This paper introduces the notions of independence and conditional independence in valuation-based systems (VBS). VBS is an axiomatic framework capable of representing many different uncertainty calculi. We define independence and conditional independence in terms of factorization of the joint valuation. The definitions of independence and conditional independence in VBS generalize the corresponding definitions in probability theory. Our definitions apply not only to probability theory, but also to Dempster-Shafer's belief-function theory, Spohn's epistemic-belief theory, and Zadeh's possibility theory. In fact, they apply to any uncertainty calculi that fit in the framework of valuation-based systems.

Many AI synthesis problems such as planning or scheduling may be modelized as constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, for many real tasks such as job-shop scheduling, time-table scheduling, design?, all these constraints have not the same significance and have not to be necessarily satisfied. A first distinction can be made between hard constraints, which every solution should satisfy and soft constraints, whose satisfaction has not to be certain. In this paper, we formalize the notion of possibilistic constraint satisfaction problems that allows the modeling of uncertainly satisfied constraints. We use a possibility distribution over labelings to represent respective possibilities of each labeling. Necessity-valued constraints allow a simple expression of the respective certainty degrees of each constraint. The main advantage of our approach is its integration in the CSP technical framework. Most classical techniques, such as Backtracking (BT), arcconsistency enforcing (AC) or Forward Checking have been extended to handle possibilistics CSP and are effectively implemented. The utility of our approach is demonstrated on a simple design problem.

The paper describes aHUGIN, a tool for creating adaptive systems. aHUGIN is an extension of the HUGIN shell, and is based on the methods reported by Spiegelhalter and Lauritzen (1990a). The adaptive systems resulting from aHUGIN are able to adjust the C011ditional probabilities in the model. A short analysis of the adaptation task is given and the features of aHUGIN are described. Finally a session with experiments is reported and the results are discussed.

The fundamental updating process in the transferable belief model is related to the concept of specialization and can be described by a specialization matrix. The degree of belief in the truth of a proposition is a degree of justified support. The Principle of Minimal Commitment implies that one should never give more support to the truth of a proposition than justified. We show that Dempster's rule of conditioning corresponds essentially to the least committed specialization, and that Dempster's rule of combination results essentially from commutativity requirements. The concept of generalization, dual to thc concept of specialization, is described.

A computational scheme for reasoning about dynamic systems using (causal) probabilistic networks is presented. The scheme is based on the framework of Lauritzen and Spiegelhalter (1988), and may be viewed as a generalization of the inference methods of classical time-series analysis in the sense that it allows description of non-linear, multivariate dynamic systems with complex conditional independence structures. Further, the scheme provides a method for efficient backward smoothing and possibilities for efficient, approximate forecasting methods. The scheme has been implemented on top of the HUGIN shell.

Data fusion allows the elaboration and the evaluation of a situation synthesized from low level informations provided by different kinds of sensors. The fusion of the collected data will result in fewer and higher level informations more easily assessed by a human operator and that will assist him effectively in his decision process. In this paper we present the suitability and the advantages of using a Possibilistic Assumption based Truth Maintenance System (0-ATMS) in a data fusion military application. We first describe the problem, the needed knowledge representation formalisms and problem solving paradigms. Then we remind the reader of the basic concepts of ATMSs, Possibilistic Logic and Il-ATMSs. Finally we detail the solution to the given data fusion problem and conclude with the results and comparison with a non-possibilistic solution.

Experts do not always feel very, comfortable when they have to give precise numerical estimations of certainty degrees. In this paper we present a qualitative approach which allows for attaching partially ordered symbolic grades to logical formulas. Uncertain information is expressed by means of parameterized modal operators. We propose a semantics for this multimodal logic and give a sound and complete axiomatization. We study the links with related approaches and suggest how this framework might be used to manage both uncertain and incomplere knowledge.

We study the problem of learning Markov decision processes with finite state and action spaces when the transition probability distributions and loss functions are chosen adversarially and are allowed to change with time. We introduce an algorithm whose regret with respect to any policy in a comparison class grows as the square root of the number of rounds of the game, provided the transition probabilities satisfy a uniform mixing condition. Our approach is efficient as long as the comparison class is polynomial and we can compute expectations over sample paths for each policy. Designing an efficient algorithm with small regret for the general case remains an open problem.

The classical approach to linear system identification is given by parametric Prediction Error Methods (PEM). In this context, model complexity is often unknown so that a model order selection step is needed to suitably trade-off bias and variance. Recently, a different approach to linear system identification has been introduced, where model order determination is avoided by using a regularized least squares framework. In particular, the penalty term on the impulse response is defined by so called stable spline kernels. They embed information on regularity and BIBO stability, and depend on a small number of parameters which can be estimated from data. In this paper, we provide new nonsmooth formulations of the stable spline estimator. In particular, we consider linear system identification problems in a very broad context, where regularization functionals and data misfits can come from a rich set of piecewise linear quadratic functions. Moreover, our anal- ysis includes polyhedral inequality constraints on the unknown impulse response. For any formulation in this class, we show that interior point methods can be used to solve the system identification problem, with complexity O(n3)+O(mn2) in each iteration, where n and m are the number of impulse response coefficients and measurements, respectively. The usefulness of the framework is illustrated via a numerical experiment where output measurements are contaminated by outliers.

We consider the problem of adaptive stratified sampling for Monte Carlo integration of a noisy function, given a finite budget n of noisy evaluations to the function. We tackle in this paper the problem of adapting to the function at the same time the number of samples into each stratum and the partition itself. More precisely, it is interesting to refine the partition of the domain in area where the noise to the function, or where the variations of the function, are very heterogeneous. On the other hand, having a (too) refined stratification is not optimal. Indeed, the more refined the stratification, the more difficult it is to adjust the allocation of the samples to the stratification, i.e. sample more points where the noise or variations of the function are larger. We provide in this paper an algorithm that selects online, among a large class of partitions, the partition that provides the optimal trade-off, and allocates the samples almost optimally on this partition.