We focus on the problem of sequential decision making in partially observable environments shared with other agents of uncertain types having similar or conflicting objectives. This problem has been previously formalized by multiple frameworks one of which is the interactive dynamic influence diagram (I-DID), which generalizes the well-known influence diagram to the multiagent setting. I-DIDs are graphical models and may be used to compute the policy of an agent given its belief over the physical state and others' models, which changes as the agent acts and observes in the multiagent setting. As we may expect, solving I-DIDs is computationally hard. This is predominantly due to the large space of candidate models ascribed to the other agents and its exponential growth over time. We present two methods for reducing the size of the model space and stemming its exponential growth. Both these methods involve aggregating individual models into equivalence classes. Our first method groups together behaviorally equivalent models and selects only those models for updating which will result in predictive behaviors that are distinct from others in the updated model space. The second method further compacts the model space by focusing on portions of the behavioral predictions. Specifically, we cluster actionally equivalent models that prescribe identical actions at a single time step. Exactly identifying the equivalences would require us to solve all models in the initial set. We avoid this by selectively solving some of the models, thereby introducing an approximation. We discuss the error introduced by the approximation, and empirically demonstrate the improved efficiency in solving I-DIDs due to the equivalences.

In many signal detection and classification problems, we have knowledge of the distribution under each hypothesis, but not the prior probabilities. This paper is aimed at providing theory to quantify the performance of detection via estimating prior probabilities from either labeled or unlabeled training data. The error or {\em risk} is considered as a function of the prior probabilities. We show that the risk function is locally Lipschitz in the vicinity of the true prior probabilities, and the error of detectors based on estimated prior probabilities depends on the behavior of the risk function in this locality. In general, we show that the error of detectors based on the Maximum Likelihood Estimate (MLE) of the prior probabilities converges to the Bayes error at a rate of $n^{-1/2}$, where $n$ is the number of training data. If the behavior of the risk function is more favorable, then detectors based on the MLE have errors converging to the corresponding Bayes errors at optimal rates of the form $n^{-(1+\alpha)/2}$, where $\alpha>0$ is a parameter governing the behavior of the risk function with a typical value $\alpha = 1$. The limit $\alpha \rightarrow \infty$ corresponds to a situation where the risk function is flat near the true probabilities, and thus insensitive to small errors in the MLE; in this case the error of the detector based on the MLE converges to the Bayes error exponentially fast with $n$. We show the bounds are achievable no matter given labeled or unlabeled training data and are minimax-optimal in labeled case.

We postulate that the nature of information items plays a vital role in the observed spread of these items in a social network. We capture this intuition by proposing a model that assigns to every information item two parameters: endogeneity and exogeneity. The endogeneity of the item quantifies its tendency to spread primarily through the connections between nodes; the exogeneity quantifies its tendency to be acquired by the nodes, independently of the underlying network. We also extend this item-based model to take into account the openness of each node to new information. We quantify openness by introducing the receptivity of a node. Given a social network and data related to the ordering of adoption of information items by nodes, we develop a maximum-likelihood framework for estimating endogeneity, exogeneity and receptivity parameters. We apply our methodology to synthetic and real data and demonstrate its efficacy as a data-analytic tool.

In this paper we present an algorithm for rapid Bayesian analysis that combines the benefits of nested sampling and artificial neural networks. The blind accelerated multimodal Bayesian inference (BAMBI) algorithm implements the MultiNest package for nested sampling as well as the training of an artificial neural network (NN) to learn the likelihood function. In the case of computationally expensive likelihoods, this allows the substitution of a much more rapid approximation in order to increase significantly the speed of the analysis. We begin by demonstrating, with a few toy examples, the ability of a NN to learn complicated likelihood surfaces. BAMBI's ability to decrease running time for Bayesian inference is then demonstrated in the context of estimating cosmological parameters from Wilkinson Microwave Anisotropy Probe and other observations. We show that valuable speed increases are achieved in addition to obtaining NNs trained on the likelihood functions for the different model and data combinations. These NNs can then be used for an even faster follow-up analysis using the same likelihood and different priors. This is a fully general algorithm that can be applied, without any pre-processing, to other problems with computationally expensive likelihood functions.

Bayesian priors offer a compact yet general means of incorporating domain knowledge into many learning tasks. The correctness of the Bayesian analysis and inference, however, largely depends on accuracy and correctness of these priors. PAC-Bayesian methods overcome this problem by providing bounds that hold regardless of the correctness of the prior distribution. This paper introduces the first PAC-Bayesian bound for the batch reinforcement learning problem with function approximation. We show how this bound can be used to perform model-selection in a transfer learning scenario. Our empirical results confirm that PAC-Bayesian policy evaluation is able to leverage prior distributions when they are informative and, unlike standard Bayesian RL approaches, ignore them when they are misleading.

Markov jump processes and continuous time Bayesian networks are important classes of continuous time dynamical systems. In this paper, we tackle the problem of inferring unobserved paths in these models by introducing a fast auxiliary variable Gibbs sampler. Our approach is based on the idea of uniformization, and sets up a Markov chain over paths by sampling a finite set of virtual jump times and then running a standard hidden Markov model forward filtering-backward sampling algorithm over states at the set of extant and virtual jump times. We demonstrate significant computational benefits over a state-of-the-art Gibbs sampler on a number of continuous time Bayesian networks.

Probabilistic inference in graphical models is the task of computing marginal and conditional densities of interest from a factorized representation of a joint probability distribution. Inference algorithms such as variable elimination and belief propagation take advantage of constraints embedded in this factorization to compute such densities efficiently. In this paper, we propose an algorithm which computes interventional distributions in latent variable causal models represented by acyclic directed mixed graphs(ADMGs). To compute these distributions efficiently, we take advantage of a recursive factorization which generalizes the usual Markov factorization for DAGs and the more recent factorization for ADMGs. Our algorithm can be viewed as a generalization of variable elimination to the mixed graph case. We show our algorithm is exponential in the mixed graph generalization of treewidth.

Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new estimators designed specifically to overcome this intractability, but virtually nothing is known about their theoretical properties. In this paper, we present a generalized estimator that unifies many of the classical and recently proposed estimators. We use results from the standard asymptotic theory for M-estimators to derive a generic expression for the asymptotic covariance matrix of our generalized estimator. We apply these results to study the relative statistical efficiency of classical pseudolikelihood and the recently-proposed ratio matching estimator.

Given a set of experiments in which varying subsets of observed variables are subject to intervention, we consider the problem of identifiability of causal models exhibiting latent confounding. While identifiability is trivial when each experiment intervenes on a large number of variables, the situation is more complicated when only one or a few variables are subject to intervention per experiment. For linear causal models with latent variables Hyttinen et al. (2010) gave precise conditions for when such data are sufficient to identify the full model. While their result cannot be extended to discrete-valued variables with arbitrary cause-effect relationships, we show that a similar result can be obtained for the class of causal models whose conditional probability distributions are restricted to a `noisy-OR' parameterization. We further show that identification is preserved under an extension of the model that allows for negative influences, and present learning algorithms that we test for accuracy, scalability and robustness.

We present a new Markov chain Monte Carlo method for estimating posterior probabilities of structural features in Bayesian networks. The method draws samples from the posterior distribution of partial orders on the nodes; for each sampled partial order, the conditional probabilities of interest are computed exactly. We give both analytical and empirical results that suggest the superiority of the new method compared to previous methods, which sample either directed acyclic graphs or linear orders on the nodes.