Time-Sliced temporal evidential networks : the case of evidential HMM with application to dynamical system analysis.

International audienceDiagnostics and prognostics of health states are important activities in the maintenance process strategy of dynamical systems. Many approaches have been developed for this purpose and we particularly focus on data-driven methods which are increasingly applied due to the availability of various cheap sensors. Most data-driven methods proposed in the literature rely on probability density estimation. However, when the training data are limited, the estimated parameters are no longer reliable. This is particularly true for data in faulty states which are generally expensive and difficult to obtain. In order to solve this problem, we propose to use the theory of belief functions as described by Dempster, Shafer (Theory of Evidence) and Smets (Transferable Belief Model). A few methods based on belief functions have been proposed for diagnostics and prognostics of dynamical systems. Among these methods, Evidential Hidden Markov Models (EvHMM) seems promising and extends usual HMM to belief functions. Inference tools in EvHMM have already been developed, but parameter training has not fully been considered until now or only with strong assumptions. In this paper, we propose to complete the generalization of HMM to belief functions with a method for automatic parameter training. The generalization of this training procedure to more general Time-Sliced Temporal Evidential Network (TSTEN) is discussed paving the way for a further generalization of Dynamic Bayesian Network to belief functions with potential applications to diagnostics and prognostics. An application to time series classification is proposed

Answering queries in hybrid Bayesian networks using importance sampling

In this paper we propose an algorithm for answering queries in hybrid Bayesian networks where the underlying probability distribution is of class MTE (mixture of truncated exponentials). The algorithm is based on importance sampling simulation. We show how, like existing importance sampling algorithms for discrete networks, it is able to provide answers to multiple queries simultaneously using a single sample. The behaviour of the new algorithm is experimentally tested and compared with previous methods existing in the literature

Learning to Address Health Inequality in the United States with a Bayesian Decision Network

Life-expectancy is a complex outcome driven by genetic, socio-demographic, environmental and geographic factors. Increasing socio-economic and health disparities in the United States are propagating the longevity-gap, making it a cause for concern. Earlier studies have probed individual factors but an integrated picture to reveal quantifiable actions has been missing. There is a growing concern about a further widening of healthcare inequality caused by Artificial Intelligence (AI) due to differential access to AI-driven services. Hence, it is imperative to explore and exploit the potential of AI for illuminating biases and enabling transparent policy decisions for positive social and health impact. In this work, we reveal actionable interventions for decreasing the longevity-gap in the United States by analyzing a County-level data resource containing healthcare, socio-economic, behavioral, education and demographic features. We learn an ensemble-averaged structure, draw inferences using the joint probability distribution and extend it to a Bayesian Decision Network for identifying policy actions. We draw quantitative estimates for the impact of diversity, preventive-care quality and stable-families within the unified framework of our decision network. Finally, we make this analysis and dashboard available as an interactive web-application for enabling users and policy-makers to validate our reported findings and to explore the impact of ones beyond reported in this work.Comment: 8 pages, 4 figures, 1 table (excluding the supplementary material), accepted for publication in AAAI 201

A Monte-Carlo Algorithm for Probabilistic Propagation in Belief Networks based on Importance Sampling and Stratified Simulation Techniques

A class of Monte Carlo algorithms for probability propagation in belief networks is given. The simulation is based on a two steps procedure. The first one is a node deletion technique to calculate the ’a posteriori’ distribution on a variable, with the particularity that when exact computations are too costly, they are carried out in an approximate way. In the second step, the computations done in the first one are used to obtain random configurations for the variables of interest. These configurations are weighted according to the importance sampling methodology. Different particular algorithms are obtained depending on the approximation procedure used in the first step and in the way of obtaining the random configurations. In this last case, a stratified sampling technique is used, which has been adapted to be applied to very large networks without problems with round-off errors