Probabilistic Methodology and Techniques for Artefact Conception and Development

The purpose of this paper is to make a state of the art on probabilistic methodology and techniques for artefact conception and development. It is the 8th deliverable of the BIBA (Bayesian Inspired Brain and Artefacts) project. We first present the incompletness problem as the central difficulty that both living creatures and artefacts have to face: how can they perceive, infer, decide and act efficiently with incomplete and uncertain knowledge?. We then introduce a generic probabilistic formalism called Bayesian Programming. This formalism is then used to review the main probabilistic methodology and techniques. This review is organized in 3 parts: first the probabilistic models from Bayesian networks to Kalman filters and from sensor fusion to CAD systems, second the inference techniques and finally the learning and model acquisition and comparison methodologies. We conclude with the perspectives of the BIBA project as they rise from this state of the art

Exploiting sparsity and sharing in probabilistic sensor data models

Probabilistic sensor models defined as dynamic Bayesian networks can possess an inherent sparsity that is not reflected in the structure of the network. Classical inference algorithms like variable elimination and junction tree propagation cannot exploit this sparsity. Also, they do not exploit the opportunities for sharing calculations among different time slices of the model. We show that, using a relational representation, inference expressions for these sensor models can be rewritten to make efficient use of sparsity and sharing

Decision making with decision event graphs

We introduce a new modelling representation, the Decision Event Graph (DEG), for asymmetric multistage decision problems. The DEG explicitly encodes conditional independences and has additional significant advantages over other representations of asymmetric decision problems. The colouring of edges makes it possible to identify conditional independences on decision trees, and these coloured trees serve as a basis for the construction of the DEG. We provide an efficient backward-induction algorithm for finding optimal decision rules on DEGs, and work through an example showing the efficacy of these graphs. Simplifications of the topology of a DEG admit analogues to the sufficiency principle and barren node deletion steps used with influence diagrams

Heuristic assignment of CPDs for probabilistic inference in junction trees

Many researches have been done for efficient computation of probabilistic queries posed to Bayesian networks (BN). One of the popular architectures for exact inference on BNs is the Junction Tree (JT) based architecture. Among all the different architectures developed, HUGIN is the most efficient JT-based architecture. The Global Propagation (GP) method used in the HUGIN architecture is arguably one of the best methods for probabilistic inference in BNs. Before the propagation, initialization is done to obtain the potential for each cluster in the JT. Then with the GP method, each cluster potential becomes cluster marginal through passing messages with its neighboring clusters. Improvements have been proposed by many researchers to make this message propagation more efficient. Still the GP method can be very slow for dense networks. As BNs are applied to larger, more complex, and realistic applications, developing more efficient inference algorithm has become increasingly important. Towards this goal, in this paper, we present some heuristics for initialization that avoids unnecessary message passing among clusters of the JT and therefore it improves the performance of the architecture by passing lesser messages

Nonparametric generalized belief propagation based on pseudo-junction tree for cooperative localization in wireless networks

Non-parametric belief propagation (NBP) is a well-known message passing method for cooperative localization in wireless networks. However, due to the over-counting problem in the networks with loops, NBP’s convergence is not guaranteed, and its estimates are typically less accurate. One solution for this problem is non-parametric generalized belief propagation based on junction tree. However, this method is intractable in large-scale networks due to the high-complexity of the junction tree formation, and the high-dimensionality of the particles. Therefore, in this article, we propose the non-parametric generalized belief propagation based on pseudo-junction tree (NGBP-PJT). The main difference comparing with the standard method is the formation of pseudo-junction tree, which represents the approximated junction tree based on thin graph. In addition, in order to decrease the number of high-dimensional particles, we use more informative importance density function, and reduce the dimensionality of the messages. As by-product, we also propose NBP based on thin graph (NBP-TG), a cheaper variant of NBP, which runs on the same graph as NGBP-PJT. According to our simulation and experimental results, NGBP-PJT method outperforms NBP and NBP-TG in terms of accuracy, computational, and communication cost in reasonably sized networks

Knowledge representation and diagnostic inference using Bayesian networks in the medical discourse

For the diagnostic inference under uncertainty Bayesian networks are investigated. The method is based on an adequate uniform representation of the necessary knowledge. This includes both generic and experience-based specific knowledge, which is stored in a knowledge base. For knowledge processing, a combination of the problem-solving methods of concept-based and case-based reasoning is used. Concept-based reasoning is used for the diagnosis, therapy and medication recommendation and evaluation of generic knowledge. Exceptions in the form of specific patient cases are processed by case-based reasoning. In addition, the use of Bayesian networks allows to deal with uncertainty, fuzziness and incompleteness. Thus, the valid general concepts can be issued according to their probability. To this end, various inference mechanisms are introduced and subsequently evaluated within the context of a developed prototype. Tests are employed to assess the classification of diagnoses by the network

Non Parametric Distributed Inference in Sensor Networks Using Box Particles Messages

This paper deals with the problem of inference in distributed systems where the probability model is stored in a distributed fashion. Graphical models provide powerful tools for modeling this kind of problems. Inspired by the box particle filter which combines interval analysis with particle filtering to solve temporal inference problems, this paper introduces a belief propagation-like message-passing algorithm that uses bounded error methods to solve the inference problem defined on an arbitrary graphical model. We show the theoretic derivation of the novel algorithm and we test its performance on the problem of calibration in wireless sensor networks. That is the positioning of a number of randomly deployed sensors, according to some reference defined by a set of anchor nodes for which the positions are known a priori. The new algorithm, while achieving a better or similar performance, offers impressive reduction of the information circulating in the network and the needed computation times