I introduce a graphical representation for modeling multiagent systems based on different kinds of reasoning about agent behavior. I seek to investigate this graphical model’s predictive and representative capabilities across various domains, and examine methods for learning the graphical structure from agent interaction data. I also propose to explore the framework’s scalability in large real-...

Graphical Markov models are multivariate statistical models which are currently under vigorous development and which combine two simple but most powerful notions, generating processes in single and joint response variables and conditional independences captured by graphs. The development of graphical Markov started with work by Wermuth (1976, 1980) and Darroch, Lauritzen and Speed (1980) which ...

We advocate the use of a new distribution family—the transelliptical—for robust inference of high dimensional graphical models. The transelliptical family is an extension of the nonparanormal family proposed by Liu et al. (2009). Just as the nonparanormal extends the normal by transforming the variables using univariate functions, the transelliptical extends the elliptical family in the same wa...

The flood of multi-context measurement data from many scientific domains has created an urgent need to reconstruct context-specific variable networks, that could significantly simplify network-driven studies. Computationally, this problem can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from samples aggregated across several conte...

Bayesian network (BN) A directed graph whose nodes represent variables, and edges represent influences. Together with conditional probability distributions, a Bayesian network represents the joint probability distribution of its variables. Conditional probability distribution Assignment of probabilities to all instances of a set of variables when the value of one or more variables is known. Con...

This paper introduces a new probabilistic architecture called Sum-Product Graphical Model (SPGM). SPGMs combine traits from Sum-Product Networks (SPNs) and Graphical Models (GMs): Like SPNs, SPGMs always enable tractable inference using a class of models that incorporate context specific independence. Like GMs, SPGMs provide a high-level model interpretation in terms of conditional independence...

Multivariate multi-way ANOVA-type models are the default tools for analyzing experimental data with multiple independent covariates. However, formulating standard multi-way models is not possible when the data comes from different sources or in cases where some covariates have (partly) unknown structure, such as time with unknown alignment. The “small n, large p”, large dimensionality p with sm...

There are many settings in which we wish to fit a model of the behavior of individuals but where our data consist only of aggregate information (counts or low-dimensional contingency tables). This paper introduces Collective Graphical Models—a framework for modeling and probabilistic inference that operates directly on the sufficient statistics of the individual model. We derive a highlyefficie...

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 finite number of values. Continuous data are different. The Gaussian graphical model is the standard parametric model for continuous data, but it makes distribu...