Catálogo de publicaciones - libros

This talk will review the basic notions of imprecise probability following Walley’s theory [1] and its application to graphical models which usually have considered precise Bayesian probabilities [2]. First approaches to imprecision were robustness studies: analysis of the sensibility of the outputs to variations of network parameters [3,4]. However, we will show that the role of imprecise probability in graphical models can be more important, providing alternative methodologies for learning and inference.

In real world applications planners are frequently faced with complex variable dependencies in high dimensional domains. In addition to that, they typically have to start from a very incomplete picture that is expanded only gradually as new information becomes available. In this contribution we deal with probabilistic graphical models, which have successfully been used for handling complex dependency structures and reasoning tasks in the presence of uncertainty. The paper discusses revision and updating operations in order to extend existing approaches in this field, where in most cases a restriction to conditioning and simple propagation algorithms can be observed. Furthermore, it is shown how all these operations can be applied to item planning and the prediction of parts demand in the automotive industry. The new theoretical results, modelling aspects, and their implementation within a software library were delivered by ISC Gebhardt and then involved in an innovative software system realized by Corporate IT for the world-wide item planning and parts demand prediction of the whole Volkswagen Group.

This paper briefly considers several research issues, some of which are on-going and some others are for further research. The starting point is that many AI topics, especially those related to the ECSQARU and KR conferences, can bring a lot to the representation and the resolution of social choice problems. I surely do not claim to make an exhaustive list of problems, but I rather list problems that I find important, give some relevant references and point out some potential research issues.

In a Bayesian network with continuous variables containing a variable(s) that is a conditionally deterministic function of its continuous parents, the joint density function does not exist. Conditional linear Gaussian distributions can handle such cases when the deterministic function is linear and the continuous variables have a multi-variate normal distribution. In this paper, operations required for performing inference with nonlinear conditionally deterministic variables are developed. We perform inference in networks with nonlinear deterministic variables and non-Gaussian continuous variables by using piecewise linear approximations to nonlinear functions and modeling probability distributions with mixtures of truncated exponentials (MTE) potentials.

Mixtures of truncated exponential (MTE) networks are a powerful alternative to discretisation when working with hybrid Bayesian networks. One of the features of the MTE model is that standard propagation algorithm can be used. In this paper we propose an approximate propagation algorithm for MTE networks which is based on the Penniless propagation method already known for discrete variables. The performance of the proposed method is analysed in a series of experiments with random networks.

Bayesian networks are efficient tools for probabilistic reasoning over large sets of variables, due to the fact that the joint distribution factorises according to the structure of the network, which captures conditional independence relations among the variables. Beyond conditional independence, the concept of asymmetric (or context specific) independence makes possible the definition of even more efficient reasoning schemes, based on the representation of probability functions through probability trees. In this paper we investigate how it is possible to achieve a finer factorisation by decomposing the original factors for which some conditions hold. We also introduce the concept of approximate factorisation and apply this methodology to the Lazy-Penniless propagation algorithm.

This paper proposes a new approach to the problem of ob- taining the most probable explanations given a set of observations in a Bayesian network. The method provides a set of possibilities ordered by their probabilities. The main novelties are that the level of detail of each one of the explanations is not uniform (with the idea of being as simple as possible in each case), the explanations are mutually exclusive, and the number of required explanations is not fixed (it depends on the particular case we are solving). Our goals are achieved by means of the construction of the so called which can have asym- metric branching and that will determine the different possibilities. This paper describes the procedure for its computation based on information theoretic criteria and shows its behaviour in some simple examples.

We present a new methodology for detecting faults and abnormal behavior in production plants. The methodology stems from a joint project with a Danish energy consortium. During the course of the project we encountered several problems that we believe are common for projects of this type. Most notably, there was a lack of both knowledge and data concerning possible faults, and it therefore turned out to be infeasible to learn/construct a standard classification model for doing fault detection. As an alternative we propose a method for doing on-line fault detection using only a model of normal system operation, i.e., it does not rely on information about the possible faults. We illustrate the proposed method using real-world data from a coal driven power plant as well as simulated data from an oil production facility.

In the presence of a river flood, operators in charge of control must take decisions based on imperfect and incomplete sources of information (e.g., data provided by a limited number sensors) and partial knowledge about the structure and behavior of the river basin. This is a case of reasoning about a complex dynamic system with uncertainty and real-time constraints where bayesian networks can be used to provide an effective support. In this paper we describe a solution with spatio-temporal bayesian networks to be used in a context of emergencies produced by river floods. In the paper we describe first a set of types of causal relations for hydrologic processes with spatial and temporal references to represent the dynamics of the river basin. Then we describe how this was included in a computer system called SAIDA to provide assistance to operators in charge of control in a river basin. Finally the paper shows experimental results about the performance of the model.

We describe an algorithm to build a graphical model—more precisely: a join tree representation of a Markov network—for a steady state analog electrical circuit. This model can be used to do probabilistic diagnosis based on manufacturer supplied information about nominal values of electrical components and their tolerances as well as measurements made on the circuit. Faulty components can be identified by looking for high probabilities for values of characteristic magnitudes that deviate from the nominal values.