Given an undirected graph G or hypergraph X model for a given set of variables V, we introduce two marginalization operators for obtaining the undirected graph GA or hypergraph HA associated with a given subset A c V such that the marginal distribution of A factorizes according to GA or HA, respectively. Finally, we illustrate the method by its application to some practical examples. With them we show that hypergraph models allow defining a finer factorization or performing a more precise conditional independence analysis than undirected graph models.

The situation assessment problem is considered, in terms of object, condition, activity, and plan recognition, based on data coming from the real-word {em via} various sensors. It is shown that uncertainty issues are linked both to the models and to the matching algorithm. Three different types of uncertainties are identified, and within each one, the numerical and the symbolic cases are distinguished. The emphasis is then put on purely symbolic uncertainties: it is shown that they can be dealt with within a purely symbolic framework resulting from a transposition of classical numerical estimation tools.

Information Retrieval (IR) is concerned with the identification of documents in a collection that are relevant to a given information need, usually represented as a query containing terms or keywords, which are supposed to be a good description of what the user is looking for. IR systems may improve their effectiveness (i.e., increasing the number of relevant documents retrieved) by using a process of query expansion, which automatically adds new terms to the original query posed by an user. In this paper we develop a method of query expansion based on Bayesian networks. Using a learning algorithm, we construct a Bayesian network that represents some of the relationships among the terms appearing in a given document collection; this network is then used as a thesaurus (specific for that collection). We also report the results obtained by our method on three standard test collections.

The monitoring and control of any dynamic system depends crucially on the ability to reason about its current status and its future trajectory. In the case of a stochastic system, these tasks typically involve the use of a belief state- a probability distribution over the state of the process at a given point in time. Unfortunately, the state spaces of complex processes are very large, making an explicit representation of a belief state intractable. Even in dynamic Bayesian networks (DBNs), where the process itself can be represented compactly, the representation of the belief state is intractable. We investigate the idea of maintaining a compact approximation to the true belief state, and analyze the conditions under which the errors due to the approximations taken over the lifetime of the process do not accumulate to make our answers completely irrelevant. We show that the error in a belief state contracts exponentially as the process evolves. Thus, even with multiple approximations, the error in our process remains bounded indefinitely. We show how the additional structure of a DBN can be used to design our approximation scheme, improving its performance significantly. We demonstrate the applicability of our ideas in the context of a monitoring task, showing that orders of magnitude faster inference can be achieved with only a small degradation in accuracy.

There exist two general forms of exact algorithms for updating probabilities in Bayesian Networks. The first approach involves using a structure, usually a clique tree, and performing local message based calculation to extract the belief in each variable. The second general class of algorithm involves the use of non-serial dynamic programming techniques to extract the belief in some desired group of variables. In this paper we present a hybrid algorithm based on the latter approach yet possessing the ability to retrieve the belief in all single variables. The technique is advantageous in that it saves a NP-hard computation step over using one algorithm of each type. Furthermore, this technique re-enforces a conjecture of Jensen and Jensen [JJ94] in that it still requires a single NP-hard step to set up the structure on which inference is performed, as we show by confirming Li and D'Ambrosio's [LD94] conjectured NP-hardness of OFP.

This paper addresses the problem of merging uncertain information in the framework of possibilistic logic. It presents several syntactic combination rules to merge possibilistic knowledge bases, provided by different sources, into a new possibilistic knowledge base. These combination rules are first described at the meta-level outside the language of possibilistic logic. Next, an extension of possibilistic logic, where the combination rules are inside the language, is proposed. A proof system in a sequent form, which is sound and complete with respect to the possibilistic logic semantics, is given.

Argumentation is a promising model for reasoning with uncertain knowledge. The key concept of acceptability enables to differentiate arguments and counterarguments: The certainty of a proposition can then be evaluated through the most acceptable arguments for that proposition. In this paper, we investigate different complementary points of view: - an acceptability based on the existence of direct counterarguments, - an acceptability based on the existence of defenders. Pursuing previous work on preference-based argumentation principles, we enforce both points of view by taking into account preference orderings for comparing arguments. Our approach is illustrated in the context of reasoning with stratified knowldge bases.

Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks for understanding how dynamical network processes cooperate across widely disparate spatiotemporal scales to solve important computational problems? And second, how can we extract meaningful models of neuronal systems from high dimensional datasets? To aid in these challenges, we give a pedagogical review of a collection of ideas and theoretical methods arising at the intersection of statistical physics, computer science and neurobiology. We introduce the interrelated replica and cavity methods, which originated in statistical physics as powerful ways to quantitatively analyze large highly heterogeneous systems of many interacting degrees of freedom. We also introduce the closely related notion of message passing in graphical models, which originated in computer science as a distributed algorithm capable of solving large inference and optimization problems involving many coupled variables. We then show how both the statistical physics and computer science perspectives can be applied in a wide diversity of contexts to problems arising in theoretical neuroscience and data analysis. Along the way we discuss spin glasses, learning theory, illusions of structure in noise, random matrices, dimensionality reduction, and compressed sensing, all within the unified formalism of the replica method. Moreover, we review recent conceptual connections between message passing in graphical models, and neural computation and learning. Overall, these ideas illustrate how statistical physics and computer science might provide a lens through which we can uncover emergent computational functions buried deep within the dynamical complexities of neuronal networks.

Recently, many regularized procedures have been proposed for variable selection in linear regression, but their performance depends on the tuning parameter selection. Here a criterion for the tuning parameter selection is proposed, which combines the strength of both stability selection and cross-validation and therefore is referred as the prediction and stability selection (PASS). The selection consistency is established assuming the data generating model is a subset of the full model, and the small sample performance is demonstrated through some simulation studies where the assumption is either held or violated.

Link prediction is one of the fundamental problems in network analysis. In many applications, notably in genetics, a partially observed network may not contain any negative examples of absent edges, which creates a difficulty for many existing supervised learning approaches. We develop a new method which treats the observed network as a sample of the true network with different sampling rates for positive and negative examples. We obtain a relative ranking of potential links by their probabilities, utilizing information on node covariates as well as on network topology. Empirically, the method performs well under many settings, including when the observed network is sparse. We apply the method to a protein-protein interaction network and a school friendship network.