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Binary models for marginal independence
 JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B
, 2005
"... A number of authors have considered multivariate Gaussian models for marginal independence. In this paper we develop models for binary data with the same independence structure. The models can be parameterized based on Möbius inversion and maximum likelihood estimation can be performed using a versi ..."
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A number of authors have considered multivariate Gaussian models for marginal independence. In this paper we develop models for binary data with the same independence structure. The models can be parameterized based on Möbius inversion and maximum likelihood estimation can be performed using a version of the Iterated Conditional Fitting algorithm. The approach is illustrated on a simple example. Relations to multivariate logistic and dependence ratio models are discussed.
QuasiSymmetric Graphical LogLinear Models
"... ABSTRACT. We propose an extension of graphical loglinear models to allow for symmetry constraints on some interaction parameters that represent homologous factors. The conditional independence structure of such quasisymmetric (QS) graphical models is described by an undirected graph with coloured ..."
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ABSTRACT. We propose an extension of graphical loglinear models to allow for symmetry constraints on some interaction parameters that represent homologous factors. The conditional independence structure of such quasisymmetric (QS) graphical models is described by an undirected graph with coloured edges, in which a particular colour corresponds to a set of equality constraints on a set of parameters. Unlike standard QS models, the proposed models apply with contingency tables for which only some variables or sets of the variables have the same categories. We study the graphical properties of such models, including conditions for decomposition of model parameters and of maximum likelihood estimates. Key words: conditional independence, decomposition, exchangeability, graphical models, homologous variables
Group symmetry and covariance regularization
, 2011
"... Abstract: Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalizethe notion of asymmetric modelvia groupinvariance. We propo ..."
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Abstract: Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalizethe notion of asymmetric modelvia groupinvariance. We propose projection onto a group fixed point subspace as a fundamental way of regularizing covariance matrices in the highdimensional regime. In terms of parameters associated to the group we derive precise rates of convergence of the regularized covariance matrix and demonstrate that significant statistical gains may be expected interms of the sample complexity. We further explore the consequences of symmetry inrelated modelselection problems such as the learning of sparse covariance and inverse covariance
Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry
, 2009
"... We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a spectrahedron, and to the problem of characterizing the image of th ..."
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We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing the determinant function over a spectrahedron, and to the problem of characterizing the image of the positive definite cone under an arbitrary linear projection. These problems at the interface of statistics and optimization are here examined from the perspective of convex algebraic geometry.
Interaction Graphs for Multivariate Binary Data
"... Abstract. We define a class of graphs that summarize in a compact visual way the interaction structure between binary multivariate characteristics. This allows studying the conditional dependency structure between the underlying stochastic variables at a finer scale than with classical probabilistic ..."
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Abstract. We define a class of graphs that summarize in a compact visual way the interaction structure between binary multivariate characteristics. This allows studying the conditional dependency structure between the underlying stochastic variables at a finer scale than with classical probabilistic Graphical Models. A model selection strategy is derived based on an iterative optimization procedure and the consistency problem is discussed. We include the analysis of two datasets to illustrate the proposed approach.
ETH Zurich Diego Colombo ETH Zurich
"... The pcalg package for R (R Development Core Team (2010)) can be used for the following two purposes: Causal structure learning and estimation of causal effects from observational data. In this document, we give a brief overview of the methodology, and demonstrate the package’s functionality in both ..."
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The pcalg package for R (R Development Core Team (2010)) can be used for the following two purposes: Causal structure learning and estimation of causal effects from observational data. In this document, we give a brief overview of the methodology, and demonstrate the package’s functionality in both toy examples and applications.