee convergence of all or $\mu$-almost all…
Even after over two decades, the total variation (TV) remains one of the most popular regularizations for image processing problems and has sparked a tremendous amount of research, particularly to move from scalar to vector-valued…
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…
This paper is concerned with the study of the consistency of a variational method for probability measure quantization, deterministically realized by means of a minimizing principle, balancing power repulsion and attraction potentials. The…
Pinsker's classical inequality asserts that the total variation $TV(\mu, \nu)$ between two probability measures is bounded by $\sqrt{ 2H(\mu|\nu)}$ where $H$ denotes the relative entropy (or Kullback-Leibler divergence). Considering the…
Total variation (TV) denoising is a nonparametric smoothing method that has good properties for preserving sharp edges and contours in objects with spatial structures like natural images. The estimate is sparse in the sense that TV…
We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…
One of the fundamental assumptions of compressive sensing (CS) is that a signal can be reconstructed from a small number of samples by solving an optimization problem with the appropriate regularization term. Two standard regularization…
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…
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…
Total variation denoising (TVD) is a classical method for denoising and curve fitting, yet an explicit pointwise description of its fitted values has only recently been established in the mean regression setting by arXiv:2410.03041v4. This…
Let $\eta_{1},\eta_2,...$ be independent (not necessarily identically distributed) zero-mean random variables (r.v.'s) such that $|\eta_i|\le1$ almost surely for all $i$, and let $Z$ stand for a standard normal r.v. Let $a_1,a_2,...$ be any…