Related papers: Lattice Conditional Independence Models and Hibi I…
Hamiltonian lattice gauge models based on the assignment of the Heisenberg double of a Lie group to each link of the lattice are constructed in arbitrary space-time dimensions. It is shown that the corresponding generalization of the…
Causal inference methods based on conditional independence construct Markov equivalent graphs, and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal…
We consider ideals arising in the context of conditional independence models that generalize the class of ideals considered by Fink [7] in a way distinct from the generalizations of Herzog-Hibi-Hreinsdottir-Kahle-Rauh [13] and Ay-Rauh [1].…
We present a comprehensive study of graphical log-linear models for contingency tables. High dimensional contingency tables arise in many areas such as computational biology, collection of survey and census data and others. Analysis of…
Inferring the potential consequences of an unobserved event is a fundamental scientific question. To this end, Pearl's celebrated do-calculus provides a set of inference rules to derive an interventional probability from an observational…
This work lies at the intersection of Gibbs models and hyperuniform point processes. Classical Gibbs models, whether defined on lattices or in continuous space, provide flexible tools to describe interacting particle systems but are…
In CI-Liaison, significant effort has been made to study ideals that are in the linkage class of a complete intersection, which are called licci ideals. In a polynomial ring, recently E. Chong defined a "sequentially bounded" condition on…
We discuss a class of problems which we call lattice exit models. At one level, these problems provide undergraduate level exercises in labeling the vertices of graphs (e.g., depth first search). At another level (theorems about large scale…
The fundamental concepts underlying in Markov networks are the conditional independence and the set of rules called Markov properties that translates conditional independence constraints into graphs. In this article we introduce the concept…
Testing for the conditional independence structure in data is a fundamental and critical task in statistics and machine learning, which finds natural applications in causal discovery - a highly relevant problem to many scientific…
Neighborhood regression has been a successful approach in graphical and structural equation modeling, with applications to learning undirected and directed graphical models. We extend these ideas by defining and studying an algebraic…
Generative models for classification use the joint probability distribution of the class variable and the features to construct a decision rule. Among generative models, Bayesian networks and naive Bayes classifiers are the most commonly…
Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior…
We study the effects of gauge-symmetry breaking (GSB) perturbations in three-dimensional lattice gauge theories with scalar fields. We study this issue at transitions in which gauge correlations are not critical and the gauge symmetry only…
It is well known that there may be many causal explanations that are consistent with a given set of data. Recent work has been done to represent the common aspects of these explanations into one representation. In this paper, we address…
Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or…
A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so-called local independences, meaning that the intensities of certain types of events are independent of some…
The conditional independence (CI) relation of a distribution in a max-linear Bayesian network depends on its weight matrix through the $C^\ast$-separation criterion. These CI~models, which we call maxoids, are compositional graphoids which…
We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process…
We study random walks on contingency tables with fixed marginals, corresponding to a (log-linear) hierarchical model. If the set of allowed moves is not a Markov basis, then there exist tables with the same marginals that are not connected.…