Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one is for likelihood maximization in discrete chain factor graphs, which we define as a wide class of discrete variable models including undirected graphical models and Bayesian networks, but also chain graphs and sigmoid belief networks. The second one is for conditional likelihood maximization in standard undirected models and Bayesian networks. In both algorithms, the iteration steps are expressed in closed form. Numerical simulations show that the algorithms are competitive with state of the art methods.

We propose an efficient method for Bayesian network inference in models with functional dependence. We generalize the multiplicative factorization method originally designed by Takikawa and D Ambrosio(1999) FOR models WITH independence OF causal influence.Using a hidden variable, we transform a probability potential INTO a product OF two - dimensional potentials.The multiplicative factorization yields more efficient inference. FOR example, IN junction tree propagation it helps TO avoid large cliques. IN ORDER TO keep potentials small, the number OF states OF the hidden variable should be minimized.We transform this problem INTO a combinatorial problem OF minimal base IN a particular space.We present an example OF a computerized adaptive test, IN which the factorization method IS significantly more efficient than previous inference methods.

We present new algorithms for inference in credal networks --- directed acyclic graphs associated with sets of probabilities. Credal networks are here interpreted as encoding strong independence relations among variables. We first present a theory of credal networks based on separately specified sets of probabilities. We also show that inference with polytrees is NP-hard in this setting. We then introduce new techniques that reduce the computational effort demanded by inference, particularly in polytrees, by exploring separability of credal sets.

We propose a formal treatment of scenarios in the context of a dialectical argumentation formalism for qualitative reasoning about uncertain propositions. Our formalism extends prior work in which arguments for and against uncertain propositions were presented and compared in interaction spaces called Agoras. We now define the notion of a scenario in this framework and use it to define a set of qualitative uncertainty labels for propositions across a collection of scenarios. This work is intended to lead to a formal theory of scenarios and scenario analysis.

We describe expectation propagation for approximate inference in dynamic Bayesian networks as a natural extension of Pearl's exact belief propagation. Expectation propagation is a greedy algorithm, converges in many practical cases, but not always. We derive a double-loop algorithm, guaranteed to converge to a local minimum of a Bethe free energy. Furthermore, we show that stable fixed points of (damped) expectation propagation correspond to local minima of this free energy, but that the converse need not be the case. We illustrate the algorithms by applying them to switching linear dynamical systems and discuss implications for approximate inference in general Bayesian networks.

In this paper, we continue our research on the algorithmic aspects of Halpern and Pearl's causes and explanations in the structural-model approach. To this end, we present new characterizations of weak causes for certain classes of causal models, which show that under suitable restrictions deciding causes and explanations is tractable. To our knowledge, these are the first explicit tractability results for the structural-model approach.

The ability to make decisions and to assess potential courses of action is a corner-stone of many AI applications, and usually this requires explicit information about the decision-maker s preferences. IN many applications, preference elicitation IS a serious bottleneck.The USER either does NOT have the time, the knowledge, OR the expert support required TO specify complex multi - attribute utility functions. IN such cases, a method that IS based ON intuitive, yet expressive, preference statements IS required. IN this paper we suggest the USE OF TCP - nets, an enhancement OF CP - nets, AS a tool FOR representing, AND reasoning about qualitative preference statements.We present AND motivate this framework, define its semantics, AND show how it can be used TO perform constrained optimization.

Recently, it has been emphasized that the possibility theory framework allows us to distinguish between i) what is possible because it is not ruled out by the available knowledge, and ii) what is possible for sure. This distinction may be useful when representing knowledge, for modelling values which are not impossible because they are consistent with the available knowledge on the one hand, and values guaranteed to be possible because reported from observations on the other hand. It is also of interest when expressing preferences, to point out values which are positively desired among those which are not rejected. This distinction can be encoded by two types of constraints expressed in terms of necessity measures and in terms of guaranteed possibility functions, which induce a pair of possibility distributions at the semantic level. A consistency condition should ensure that what is claimed to be guaranteed as possible is indeed not impossible. The present paper investigates the representation of this bipolar view, including the case when it is stated by means of conditional measures, or by means of comparative context-dependent constraints. The interest of this bipolar framework, which has been recently stressed for expressing preferences, is also pointed out in the representation of diagnostic knowledge.

Robust optimization is one of the fundamental approaches to deal with uncertainty in combinatorial optimization. This paper considers the robust spanning tree problem with interval data, which arises in a variety of telecommunication applications. It proposes a constraint satisfaction approach using a combinatorial lower bound, a pruning component that removes infeasible and suboptimal edges, as well as a search strategy exploring the most uncertain edges first. The resulting algorithm is shown to produce very dramatic improvements over the mathematical programming approach of Yaman et al. and to enlarge considerably the class of problems amenable to effective solutions

Ancestral graphs provide a class of graphs that can encode conditional independence relations that arise in directed acyclic graph (DAG) models with latent and selection variables, corresponding to marginalization and conditioning. However, for any ancestral graph, there may be several other graphs to which it is Markov equivalent. We introduce a simple representation of a Markov equivalence class of ancestral graphs, thereby facilitating the model search process for some given data. More specifically, we define a join operation on ancestral graphs which will associate a unique graph with an equivalence class. We also extend the separation criterion for ancestral graphs (which is an extension of d-separation) and provide a proof of the pairwise Markov property for joined ancestral graphs. Proving the pairwise Markov property is the first step towards developing a global Markov property for these graphs. The ultimate goal of this work is to obtain a full characterization of the structure of Markov equivalence classes for maximal ancestral graphs, thereby extending analogous results for DAGs given by Frydenberg (1990), Verma and Pearl (1991), Chickering (1995) and Andersson et a!.