Related papers: Random Variables, Conditional Independence and Cat…

In this paper we study different concepts of independence for convex sets of probabilities. There will be two basic ideas for independence. The first is irrelevance. Two variables are independent when a change on the knowledge about one…

This paper introduces a new concept of stochastic dependence among many random variables which we call conditional neighborhood dependence (CND). Suppose that there are a set of random variables and a set of sigma algebras where both sets…

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…

We consider a pair of causally independent processes, modelled as the tensor product of two channels, acting on a possibly correlated input to produce random outputs X and Y. We show that, assuming the processes produce a sufficient amount…

With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ordered sequence of…

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…

Species sampling processes have long served as the fundamental framework for modeling random discrete distributions and exchangeable sequences. However, data arising from distinct but related sources require a broader notion of…

A growing body of research on probabilistic programs and causal models has highlighted the need to reason compositionally about model classes that extend directed graphical models. Both probabilistic programs and causal models define a…

Structural independence is the (conditional) independence that arises from the structure rather than the precise numerical values of a distribution. We develop this concept and relate it to $d$-separation and structural causal models.…

We introduce a sound and complete equational theory capturing equivalence of discrete probabilistic programs, that is, programs extended with primitives for Bernoulli distributions and conditioning, to model distributions over finite sets…

Markov random fields provide a compact representation of joint probability distributions by representing its independence properties in an undirected graph. The well-known Hammersley-Clifford theorem uses these conditional independences to…

Motivated by the fundamental problem of measuring species diversity, this paper introduces the concept of a cluster structure to define an exchangeable cluster probability function that governs the joint distribution of a random count and…

This paper presents a topological learning-theoretic perspective on causal inference by introducing a series of topologies defined on general spaces of structural causal models (SCMs). As an illustration of the framework we prove a…

This paper presents a focused review of Markov random fields (MRFs)--commonly used probabilistic representations of spatial dependence in discrete spatial domains--for categorical data, with an emphasis on models for binary-valued…

Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…

We establish a bijection between marginal independence models on $n$ random variables and split closed order ideals in the poset of partial set partitions. We also establish that every discrete marginal independence model is toric in cdf…

Triplet Markov chains are general generative models for sequential data which take into account three kinds of random variables: (noisy) observations, their associated discrete labels and latent variables which aim at strengthening the…

We present general principles underlying analysis of the dependence of random variables (outputs) on deterministic conditions (inputs). Random outputs recorded under mutually exclusive input values are labeled by these values and considered…

Representing the conditional independences present in a multivariate random vector via graphs has found widespread use in applications, and such representations are popularly known as graphical models or Markov random fields. These models…

An empirical model is a generalization of a probability space. It consists of a simplicial complex of subsets of a class X of random variables such that each simplex has an associated probability distribution. The ensuing marginalizations…