This paper examines the problem of learning with a finite and possibly large set of p base kernels. It presents a theoretical and empirical analysis of an approach addressing this problem based on ensembles of kernel predictors. This includes novel theoretical guarantees based on the Rademacher complexity of the corresponding hypothesis sets, the introduction and analysis of a learning algorithm based on these hypothesis sets, and a series of experiments using ensembles of kernel predictors with several data sets. Both convex combinations of kernel-based hypotheses and more general Lq-regularized nonnegative combinations are analyzed. These theoretical, algorithmic, and empirical results are compared with those achieved by using learning kernel techniques, which can be viewed as another approach for solving the same problem.

Conditional Restricted Boltzmann Machines (CRBMs) are rich probabilistic models that have recently been applied to a wide range of problems, including collaborative filtering, classification, and modeling motion capture data. While much progress has been made in training non-conditional RBMs, these algorithms are not applicable to conditional models and there has been almost no work on training and generating predictions from conditional RBMs for structured output problems. We first argue that standard Contrastive Divergence-based learning may not be suitable for training CRBMs. We then identify two distinct types of structured output prediction problems and propose an improved learning algorithm for each. The first problem type is one where the output space has arbitrary structure but the set of likely output configurations is relatively small, such as in multi-label classification. The second problem is one where the output space is arbitrarily structured but where the output space variability is much greater, such as in image denoising or pixel labeling. We show that the new learning algorithms can work much better than Contrastive Divergence on both types of problems.

We present a novel approach to constraint-based causal discovery, that takes the form of straightforward logical inference, applied to a list of simple, logical statements about causal relations that are derived directly from observed (in)dependencies. It is both sound and complete, in the sense that all invariant features of the corresponding partial ancestral graph (PAG) are identified, even in the presence of latent variables and selection bias. The approach shows that every identifiable causal relation corresponds to one of just two fundamental forms. More importantly, as the basic building blocks of the method do not rely on the detailed (graphical) structure of the corresponding PAG, it opens up a range of new opportunities, including more robust inference, detailed accountability, and application to large models.

The First-Order Variable Elimination (FOVE) algorithm allows exact inference to be applied directly to probabilistic relational models, and has proven to be vastly superior to the application of standard inference methods on a grounded propositional model. Still, FOVE operators can be applied under restricted conditions, often forcing one to resort to propositional inference. This paper aims to extend the applicability of FOVE by providing two new model conversion operators: the first and the primary is joint formula conversion and the second is just-different counting conversion. These new operations allow efficient inference methods to be applied directly on relational models, where no existing efficient method could be applied hitherto. In addition, aided by these capabilities, we show how to adapt FOVE to provide exact solutions to Maximum Expected Utility (MEU) queries over relational models for decision under uncertainty. Experimental evaluations show our algorithms to provide significant speedup over the alternatives.

To deal with the prohibitive complexity of calculating policies in Decentralized MDPs, researchers have proposed models that exploit structured agent interactions. Settings where most agent actions are independent except for few actions that affect the transitions and/or rewards of other agents can be modeled using Event-Driven Interactions with Complex Rewards (EDI-CR). Finding the optimal joint policy can be formulated as an optimization problem. However, existing formulations are too verbose and/or lack optimality guarantees. We propose a compact Mixed Integer Linear Program formulation of EDI-CR instances. The key insight is that most action sequences of a group of agents have the same effect on a given agent. This allows us to treat these sequences similarly and use fewer variables. Experiments show that our formulation is more compact and leads to faster solution times and better solutions than existing formulations.

Compiling Bayesian networks (BNs) to junction trees and performing belief propagation over them is among the most prominent approaches to computing posteriors in BNs. However, belief propagation over junction tree is known to be computationally intensive in the general case. Its complexity may increase dramatically with the connectivity and state space cardinality of Bayesian network nodes. In this paper, we address this computational challenge using GPU parallelization. We develop data structures and algorithms that extend existing junction tree techniques, and specifically develop a novel approach to computing each belief propagation message in parallel. We implement our approach on an NVIDIA GPU and test it using BNs from several applications. Experimentally, we study how junction tree parameters affect parallelization opportunities and hence the performance of our algorithm. We achieve speedups ranging from 0.68 to 9.18 for the BNs studied.

At the heart of many scientific conferences is the problem of matching submitted papers to suitable reviewers. Arriving at a good assignment is a major and important challenge for any conference organizer. In this paper we propose a framework to optimize paper-to-reviewer assignments. Our framework uses suitability scores to measure pairwise affinity between papers and reviewers. We show how learning can be used to infer suitability scores from a small set of provided scores, thereby reducing the burden on reviewers and organizers. We frame the assignment problem as an integer program and propose several variations for the paper-to-reviewer matching domain. We also explore how learning and matching interact. Experiments on two conference data sets examine the performance of several learning methods as well as the effectiveness of the matching formulations.

We present a distributed anytime algorithm for performing MAP inference in graphical models. The problem is formulated as a linear programming relaxation over the edges of a graph. The resulting program has a constraint structure that allows application of the Dantzig-Wolfe decomposition principle. Subprograms are defined over individual edges and can be computed in a distributed manner. This accommodates solutions to graphs whose state space does not fit in memory. The decomposition master program is guaranteed to compute the optimal solution in a finite number of iterations, while the solution converges monotonically with each iteration. Formulating the MAP inference problem as a linear program allows additional (global) constraints to be defined; something not possible with message passing algorithms. Experimental results show that our algorithm's solution quality outperforms most current algorithms and it scales well to large problems.

Computing maximum a posteriori (MAP) estimation in graphical models is an important inference problem with many applications. We present message-passing algorithms for quadratic programming (QP) formulations of MAP estimation for pairwise Markov random fields. In particular, we use the concave-convex procedure (CCCP) to obtain a locally optimal algorithm for the non-convex QP formulation. A similar technique is used to derive a globally convergent algorithm for the convex QP relaxation of MAP. We also show that a recently developed expectation-maximization (EM) algorithm for the QP formulation of MAP can be derived from the CCCP perspective. Experiments on synthetic and real-world problems confirm that our new approach is competitive with max-product and its variations. Compared with CPLEX, we achieve more than an order-of-magnitude speedup in solving optimally the convex QP relaxation.

Traditional economic models typically treat private information, or signals, as generated from some underlying state. Recent work has explicated alternative models, where signals correspond to interpretations of available information. We show that the difference between these formulations can be sharply cast in terms of causal dependence structure, and employ graphical models to illustrate the distinguishing characteristics. The graphical representation supports inferences about signal patterns in the interpreted framework, and suggests how results based on the generated model can be extended to more general situations. Specific insights about bidding games in classical auction mechanisms derive from qualitative graphical models.