Based on a recent development in the area of error control coding, we introduce the notion of convolutional factor graphs (CFGs) as a new class of probabilistic graphical models. In this context, the conventional factor graphs are referred to as multiplicative factor graphs (MFGs). This paper shows that CFGs are natural models for probability functions when summation of independent latent random variables is involved. In particular, CFGs capture a large class of linear models, where the linearity is in the sense that the observed variables are obtained as a linear ransformation of the latent variables taking arbitrary distributions. We use Gaussian models and independent factor models as examples to emonstrate the use of CFGs. The requirement of a linear transformation between latent variables (with certain independence restriction) and the bserved variables, to an extent, limits the modelling flexibility of CFGs. This structural restriction however provides a powerful analytic tool to the framework of CFGs; that is, upon taking the Fourier transform of the function represented by the CFG, the resulting function is represented by a FG with identical structure. This Fourier transform duality allows inference problems on a CFG to be solved on the corresponding dual MFG.

We introduce a probabilistic formalism subsuming Markov random fields of bounded tree width and probabilistic context free grammars. Our models are based on a representation of Boolean formulas that we call case-factor diagrams (CFDs). CFDs are similar to binary decision diagrams (BDDs) but are concise for circuits of bounded tree width (unlike BDDs) and can concisely represent the set of parse trees over a given string under a given context free grammar (also unlike BDDs). A probabilistic model consists of a CFD defining a feasible set of Boolean assignments and a weight (or cost) for each individual Boolean variable. We give an insideoutside algorithm for simultaneously computing the marginal of each Boolean variable, and a Viterbi algorithm for finding the mininum cost variable assignment. Both algorithms run in time proportional to the size of the CFD.

A key prerequisite to optimal reasoning under uncertainty in intelligent systems is to start with good class probability estimates. This paper improves on the current best probability estimation trees (Bagged-PETs) and also presents a new ensemble-based algorithm (MOB-ESP). Comparisons are made using several benchmark datasets and multiple metrics. These experiments show that MOB-ESP outputs significantly more accurate class probabilities than either the baseline B-PETs algorithm or the enhanced version presented here (EB-PETs). These results are based on metrics closely associated with the average accuracy of the predictions. MOB-ESP also provides much better probability rankings than B-PETs. The paper further suggests how these estimation techniques can be applied in concert with a broader category of classifiers.

Humans currently use arguments for explaining choices which are already made, or for evaluating potential choices. Each potential choice has usually pros and cons of various strengths. In spite of the usefulness of arguments in a decision making process, there have been few formal proposals handling this idea if we except works by Fox and Parsons and by Bonet and Geffner. In this paper we propose a possibilistic logic framework where arguments are built from an uncertain knowledge base and a set of prioritized goals. The proposed approach can compute two kinds of decisions by distinguishing between pessimistic and optimistic attitudes. When the available, maybe uncertain, knowledge is consistent, as well as the set of prioritized goals (which have to be fulfilled as far as possible), the method for evaluating decisions on the basis of arguments agrees with the possibility theory-based approach to decision-making under uncertainty. Taking advantage of its relation with formal approaches to defeasible argumentation, the proposed framework can be generalized in case of partially inconsistent knowledge, or goal bases.

The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that the conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity where instantiated variables are removed. If the assigned variables constitute a cycle-cutset, the rest of the network is singly-connected and therefore can be solved by linear propagation algorithms. A w-cutset is a generalization of a cycle-cutset defined as a subset of nodes such that the subgraph with cutset nodes removed has induced-width of w or less. In this paper we address the problem of finding a minimal w-cutset in a graph. We relate the problem to that of finding the minimal w-cutset of a treedecomposition. The latter can be mapped to the well-known set multi-cover problem. This relationship yields a proof of NP-completeness on one hand and a greedy algorithm for finding a w-cutset of a tree decomposition on the other. Empirical evaluation of the algorithms is presented.

We consider the challenge of preference elicitation in systems that help users discover the most desirable item(s) within a given database. Past work on preference elicitation focused on structured models that provide a factored representation of users' preferences. Such models require less information to construct and support efficient reasoning algorithms. This paper makes two substantial contributions to this area: (1) Strong representation theorems for factored value functions. (2) A methodology that utilizes our representation results to address the problem of optimal item selection.

Previous work on sensitivity analysis in Bayesian networks has focused on single parameters, where the goal is to understand the sensitivity of queries to single parameter changes, and to identify single parameter changes that would enforce a certain query constraint. In this paper, we expand the work to multiple parameters which may be in the CPT of a single variable, or the CPTs of multiple variables. Not only do we identify the solution space of multiple parameter changes that would be needed to enforce a query constraint, but we also show how to find the optimal solution, that is, the one which disturbs the current probability distribution the least (with respect to a specific measure of disturbance). We characterize the computational complexity of our new techniques and discuss their applications to developing and debugging Bayesian networks, and to the problem of reasoning about the value (reliability) of new information.

Defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning from incomplete and potentially inconsistent knowledge. Defeasible Logic Programming (DeLP) is a defeasible argumentation formalism based on an extension of logic programming. Although DeLP has been successfully integrated in a number of different real-world applications, DeLP cannot deal with explicit uncertainty, nor with vague knowledge, as defeasibility is directly encoded in the object language. This paper introduces P-DeLP, a new logic programming language that extends original DeLP capabilities for qualitative reasoning by incorporating the treatment of possibilistic uncertainty and fuzzy knowledge. Such features will be formalized on the basis of PGL, a possibilistic logic based on Gödel fuzzy logic.

Early, reliable detection of disease outbreaks is a critical problem today. This paper reports an investigation of the use of causal Bayesian networks to model spatio-temporal patterns of a non-contagious disease (respiratory anthrax infection) in a population of people. The number of parameters in such a network can become enormous, if not carefully managed. Also, inference needs to be performed in real time as population data stream in. We describe techniques we have applied to address both the modeling and inference challenges. A key contribution of this paper is the explication of assumptions and techniques that are sufficient to allow the scaling of Bayesian network modeling and inference to millions of nodes for real-time surveillance applications. The results reported here provide a proof-of-concept that Bayesian networks can serve as the foundation of a system that effectively performs Bayesian biosurveillance of disease outbreaks.

This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with precise, imprecise, indeterminate and qualitative probabilistic assessments. The paper shows how this can be achieved through the theory of credal networks. New exact and approximate inference algorithms based on multilinear programming and iterated/loopy propagation of interval probabilities are presented; their superior performance, compared to existing ones, is shown empirically.