Dynamic Probabilistic Networks for Modelling and Identifying Dynamic Systems: a MCMC Approach

In this article we deal with the problem of interpreting data coming from a dynamic system by using causal probabilistic CPN, a probabilistic graphical model particularly appealing in Intelligent Data Analysis. We discuss the different approaches presented in the literature, outlining their pros and cons through a simple training example. Then, we present a new method for reconstructing the state of the dynamic system, based on Markov Chain Monte Carlo algorithms, called dynamic probabilistic network smoothing DPN-smoothing. Finally, we present an example of the application of DPN-smoothing in the field of signal deconvolution.

[1]  Grace Wahba,et al.  Spline Models for Observational Data , 1990 .

[2]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[3]  Wray L. Buntine,et al.  Graphical models for discovering knowledge , 1996, KDD 1996.

[4]  Sylvia Richardson,et al.  Markov Chain Monte Carlo in Practice , 1997 .

[5]  K. Åström Introduction to Stochastic Control Theory , 1970 .

[6]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[7]  Gregory F. Cooper,et al.  The Computational Complexity of Probabilistic Inference Using Bayesian Belief Networks , 1990, Artif. Intell..

[8]  D. Liberati,et al.  Deconvolution of infrequently sampled data for the estimation of growth hormone secretion , 1995, IEEE Transactions on Biomedical Engineering.

[9]  David Heckerman,et al.  Structure and Parameter Learning for Causal Independence and Causal Interaction Models , 1997, UAI.

[10]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[11]  Upendra Dave,et al.  Probabilistic Reasoning and Bayesian Belief Networks , 1996 .

[12]  Uffe Kjærulff,et al.  A Computational Scheme for Reasoning in Dynamic Probabilistic Networks , 1992, UAI.

[13]  S. Lauritzen Propagation of Probabilities, Means, and Variances in Mixed Graphical Association Models , 1992 .

[14]  Giuseppe De Nicolao,et al.  Gibbs Sampling for Signal Reconstruction , 1997 .

[15]  Paul Dagum,et al.  Time series prediction using belief network models , 1995, Int. J. Hum. Comput. Stud..

[16]  Kuo-Chu Chang,et al.  Symbolic probabilistic inference with both discrete and continuous variables , 1995, IEEE Trans. Syst. Man Cybern..

[17]  R. McCulloch,et al.  Bayesian Inference and Prediction for Mean and Variance Shifts in Autoregressive Time Series , 1993 .

[18]  Cristiana Larizza,et al.  A Unified Approach for Modeling Longitudinal and Failure Time Data, With Application in Medical Monitoring , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Adrian F. M. Smith,et al.  Sampling-Based Approaches to Calculating Marginal Densities , 1990 .

[20]  Donald Geman,et al.  Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images , 1984 .

[21]  David J. Spiegelhalter,et al.  Bayesian networks for patient monitoring , 1992, Artif. Intell. Medicine.

[22]  R. Bellazzi Drug delivery optimization through Bayesian networks: an application to erythropoietin therapy in uremic anemia. , 1993, Computers and biomedical research, an international journal.

[23]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[24]  R. M. Oliver,et al.  Influence diagrams, belief nets and decision analysis , 1992 .

[25]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[26]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems , 1988 .

[27]  Wray L. Buntine Operations for Learning with Graphical Models , 1994, J. Artif. Intell. Res..

[28]  E. Carson,et al.  A probabilistic approach to glucose prediction and insulin dose adjustment: description of metabolic model and pilot evaluation study. , 1994, Computer methods and programs in biomedicine.

[29]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[30]  Sylvia Richardson,et al.  Inference and monitoring convergence , 1995 .

[31]  Stuart J. Russell,et al.  Approximating Optimal Policies for Partially Observable Stochastic Domains , 1995, IJCAI.

[32]  G. Wahba Spline models for observational data , 1990 .

[33]  H. Kushner Introduction to stochastic control , 1971 .

[34]  S Andreassen,et al.  Model-Based Biosignal Interpretation , 1994, Methods of Information in Medicine.

[35]  Michael Luby,et al.  Approximating Probabilistic Inference in Bayesian Belief Networks is NP-Hard , 1993, Artif. Intell..