Structure and parameters in a Bayesian network uniquely specify the probability distribution of the modeled domain. The locality of both structure and probabilistic information are the great benefits of Bayesian networks and require the modeler to only specify local information. On the other hand this locality of information might prevent the modeler - and even more any other person - from obtaining a general overview of the important relationships within the domain. The goal of the work presented in this paper is to provide an "alternative" view on the knowledge encoded in a Bayesian network which might sometimes be very helpful for providing insights into the underlying domain. The basic idea is to calculate a mixture approximation to the probability distribution represented by the Bayesian network. The mixture component densities can be thought of as representing typical scenarios implied by the Bayesian model, providing intuition about the basic relationships. As an additional benefit, performing inference in the approximate model is very simple and intuitive and can provide additional insights. The computational complexity for the calculation of the mixture approximations criticaly depends on the measure which defines the distance between the probability distribution represented by the Bayesian network and the approximate distribution. Both the KL-divergence and the backward KL-divergence lead to inefficient algorithms. Incidentally, the latter is used in recent work on mixtures of mean field solutions to which the work presented here is closely related. We show, however, that using a mean squared error cost function leads to update equations which can be solved using the junction tree algorithm. We conclude that the mean squared error cost function can be used for Bayesian networks in which inference based on the junction tree is tractable. For large networks, however, one may have to rely on mean field approximations.

Decision-making problems in uncertain or stochastic domains are often formulated as Markov decision processes (MDPs). Policy iteration (PI) is a popular algorithm for searching over policy-space, the size of which is exponential in the number of states. We are interested in bounds on the complexity of PI that do not depend on the value of the discount factor. In this paper we prove the first such non-trivial, worst-case, upper bounds on the number of iterations required by PI to converge to the optimal policy. Our analysis also sheds new light on the manner in which PI progresses through the space of policies.

We present a hybrid constraint-based/Bayesian algorithm for learning causal networks in the presence of sparse data. The algorithm searches the space of equivalence classes of models (essential graphs) using a heuristic based on conventional constraint-based techniques. Each essential graph is then converted into a directed acyclic graph and scored using a Bayesian scoring metric. Two variants of the algorithm are developed and tested using data from randomly generated networks of sizes from 15 to 45 nodes with data sizes ranging from 250 to 2000 records. Both variations are compared to, and found to consistently outperform two variations of greedy search with restarts.

In this article we propose a qualitative (ordinal) counterpart for the Partially Observable Markov Decision Processes model (POMDP) in which the uncertainty, as well as the preferences of the agent, are modeled by possibility distributions. This qualitative counterpart of the POMDP model relies on a possibilistic theory of decision under uncertainty, recently developed. One advantage of such a qualitative framework is its ability to escape from the classical obstacle of stochastic POMDPs, in which even with a finite state space, the obtained belief state space of the POMDP is infinite. Instead, in the possibilistic framework even if exponentially larger than the state space, the belief state space remains finite.

The paper is a second in a series of two papers evaluating the power of a new scheme that generates search heuristics mechanically. The heuristics are extracted from an approximation scheme called mini-bucket elimination that was recently introduced. The first paper introduced the idea and evaluated it within Branch-and-Bound search. In the current paper the idea is further extended and evaluated within Best-First search. The resulting algorithms are compared on coding and medical diagnosis problems, using varying strength of the mini-bucket heuristics. Our results demonstrate an effective search scheme that permits controlled tradeoff between preprocessing (for heuristic generation) and search. Best-first search is shown to outperform Branch-and-Bound, when supplied with good heuristics, and sufficient memory space.

Hybrid Probabilistic Programs (HPPs) are logic programs that allow the programmer to explicitly encode his knowledge of the dependencies between events being described in the program. In this paper, we classify HPPs into three classes called HPP_1,HPP_2 and HPP_r,r>= 3. For these classes, we provide three types of results for HPPs. First, we develop algorithms to compute the set of all ground consequences of an HPP. Then we provide algorithms and complexity results for the problems of entailment ("Given an HPP P and a query Q as input, is Q a logical consequence of P?") and consistency ("Given an HPP P as input, is P consistent?"). Our results provide a fine characterization of when polynomial algorithms exist for the above problems, and when these problems become intractable.

The need to help people choose among large numbers of items and to filter through large amounts of information has led to a flood of research in construction of personal recommendation agents. One of the central issues in constructing such agents is the representation and elicitation of user preferences or interests. This topic has long been studied in Decision Theory, but surprisingly little work in the area of recommender systems has made use of formal decision-theoretic techniques. This paper describes DIVA, a decision-theoretic agent for recommending movies that contains a number of novel features. DIVA represents user preferences using pairwise comparisons among items, rather than numeric ratings. It uses a novel similarity measure based on the concept of the probability of conflict between two orderings of items. The system has a rich representation of preference, distinguishing between a user's general taste in movies and his immediate interests. It takes an incremental approach to preference elicitation in which the user can provide feedback if not satisfied with the recommendation list. We empirically evaluate the performance of the system using the EachMovie collaborative filtering database.

We investigate the problem of active learning on a given tree whose nodes are assigned binary labels in an adversarial way. Inspired by recent results by Guillory and Bilmes, we characterize (up to constant factors) the optimal placement of queries so to minimize the mistakes made on the non-queried nodes. Our query selection algorithm is extremely efficient, and the optimal number of mistakes on the non-queried nodes is achieved by a simple and efficient mincut classifier. Through a simple modification of the query selection algorithm we also show optimality (up to constant factors) with respect to the trade-off between number of queries and number of mistakes on non-queried nodes. By using spanning trees, our algorithms can be efficiently applied to general graphs, although the problem of finding optimal and efficient active learning algorithms for general graphs remains open. Towards this end, we provide a lower bound on the number of mistakes made on arbitrary graphs by any active learning algorithm using a number of queries which is up to a constant fraction of the graph size.

Efficient online learning with pairwise loss functions is a crucial component in building large-scale learning system that maximizes the area under the Receiver Operator Characteristic (ROC) curve. In this paper we investigate the generalization performance of online learning algorithms with pairwise loss functions. We show that the existing proof techniques for generalization bounds of online algorithms with a univariate loss can not be directly applied to pairwise losses. In this paper, we derive the first result providing data-dependent bounds for the average risk of the sequence of hypotheses generated by an arbitrary online learner in terms of an easily computable statistic, and show how to extract a low risk hypothesis from the sequence. We demonstrate the generality of our results by applying it to two important problems in machine learning. First, we analyze two online algorithms for bipartite ranking; one being a natural extension of the perceptron algorithm and the other using online convex optimization. Secondly, we provide an analysis for the risk bound for an online algorithm for supervised metric learning.

Artifact systems are a novel paradigm for specifying and implementing business processes described in terms of interacting modules called artifacts. Artifacts consist of data and lifecycles, accounting respectively for the relational structure of the artifacts' states and their possible evolutions over time. In this paper we put forward artifact-centric multi-agent systems, a novel formalisation of artifact systems in the context of multi-agent systems operating on them. Differently from the usual process-based models of services, the semantics we give explicitly accounts for the data structures on which artifact systems are defined. We study the model checking problem for artifact-centric multi-agent systems against specifications written in a quantified version of temporal-epistemic logic expressing the knowledge of the agents in the exchange. We begin by noting that the problem is undecidable in general. We then identify two noteworthy restrictions, one syntactical and one semantical, that enable us to find bisimilar finite abstractions and therefore reduce the model checking problem to the instance on finite models. Under these assumptions we show that the model checking problem for these systems is EXPSPACE-complete. We then introduce artifact-centric programs, compact and declarative representations of the programs governing both the artifact system and the agents. We show that, while these in principle generate infinite-state systems, under natural conditions their verification problem can be solved on finite abstractions that can be effectively computed from the programs. Finally we exemplify the theoretical results of the paper through a mainstream procurement scenario from the artifact systems literature.