Related papers: Gaussian conditional independence relations have n…
We propose a new class of extreme-value copulas which are extreme-value limits of conditional normal models. Conditional normal models are generalizations of conditional independence models, where the dependence among observed variables is…
Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates,…
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…
We study the properties of algebraic independence and pointwise algebraic independence in a class of continuous theories, the randomizations $T^R$ of complete first order theories $T$. If algebraic and definable closure coincide in $T$,…
We introduce the notion of a conditionally free product and conditionally free convolution. We describe this convolution both from a combinatorial point of view, by showing its connection with the lattice of non-crossing partitions, and…
We describe a procedure to introduce general dependence structures on a set of random variables. These include order-$q$ moving average-type structures, as well as seasonal, periodic, spatial and spatio-temporal dependences. The invariant…
We introduce binomial edge ideals attached to a simple graph $G$ and study their algebraic properties. We characterize those graphs for which the quadratic generators form a Gr\"obner basis in a lexicographic order induced by a vertex…
In this paper, we revisit the notion of partial copula, originally introduced to test conditional independence, highlighting its capability to represent the dependence between two random variables after removing their dependence with a…
We characterize the limiting distributions of random variables of the form $P_n\left( (X_i)_{i \ge 1} \right)$, where: (i) $(P_n)_{n \ge 1}$ is a sequence of multivariate polynomials, each potentially involving countably many variables;…
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in case-control studies. Graphical models represent assumptions about the…
Causal discovery is to learn cause-effect relationships among variables given observational data and is important for many applications. Existing causal discovery methods assume data sufficiency, which may not be the case in many real world…
We present a complete logic for reasoning with functional dependencies (FDs) with semantics defined over classes of commutative integral partially ordered monoids and complete residuated lattices. The dependencies allow us to express…
When a hybrid Bayesian network has conditionally deterministic variables with continuous parents, the joint density function for the continuous variables does not exist. Conditional linear Gaussian distributions can handle such cases when…
Conditional independence of treatment assignment from potential outcomes is a commonly used but nonrefutable assumption. We derive identified sets for various treatment effect parameters under nonparametric deviations from this conditional…
Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
We present an elementary and explicit proof of the separability criterion for continuous variable two-party Gaussian systems. Our proof is based on an elementary formulation of uncertainty relations and an explicit determination of…
Whereas acausal Bayesian networks represent probabilistic independence, causal Bayesian networks represent causal relationships. In this paper, we examine Bayesian methods for learning both types of networks. Bayesian methods for learning…
Linear non-Gaussian causal models postulate that each random variable is a linear function of parent variables and non-Gaussian exogenous error terms. We study identification of the linear coefficients when such models contain latent…