Discrete chain graph models

By Mathias Drton. 2009

130 citations recorded by the source corpus.

The statistical literature discusses different types of Markov properties for chain graphs that lead to four possible classes of chain graph Markov models. The different models are rather well understood when the observations are continuous and multivariate normal, and it is also known that one model class, referred to as models of LWF (Lauritzen-Wermuth-Frydenberg) or block concentration type, yields discrete models for categorical data that are smooth. This paper considers the structural properties of the discrete models based on the three alternative Markov properties. It is shown by example that two of the alternative Markov properties can lead to non-smooth models. The remaining model class, which can be viewed as a discrete version of multivariate regressions, is proven to comprise only smooth models. The proof employs a sim ple change of coordinates that also reveals that the model's likelihood function is unimodal if the chain components of the graph are complete sets.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e9c5f23365d5d3964cac9bfcd5014c7d34c4d3d1

How researchers see this paper

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In Artificial Intelligence

1. Nanny Wermuth
2. Yee Whye Teh
3. Charles Blundell
4. Kayvan Sadeghi
5. Sergey Levine
6. Steffen L. Lauritzen
7. Monia Lupparelli
8. Robin J. Evans

In Statistics and Probability

1. Nanny Wermuth
2. Ricardo M. A. Silva
3. Kayvan Sadeghi
4. Robin J. Evans
5. Steffen L. Lauritzen
6. Charles Blundell
7. Yee Whye Teh
8. Monia Lupparelli

Citations in the corpus

• Markov properties for mixed graphs (2011, methodology): “texceptionsinclude certainindependence modelsforchaingraphs.Chaingraphs themselves are LMGs, but at least four different Markov properties for chain graphs have been discussed in the literature. Drton [8] has classified them into (i) the LWF or block concentration Markov property, (ii) the AMP or conc”
• Multivariate Statistical Analysis (2011, background): “These models are now recognized as special cases of both linear structural equations and of multivariate regression chains, a subclass of graphical Markov models; see Cox and Wermuth (1993), Drton (2009), Marchetti and Lupparelli (2010).”
• Sequences of regressions and their independences (2011, background): “There may even exist several solutions to the likelihood equations; see Drton and Richardson (2004). However for the present data, the structure is so evidently well-fitting in a covering model that none of these potential problems are relevant, that is in the unconstrained multivariate regression o”
• Margins of discrete Bayesian networks (2015, background): “Latent variable models generally do not have fully identifiable parameterizations [Allman, Matias and Rhodes (2009)], and contain “singularities” that lead to nonregular asymptotics [Drton (2009)].”
• Mixed Cumulative Distribution Networks (2010, background): “Notice that the structure of type IV chain graphs [3] is a spec ial ase of ADMGs with barren districts.”
• Chain graph models of multivariate regression type for categorical data (2009, methodology): “Recently, [9] distinguished four types of chain graphs comprising the classical and the alternative (Andersson, Madigan, Perlman, [1]) chain graph models, called of type I and II, respectively.”