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We present first a brief review of the existing literature on shape optimization, stressing the recent use of Hamiltonian systems in topology optimization. In the second section, we collect some preliminaries on the implicit parametrization…
We propose a probability distribution for multivariate binary random variables. The probability distribution is expressed as principal minors of the parameter matrix, which is a matrix analogous to the inverse covariance matrix in the…
We introduce a novel class of graphical models, termed profile graphical models, that represent, within a single graph, how an external factor influences the dependence structure of a multivariate set of variables. This class is quite…
Directed graphs naturally model systems with asymmetric, ordered relationships, essential to applications in biology, transportation, social networks, and visual understanding. Generating such graphs enables tasks such as simulation, data…
Directed acyclic graphs provide a fundamental tool for representing directed dependence structures in multivariate network data, and are widely used to model financial and economic networks. However, accurate and interpretable estimation…
Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure $\Lambda$ on the punctured Euclidean space $\mathbb…
This article describes a method for using optimization to derive efficient independent transition functions for Markov chain Monte Carlo simulations. Our interest is in sampling from a posterior density $\pi(x)$ for problems in which the…
The present work deals with active sampling of graph nodes representing training data for binary classification. The graph may be given or constructed using similarity measures among nodal features. Leveraging the graph for classification…
This paper introduces a novel class of models for binary data, which we call log-mean linear models. The characterizing feature of these models is that they are specified by linear constraints on the log-mean linear parameter, defined as a…
Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation 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…
This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected…
We study mixed models with a single grouping factor, where inference about unknown parameters requires optimizing a marginal likelihood defined by an intractable integral. Low-dimensional numerical integration techniques are regularly used…
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…
Estimating the parameters of a probabilistic directed graphical model from incomplete data is a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are…
Modeling is a challenging topic and using parametric models is an important stage to reach flexible function for modeling. Weibull distribution has two parameters which are shape $\alpha$ and scale $\beta$. In this study, bimodality…
In this paper, we outline a model of graph (or network) dynamics based on two ingredients. The first ingredient is a Markov chain on the space of possible graphs. The second ingredient is a semi-Markov counting process of renewal type. The…
Markov networks and Bayesian networks are effective graphic representations of the dependencies embedded in probabilistic models. It is well known that independencies captured by Markov networks (called graph-isomorphs) have a finite…
We present some nonparametric methods for graphical modeling. In the discrete case, where the data are binary or drawn from a finite alphabet, Markov random fields are already essentially nonparametric, since the cliques can take only a…
We introduce a nonparametric graphical model for discrete node variables based on additive conditional independence. Additive conditional independence is a three way statistical relation that shares similar properties with conditional…