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Causal graphs (CGs) are compact representations of the knowledge of the data generating processes behind the data distributions. When a CG is available, e.g., from the domain knowledge, we can infer the conditional independence (CI)…
We reduce the conditionally monotone (c-monotone) independence of Hasebe to tensor independence. For that purpose, we use the approach developed for the reduction of boolean, free and monotone independences to tensor independence. We apply…
The subject of this paper is the elucidation of effects of actions from causal assumptions represented as a directed graph, and statistical knowledge given as a probability distribution. In particular, we are interested in predicting…
We address the problem of likelihood based inference for correlated diffusion processes using Markov chain Monte Carlo (MCMC) techniques. Such a task presents two interesting problems. First, the construction of the MCMC scheme should…
Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate…
New theoretical results are presented here on the recently introduced model called mixed states MRF. Such models were introduced in the context of image motion analysis and are useful to represent information which can take both discrete…
In the process of building (structural learning) a probabilistic graphical model from a set of observed data, the directional, cyclic dependencies between the random variables of the model are often found. Existing graphical models such as…
Constraint-based causal discovery algorithms learn part of the causal graph structure by systematically testing conditional independences observed in the data. These algorithms, such as the PC algorithm and its variants, rely on graphical…
Gibbs distribution of binary Markov random fields on a sparse on average graph is considered in this paper. The strong spatial mixing is proved under the condition that the `external field' is uniformly large or small. Such condition on…
We consider local Markov chain Monte-Carlo algorithms for sampling from the weighted distribution of independent sets with activity $\l$, where the weight of an independent set $I$ is $\l^{|I|}$. A recent result has established that Gibbs…
The graphical structure of Probabilistic Graphical Models (PGMs) represents the conditional independence (CI) relations that hold in the modeled distribution. Every separator in the graph represents a conditional independence relation in…
We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are non-nested and their intersection is a union of two marginal independences. We consider two sequences of such…
An extension of non-deterministic processes driven by the random telegraph signal is introduced in the framework of "piecewise deterministic Markov processes" [Davis], including a broader category of random systems. The corresponding…
We consider conditional tests for non-negative discrete exponential families. We develop two Markov Chain Monte Carlo (MCMC) algorithms which allow us to sample from the conditional space and to perform approximated tests. The first…
We consider the problem of inferring the directed, causal graph from observational data, assuming no hidden confounders. We take an information theoretic approach, and make three main contributions. First, we show how through algorithmic…
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…
For spatial and network data, we consider models formed from a Markov random field (MRF) structure and the specification of a conditional distribution for each observation. Fast simulation from such MRF models is often an important…
We present new MCMC algorithms for computing the posterior distributions and expectations of the unknown variables in undirected graphical models with regular structure. For demonstration purposes, we focus on Markov Random Fields (MRFs).…
Undirected probabilistic graphical models represent the conditional dependencies, or Markov properties, of a collection of random variables. Knowing the sparsity of such a graphical model is valuable for modeling multivariate distributions…
Bayesian belief networks have grown to prominence because they provide compact representations for many problems for which probabilistic inference is appropriate, and there are algorithms to exploit this compactness. The next step is to…