Related papers: Decomposable context-specific models
Decomposable graphical models, also known as perfect DAG models, play a fundamental role in standard approaches to probabilistic inference via graph representations in modern machine learning and statistics. However, such models are limited…
Decomposable dependency models possess a number of interesting and useful properties. This paper presents new characterizations of decomposable models in terms of independence relationships, which are obtained by adding a single axiom to…
Log-linear models are the popular workhorses of analyzing contingency tables. A log-linear parameterization of an interaction model can be more expressive than a direct parameterization based on probabilities, leading to a powerful way of…
Decomposable graphs are known for their tedious and complicated Markov update steps. Instead of modelling them directly, this work introduces a class of tree-dependent bipartite graphs that span the projective space of decomposable graphs.…
Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and…
For a given discrete decomposable graphical model, we identify several alternative parametrizations, and construct the corresponding reference priors for suitable groupings of the parameters. Specifically, assuming that the cliques of the…
We address the problem of representing context-specific causal models based on both observational and experimental data collected under general (e.g. hard or soft) interventions by introducing a new family of context-specific conditional…
Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide…
We formulate necessary and sufficient conditions for an arbitrary discrete probability distribution to factor according to an undirected graphical model, or a log-linear model, or other more general exponential models. For decomposable…
Markov networks are popular models for discrete multivariate systems where the dependence structure of the variables is specified by an undirected graph. To allow for more expressive dependence structures, several generalizations of Markov…
Using the moduli space of semiorthogonal decompositions in a smooth projective family, introduced by the second, the third and the fourth author, we propose a novel approach to indecomposability questions for derived categories. Modulo a…
Learning the Markov network structure from data is a problem that has received considerable attention in machine learning, and in many other application fields. This work focuses on a particular approach for this purpose called…
In this work we handle with categorical (ordinal) variables and we focus on the (in)dependence relationship under the marginal, conditional and context-specific perspective. If the first two are well known, the last one concerns…
We present a categorical framework for relating causal models that represent the same system at different levels of abstraction. We define a causal abstraction as natural transformations between appropriate Markov functors, which concisely…
Causal structure learning with data from multiple contexts carries both opportunities and challenges. Opportunities arise from considering shared and context-specific causal graphs enabling to generalize and transfer causal knowledge across…
We define the decomposition property for partial actions of discrete groups on $C^*$-algebras. Decomposable partial systems appear naturally in practice, and many commonly occurring partial actions can be decomposed into partial actions…
The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…
Ron et al (1998) introduced a rich family of models for discrete longitudinal data, called acyclic probabilistic finite automata. These may be described as context-specific graphical models, since they are represented as directed…
Several approaches to graphically representing context-specific relations among jointly distributed categorical variables have been proposed, along with structure learning algorithms. While existing optimization-based methods have limited…
Causality plays an important role in understanding intelligent behavior, and there is a wealth of literature on mathematical models for causality, most of which is focused on causal graphs. Causal graphs are a powerful tool for a wide range…