相关论文: Independence Testing for Bounded Degree Bayesian N…

Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $\epsilon$-far from all…

In this paper we present a method ofcomputing the posterior probability ofconditional independence of two or morecontinuous variables from data,examined at several resolutions. Ourapproach is motivated by theobservation that the appearance…

Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is…

We study the problem of testing \emph{conditional independence} for discrete distributions. Specifically, given samples from a discrete random variable $(X, Y, Z)$ on domain $[\ell_1]\times[\ell_2] \times [n]$, we want to distinguish, with…

Given well-shuffled data, can we determine whether the data items are statistically (in)dependent? Formally, we consider the problem of testing whether a set of exchangeable random variables are independent. We will show that this is…

Testing conditional independence has many applications, such as in Bayesian network learning and causal discovery. Different test methods have been proposed. However, existing methods generally can not work when only discretized…

The local Markov condition for a DAG to be an independence map of a probability distribution is well known. For DAGs with latent variables, represented as bi-directed edges in the graph, the local Markov property may invoke exponential…

Testing the validity of probabilistic models containing unmeasured (hidden) variables is shown to be a hard task. We show that the task of testing whether models are structurally incompatible with the data at hand, requires an exponential…

In this article, we propose a new method for the fundamental task of testing for dependence between two groups of variables. The response densities under the null hypothesis of independence and the alternative hypothesis of dependence are…

This paper analyzes independence concepts for sets of probability measures associated with directed acyclic graphs. The paper shows that epistemic independence and the standard Markov condition violate desirable separation properties. The…

Testing independence among a number of (ultra) high-dimensional random samples is a fundamental and challenging problem. By arranging $n$ identically distributed $p$-dimensional random vectors into a $p \times n$ data matrix, we investigate…

Over the last couple of decades, several copula based methods have been proposed in the literature to test for the independence among several random variables. But these existing tests are not invariant under monotone transformations of the…

Given samples from an unknown multivariate distribution $p$, is it possible to distinguish whether $p$ is the product of its marginals versus $p$ being far from every product distribution? Similarly, is it possible to distinguish whether…

This paper considers the problem of testing the maximum in-degree of the Bayes net underlying an unknown probability distribution $P$ over $\{0,1\}^n$, given sample access to $P$. We show that the sample complexity of the problem is…

Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed…

Testing for independence between graphs is a problem that arises naturally in social network analysis and neuroscience. In this paper, we address independence testing for inhomogeneous Erd\H{o}s-R\'{e}nyi random graphs on the same vertex…

We wish to test whether a real-valued variable $Z$ has explanatory power, in addition to a multivariate variable $X$, for a binary variable $Y$. Thus, we are interested in testing the hypothesis $\mathbb{P}(Y=1\, | \, X,Z)=\mathbb{P}(Y=1\,…

Understanding causal relationships between variables is a fundamental problem with broad impact in numerous scientific fields. While extensive research has been dedicated to learning causal graphs from data, its complementary concept of…

Learning the directed acyclic graph (DAG) structure of a Bayesian network from observational data is a notoriously difficult problem for which many hardness results are known. In this paper we propose a provably polynomial-time algorithm…

Constraint-based causal discovery algorithms utilize many statistical tests for conditional independence to uncover networks of causal dependencies. These approaches to causal discovery rely on an assumed correspondence between the…