MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network given some evidence. Unlike computing posterior probabilities, or MPE (a special case of MAP), the time and space complexity of structural solutions for MAP are not only exponential in the network treewidth, but in a larger parameter known as the "constrained" treewidth. In practice, this means that computing MAP can be orders of magnitude more expensive than computing posterior probabilities or MPE. This paper introduces a new, simple upper bound on the probability of a MAP solution, which admits a tradeoff between the bound quality and the time needed to compute it. The bound is shown to be generally much tighter than those of other methods of comparable complexity. We use this proposed upper bound to develop a branch-and-bound search algorithm for solving MAP exactly. Experimental results demonstrate that the search algorithm is able to solve many problems that are far beyond the reach of any structure-based method for MAP. For example, we show that the proposed algorithm can compute MAP exactly and efficiently for some networks whose constrained treewidth is more than 40.

The paper continues the study of partitioning based inference of heuristics for search in the context of solving the Most Probable Explanation task in Bayesian Networks. We compare two systematic Branch and Bound search algorithms, BBBT (for which the heuristic information is constructed during search and allows dynamic variable/value ordering) and its predecessor BBMB (for which the heuristic information is pre-compiled), against a number of popular local search algorithms for the MPE problem. We show empirically that, when viewed as approximation schemes, BBBT/BBMB are superior to all of these best known SLS algorithms, especially when the domain sizes increase beyond 2. This is in contrast with the performance of SLS vs. systematic search on CSP/SAT problems, where SLS often significantly outperforms systematic algorithms. As far as we know, BBBT/BBMB are currently the best performing algorithms for solving the MPE task.

This paper examines a number of solution methods for decision processes with non-Markovian rewards (NMRDPs). They all exploit a temporal logic specification of the reward function to automatically translate the NMRDP into an equivalent Markov decision process (MDP) amenable to well-known MDP solution methods. They differ however in the representation of the target MDP and the class of MDP solution methods to which they are suited. As a result, they adopt different temporal logics and different translations. Unfortunately, no implementation of these methods nor experimental let alone comparative results have ever been reported. This paper is the first step towards filling this gap. We describe an integrated system for solving NMRDPs which implements these methods and several variants under a common interface; we use it to compare the various approaches and identify the problem features favoring one over the other.

Inferences in directed acyclic graphs associated with probability sets and probability intervals are NP-hard, even for polytrees. In this paper we focus on such inferences, and propose: 1) a substantial improvement on Tessems A / R algorithm FOR polytrees WITH probability intervals; 2) a new algorithm FOR direction - based local search(IN sets OF probability) that improves ON existing methods; 3) a collection OF branch - AND - bound algorithms that combine the previous techniques.The first two techniques lead TO approximate solutions, WHILE branch - AND - bound procedures can produce either exact OR approximate solutions.We report ON dramatic improvements ON existing techniques FOR inference WITH probability sets AND intervals, IN SOME cases reducing the computational effort BY many orders OF magnitude.

We analyze a new property of directed acyclic graphs (DAGs), called layerwidth, arising from a class of DAGs proposed by Eiter and Lukasiewicz. This class of DAGs permits certain problems of structural model-based causality and explanation to be tractably solved. In this paper, we first address an open question raised by Eiter and Lukasiewicz - the computational complexity of deciding whether a given graph has a bounded layerwidth. After proving that this problem is NP-complete, we proceed by proving numerous important properties of layerwidth that are helpful in efficiently computing the optimal layerwidth. Finally, we compare this new DAG property to two other important DAG properties: treewidth and bandwidth.

Published experiments on spidering the Web suggest that, given training data in the form of a (relatively small) subgraph of the Web containing a subset of a selected class of target pages, it is possible to conduct a directed search and find additional target pages significantly faster (with fewer page retrievals) than by performing a blind or uninformed random or systematic search, e.g., breadth-first search. If true, this claim motivates a number of practical applications. Unfortunately, these experiments were carried out in specialized domains or under conditions that are difficult to replicate. We present and apply an experimental framework designed to reexamine and resolve the basic claims of the earlier work, so that the supporting experiments can be replicated and built upon. We provide high-performance tools for building experimental spiders, make use of the ground truth and static nature of the WT10g TREC Web corpus, and rely on simple well understand machine learning techniques to conduct our experiments. In this paper, we describe the basic framework, motivate the experimental design, and report on our findings supporting and qualifying the conclusions of the earlier research.

Backtracking search is a powerful algorithmic paradigm that can be used to solve many problems. It is in a certain sense the dual of variable elimination; but on many problems, e.g., SAT, it is vastly superior to variable elimination in practice. Motivated by this we investigate the application of backtracking search to the problem of Bayesian inference (Bayes). We show that natural generalizations of known techniques allow backtracking search to achieve performance guarantees similar to standard algorithms for Bayes, and that there exist problems on which backtracking can in fact do much better. We also demonstrate that these ideas can be applied to implement a Bayesian inference engine whose performance is competitive with standard algorithms. Since backtracking search can very naturally take advantage of context specific structure, the potential exists for performance superior to standard algorithms on many problems.

This paper is devoted to the search of robust solutions in state space graphs when costs depend on scenarios. We first present axiomatic requirements for preference compatibility with the intuitive idea of robustness.This leads us to propose the Lorenz dominance rule as a basis for robustness analysis. Then, after presenting complexity results about the determination of robust solutions, we propose a new sophistication of A* specially designed to determine the set of robust paths in a state space graph. The behavior of the algorithm is illustrated on a small example. Finally, an axiomatic justification of the refinement of robustness by an OWA criterion is provided.

Many latent (factorized) models have been proposed for recommendation tasks like collaborative filtering and for ranking tasks like document or image retrieval and annotation. Common to all those methods is that during inference the items are scored independently by their similarity to the query in the latent embedding space. The structure of the ranked list (i.e. considering the set of items returned as a whole) is not taken into account. This can be a problem because the set of top predictions can be either too diverse (contain results that contradict each other) or are not diverse enough. In this paper we introduce a method for learning latent structured rankings that improves over existing methods by providing the right blend of predictions at the top of the ranked list. Particular emphasis is put on making this method scalable. Empirical results on large scale image annotation and music recommendation tasks show improvements over existing approaches.

Dual decomposition provides a tractable framework for designing algorithms for finding the most probable (MAP) configuration in graphical models. However, for many real-world inference problems, the typical decomposition has a large integrality gap, due to frustrated cycles. One way to tighten the relaxation is to introduce additional constraints that explicitly enforce cycle consistency. Earlier work showed that cluster-pursuit algorithms, which iteratively introduce cycle and other higherorder consistency constraints, allows one to exactly solve many hard inference problems. However, these algorithms explicitly enumerate a candidate set of clusters, limiting them to triplets or other short cycles. We solve the search problem for cycle constraints, giving a nearly linear time algorithm for finding the most frustrated cycle of arbitrary length. We show how to use this search algorithm together with the dual decomposition framework and clusterpursuit. The new algorithm exactly solves MAP inference problems arising from relational classification and stereo vision.