As probabilistic systems gain popularity and are coming into wider use, the need for a mechanism that explains the system's findings and recommendations becomes more critical. The system will also need a mechanism for ordering competing explanations. We examine two representative approaches to explanation in the literature - one due to G\"ardenfors and one due to Pearl - and show that both suffer from significant problems. We propose an approach to defining a notion of "better explanation" that combines some of the features of both together with more recent work by Pearl and others on causality.

Most exact algorithms for general partially observable Markov decision processes (POMDPs) use a form of dynamic programming in which a piecewise-linear and convex representation of one value function is transformed into another. We examine variations of the "incremental pruning" method for solving this problem and compare them to earlier algorithms from theoretical and empirical perspectives. We find that incremental pruning is presently the most efficient exact method for solving POMDPs.

Decomposable dependency models and their graphical counterparts, i.e., chordal graphs, possess a number of interesting and useful properties. On the basis of two characterizations of decomposable models in terms of independence relationships, we develop an exact algorithm for recovering the chordal graphical representation of any given decomposable model. We also propose an algorithm for learning chordal approximations of dependency models isomorphic to general undirected graphs.

Performance prediction or forecasting sporting outcomes involves a great deal of insight into the particular area one is dealing with, and a considerable amount of intuition about the factors that bear on such outcomes and performances. The mathematical Theory of Evidence offers representation formalisms which grant experts a high degree of freedom when expressing their subjective beliefs in the context of decision-making situations like performance prediction. Furthermore, this reasoning framework incorporates a powerful mechanism to systematically pool the decisions made by individual subject matter experts. The idea behind such a combination of knowledge is to improve the competence (quality) of the overall decision-making process. This paper reports on a performance prediction experiment carried out during the European Football Championship in 1996. Relying on the knowledge of four predictors, Evidence Theory was used to forecast the final scores of all 31 matches. The results of this empirical study are very encouraging.

Much recent research in decision theoretic planning has adopted Markov decision processes (MDPs) as the model of choice, and has attempted to make their solution more tractable by exploiting problem structure. One particular algorithm, structured policy construction achieves this by means of a decision theoretic analog of goal regression using action descriptions based on Bayesian networks with tree-structured conditional probability tables. The algorithm as presented is not able to deal with actions with correlated effects. We describe a new decision theoretic regression operator that corrects this weakness. While conceptually straightforward, this extension requires a somewhat more complicated technical approach.

A modelling language is described which is suitable for the correlation of information when the underlying functional model of the system is incomplete or uncertain and the temporal dependencies are imprecise. An efficient and incremental implementation is outlined which depends on cost functions satisfying certain criteria. Possibilistic logic and probability theory (as it is used in the applications targetted) satisfy these criteria.

Wide-angle sonar mapping of the environment by mobile robot is nontrivial due to several sources of uncertainty: dropouts due to "specular" reflections, obstacle location uncertainty due to the wide beam, and distance measurement error. Earlier papers address the latter problems, but dropouts remain a problem in many environments. We present an approach that lifts the overoptimistic independence assumption used in earlier work, and use Bayes nets to represent the dependencies between objects of the model. Objects of the model consist of readings, and of regions in which "quasi location invariance" of the (possible) obstacles exists, with respect to the readings. Simulation supports the method's feasibility. The model is readily extensible to allow for prior distributions, as well as other types of sensing operations.

The paper considers the class of information systems capable of solving heuristic problems on basis of formal theory that was termed modal and vector theory of formal intelligent systems (FIS). The paper justifies the construction of FIS resolution algorithm, defines the main features of these systems and proves theorems that underlie the theory. The principle of representation diversity of FIS construction is formulated. The paper deals with the main principles of constructing and functioning formal intelligent system (FIS) on basis of FIS modal and vector theory. The following phenomena are considered: modular architecture of FIS presentation sub-system, algorithms of data processing at every step of the stage of creating presentations. Besides the paper suggests the structure of neural elements, i.e. zone detectors and processors that are the basis for FIS construction.

The complex wave representation (CWR) converts unsigned 2D distance transforms into their corresponding wave functions. Here, the distance transform S(X) appears as the phase of the wave function \phi(X)---specifically, \phi(X)=exp(iS(X)/\tau where \tau is a free parameter. In this work, we prove a novel result using the higher-order stationary phase approximation: we show convergence of the normalized power spectrum (squared magnitude of the Fourier transform) of the wave function to the density function of the distance transform gradients as the free parameter \tau-->0. In colloquial terms, spatial frequencies are gradient histogram bins. Since the distance transform gradients have only orientation information (as their magnitudes are identically equal to one almost everywhere), as \tau-->0, the 2D Fourier transform values mainly lie on the unit circle in the spatial frequency domain. The proof of the result involves standard integration techniques and requires proper ordering of limits. Our mathematical relation indicates that the CWR of distance transforms is an intriguing, new representation.

Many applications concern sparse signals, for example, detecting anomalies from the differences between consecutive images taken by surveillance cameras. This paper focuses on the problem of recovering a K-sparse signal x in N dimensions. In the mainstream framework of compressed sensing (CS), the vector x is recovered from M non-adaptive linear measurements y = xS, where S (of size N x M) is typically a Gaussian (or Gaussian-like) design matrix, through some optimization procedure such as linear programming (LP). In our proposed method, the design matrix S is generated from an $\alpha$-stable distribution with $\alpha\approx 0$. Our decoding algorithm mainly requires one linear scan of the coordinates, followed by a few iterations on a small number of coordinates which are "undetermined" in the previous iteration. Comparisons with two strong baselines, linear programming (LP) and orthogonal matching pursuit (OMP), demonstrate that our algorithm can be significantly faster in decoding speed and more accurate in recovery quality, for the task of exact spare recovery. Our procedure is robust against measurement noise. Even when there are no sufficient measurements, our algorithm can still reliably recover a significant portion of the nonzero coordinates. To provide the intuition for understanding our method, we also analyze the procedure by assuming an idealistic setting. Interestingly, when K=2, the "idealized" algorithm achieves exact recovery with merely 3 measurements, regardless of N. For general K, the required sample size of the "idealized" algorithm is about 5K.