Graphical games provide compact representation of a multiagent interaction when agents’ payoffs depend only on actions of agents in their local neighborhood. We formally describe the problem of learning a graphical game model from limited observation of the payoff function, define three performance metrics for evaluating learned games, and investigate several learning algorithms based on minimi...

This is a PhD-level course about how to develop and use probability models. We will study their mathematical properties, algorithms for computing with them, and applications to real problems. We will study both the foundations and modern methods in this field, such as large-scale inference and Bayesian nonparametrics. Our goals are to understand the cutting edge of modern probabilistic modeling...

Many time series are generated by a set of entities that interact with one another over time. This paper introduces a broad, flexible framework to learn from multiple inter-dependent time series generated by such entities. Our framework explicitly models the entities and their interactions through time. It achieves this by building on the capabilities of Recurrent Neural Networks, while also of...

We investigate the problem of reducing the complexity of a graphical model (G,PG) by finding a subgraph H of G, chosen from a class of subgraphs H, such that H is optimal with respect to KL-divergence. We do this by first defining a decomposition tree representation for G, which is closely related to the junction-tree representation for G. We then give an algorithm which uses this representatio...

We describe how graphical Markov models emerged in the last 40 years, based on three essential concepts that had been developed independently more than a century ago. Sequences of joint or single regressions and their regression graphs are singled out as being the subclass that is best suited for analyzing longitudinal data and for tracing developmental pathways, both in observational and in in...

Recently, it has been demonstrated that graphical models promise some potential for expressing causal concepts, see for example Pearl (2000), Lauritzen (2001), or Dawid (2002). The causal interpretation is most direct in models based on directed acyclic graphs, whereas causal interpretation for chain graph models generally is more subtle and complex (Lauritzen and Richardson 2002). In the artic...

This report1 presents probabilistic graphical models that are based on imprecise probabilities using a comprehensive language. In particular, the discussion is focused on credal networks and discrete domains. It describes the building blocks of credal networks, algorithms to perform inference, and discusses on complexity results and related work. The goal is to present an easy-to-follow introdu...

Graphical models provide a powerful framework for probabilistic modelling and reasoning. Although theory behind learning and inference is well understood, most practical applications require approximation to known algorithms. We review learning of thin junction trees–a class of graphical models that permits efficient inference. We discuss particular cases in clique graphs where exact inference ...

Read: Chapters 5 and 6 of [CGH]. The first model for a joint probability distribution that we will consider is the undirected graph. We will undirected graphs using two different methods. First, we will show the relationship between undirected graphs and joint probability distributions. Second, we will show the relationship between undirected graphs, and an abstract independence model (called a...

Graphical models have attracted increasing attention in recent years, especially in settings involving high dimensional data. In particular Gaussian graphical models are used to model the conditional dependence structure among p Gaussian random variables. As a result of its computational efficiency the graphical lasso (glasso) has become one of the most popular approaches for fitting high dimen...