9 accepted papers
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 spe…
This work establishes a novel link between the problem of PAC-learning high-dimensional graphical models and the task of (efficient) counting and sampling of graph structures, using an online learning framework. The problem of efficiently counting and sampling graphical structures, such as spanning…
Bayes nets are extensively used in practice to efficiently represent joint probability distributions over a set of random variables and capture dependency relations. Prior work has shown that given a distribution P defined as the marginal distribution of a Bayes net, it is NP-hard to decide whether…
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 to probabilistic inference over directed graphical models. Th…
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 {0,1}^n. In particular, we establish the following results. 1. T…
We consider the problem of efficiently inferring interventional distributions in a causal Bayesian network from a finite number of observations. Let P be a causal model on a set V of observable variables on a given causal graph G. For sets $X,Y \subseteq V$, and setting x to $X$, $P_x(Y)$ denotes th…
Gaussian Bayesian networks are widely used to model causal interactions among continuous variables. In this work, we study the problem of learning a fixed-structure Gaussian Bayesian network up to a bounded error in total variation distance. We analyze the commonly used node-wise least squares regre…
We design efficient distance approximation algorithms for several classes of well-studied structured high-dimensional distributions. Specifically, we present algorithms for the following problems (where dTV is the total variation distance):
We study the problem of efficiently estimating the effect of an intervention on a single variable using observational samples. Our goal is to give algorithms with polynomial time and sample complexity in a non-parametric setting. Tian and Pearl (AAAI ’02) have exactly characterized the class of caus…