Related papers: Two generalizations of Markov blankets
A general setting for nested subdivisions of a bounded real set into intervals defining the digits $X_1,X_2,...$ of a random variable $X$ with a probability density function $f$ is considered. Under the weak condition that $f$ is almost…
Markov networks are frequently used in sciences to represent conditional independence relationships underlying observed variables arising from a complex system. It is often of interest to understand how an underlying network differs between…
Causal discovery automates the learning of causal Bayesian networks from data and has been of active interest from their beginning. With the sourcing of large data sets off the internet, interest in scaling up to very large data sets has…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
The standard Bayesian Information Criterion (BIC) is derived under regularity conditions which are not always satisfied by the graphical models with hidden variables. In this paper we derive the BIC score for Bayesian networks in the case…
Large-scale multiple testing tasks often exhibit dependence, and leveraging the dependence between individual tests is still one challenging and important problem in statistics. With recent advances in graphical models, it is feasible to…
Under standard graphical assumptions, the Markov boundary of a target variable is the smallest set of features that renders every other feature redundant. Once the boundary is observed, the target is conditionally independent of the rest of…
We introduce a novel class of graphical models, termed profile graphical models, that represent, within a single graph, how an external factor influences the dependence structure of a multivariate set of variables. This class is quite…
Chain graphs give a natural unifying point of view on Markov and Bayesian networks and enlarge the potential of graphical models for description of conditional independence structures. In the paper a direct graphical separation criterion…
A diffusion taking value in probability measures on a graph with a vertex set $V$, $\sum_{i\in V}x_i\delta_i$, is studied. The masses on each vertices satisfy the stochastic differential equation of the form $dx_i=\sum_{j\in…
A statistical language model assigns probability to strings of arbitrary length. Unfortunately, it is not possible to gather reliable statistics on strings of arbitrary length from a finite corpus. Therefore, a statistical language model…
We study a notion of robustness of a Markov kernel that describes a system of several input random variables and one output random variable. Robustness requires that the behaviour of the system does not change if one or several of the input…
Decoding complex relationships among large numbers of variables with relatively few observations is one of the crucial issues in science. One approach to this problem is Gaussian graphical modeling, which describes conditional independence…
Markov chains are convenient means of generating realizations of networks with a given (joint or otherwise) degree distribution, since they simply require a procedure for rewiring edges. The major challenge is to find the right number of…
The Markov Blanket Bayesian Classifier is a recently-proposed algorithm for construction of probabilistic classifiers. This paper presents an empirical comparison of the MBBC algorithm with three other Bayesian classifiers: Naive Bayes,…
We consider the problem of learning a directed graph $G^\star$ from observational data. We assume that the distribution which gives rise to the samples is Markov and faithful to the graph $G^\star$ and that there are no unobserved…
Undirected graphical models known as Markov networks are popular for a wide variety of applications ranging from statistical physics to computational biology. Traditionally, learning of the network structure has been done under the…
Hidden variables are ubiquitous in practical data analysis, and therefore modeling marginal densities and doing inference with the resulting models is an important problem in statistics, machine learning, and causal inference. Recently, a…
Markov chains are a convenient means of generating realizations of networks, since they require little more than a procedure for rewiring edges. If a rewiring procedure exists for generating new graphs with specified statistical properties,…
In this paper, we present a simple non-parametric method for learning the structure of undirected graphs from data that drawn from an underlying unknown distribution. We propose to use Brownian distance covariance to estimate the…