Markov decisions processes (MDPs) are becoming increasing popular as models of decision theoretic planning. While traditional dynamic programming methods perform well for problems with small state spaces, structured methods are needed for large problems. We propose and examine a value iteration algorithm for MDPs that uses algebraic decision diagrams(ADDs) to represent value functions and policies. An MDP is represented using Bayesian networks and ADDs and dynamic programming is applied directly to these ADDs. We demonstrate our method on large MDPs (up to 63 million states) and show that significant gains can be had when compared to tree-structured representations (with up to a thirty-fold reduction in the number of nodes required to represent optimal value functions).

We are interested in the problem of planning for factored POMDPs. Building on the recent results of Kearns, Mansour and Ng, we provide a planning algorithm for factored POMDPs that exploits the accuracy-efficiency tradeoff in the belief state simplification introduced by Boyen and Koller.

This paper describes stochastic search approaches, including a new stochastic algorithm and an adaptive mutation operator, for learning Bayesian networks from incomplete data. This problem is characterized by a huge solution space with a highly multimodal landscape. State-of-the-art approaches all involve using deterministic approaches such as the expectation-maximization algorithm. These approaches are guaranteed to find local maxima, but do not explore the landscape for other modes. Our approach evolves structure and the missing data. We compare our stochastic algorithms and show they all produce accurate results.

We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian, which facilitates exact inference, and then iteratively adjust the variational parameters to improve the quality of the approximation. We demonstrate experimentally that this approximation is faster and potentially more accurate than sampling. We also introduce a simple new technique for handling evidence, which allows us to handle arbitrary distributions on observed nodes, as well as achieving a significant speedup in networks with discrete variables of large cardinality.

In this paper, we empirically evaluate algorithms for learning four types of Bayesian network (BN) classifiers - Naive-Bayes, tree augmented Naive-Bayes, BN augmented Naive-Bayes and general BNs, where the latter two are learned using two variants of a conditional-independence (CI) based BN-learning algorithm. Experimental results show the obtained classifiers, learned using the CI based algorithms, are competitive with (or superior to) the best known classifiers, based on both Bayesian networks and other formalisms; and that the computational time for learning and using these classifiers is relatively small. Moreover, these results also suggest a way to learn yet more effective classifiers; we demonstrate empirically that this new algorithm does work as expected. Collectively, these results argue that BN classifiers deserve more attention in machine learning and data mining communities.

Recently, researchers have demonstrated that loopy belief propagation - the use of Pearls polytree algorithm IN a Bayesian network WITH loops OF error- correcting codes.The most dramatic instance OF this IS the near Shannon - limit performance OF Turbo Codes codes whose decoding algorithm IS equivalent TO loopy belief propagation IN a chain - structured Bayesian network. IN this paper we ask : IS there something special about the error - correcting code context, OR does loopy propagation WORK AS an approximate inference schemeIN a more general setting? We compare the marginals computed using loopy propagation TO the exact ones IN four Bayesian network architectures, including two real - world networks : ALARM AND QMR.We find that the loopy beliefs often converge AND WHEN they do, they give a good approximation TO the correct marginals.However,ON the QMR network, the loopy beliefs oscillated AND had no obvious relationship TO the correct posteriors. We present SOME initial investigations INTO the cause OF these oscillations, AND show that SOME simple methods OF preventing them lead TO the wrong results.

In current perception systems applied to the rebuilding of the environment for intelligent vehicles, the part reserved to object association for the tracking is increasingly significant. This allows firstly to follow the objects temporal evolution and secondly to increase the reliability of environment perception. We propose in this communication the development of a multi-objects association algorithm with ambiguity removal entering into the design of such a dynamic perception system for intelligent vehicles. This algorithm uses the belief theory and data modelling with fuzzy mathematics in order to be able to handle inaccurate as well as uncertain information due to imperfect sensors. These theories also allow the fusion of numerical as well as symbolic data. We develop in this article the problem of matching between known and perceived objects. This makes it possible to update a dynamic environment map for a vehicle. The belief theory will enable us to quantify the belief in the association of each perceived object with each known object. Conflicts can appear in the case of object appearance or disappearance, or in the case of a confused situation or bad perception. These conflicts are removed or solved using an assignment algorithm, giving a solution called the " best " and so ensuring the tracking of some objects present in our environment.

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.

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.

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.