On non-graphical description of models of conditional independence structure
نویسنده
چکیده
Several graphical structural models, including some models with latent variables can be viewed as models of conditional independence structure. However, usual graphical methods do not allow one to describe all possible stochastic conditional independence structures. Therefore an attempt to develop a general method of mathematical description of conditional independence structures by means of certain integer-valued functions, called structural imsets, was made. The main part of the paper is an outline of this approach. The presented results concern the mathematical basis of this method. After exposition of theoretical background some open questions are discussed: the problem of internal computer representation of models, inferential problems and interpretation question. The paper is concluded by a cursory reflection on what are suitable learning strategies and relevant data generating procedures for models of conditional independence structure.
منابع مشابه
Non-intuitive conditional independence facts hold in models of network data
Many social scientists and researchers across a wide range of fields focus on analyzing a single causal dependency or a conditional model of some outcome variable. However, to reason about interventions or conditional independence, it is useful to construct a joint model of a domain. Researchers in computer science, statistics, and philosophy have developed representations (e.g., Bayesian netwo...
متن کاملA Brief Introduction to Graphical Models and How to Learn Them from Data
Graphical Models: Core Ideas and Notions A Simple Example: How does it work in principle? Conditional Independence Graphs conditional independence and the graphoid axioms separation in (directed and undirected) graphs decomposition/factorization of distributions Evidence Propagation in Graphical Models Building Graphical Models Learning Graphical Models from Data quantitative (parameter) and qu...
متن کاملSimulating from graphical models for ordinal categorical data
Multivariate ordinal categorical data is encountered in many fields of research. For analysis and data reduction the conditional independence properties of these data are studied in graphical models. However, to simulate multivariate ordinal data with a specific conditional independence structure, for use in simulation studies or computer intensive methods of inference, is non-trivial. We prese...
متن کاملDistribution-Free Learning of Graphical Model Structure in Continuous Domains
In this paper we present a probabilistic non-parametric conditional independence test of X and Y given a third variable Z in domains where X, Y , and Z are continuous. This test can be used for the induction of the structure of a graphical model (such as a Bayesian or Markov network) from experimental data. We also provide an effective method for calculating it from data. We show that our metho...
متن کاملIdentifying Independence in Relational Models
The rules of d -separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d -separation, a theory for deriving conditional independence in relational models. We provide a sound, complete, and computationally efficient method for relational d -separation, and we p...
متن کامل