Uncertain Reasoning and Forecasting

Paul Dagum, Adam Galper, Eric Horvitz, and Adam Seiver

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We develop a probability forecasting methodology through a synthesis of Bayesian belief-network models and classical time-series analysis. By casting Bayesian time-series analyses as temporal belief-network problems, we introduce arbitrary dependency models that capture richer, and more realistic, models of dynamic dependencies. The richer models and associated computational methods allow us to move beyond rigid classical assumptions of linearity in the relationships among variables and of normality of their probability distributions. We explore the implications of the model assumptions and the preconditions necessary to validate these assumptions. We define noncontemporaneous intercausal dependence, which, together with our earlier work on additive generalizations of belief networks, allows us to construct large, expressive models from far fewer data observations. In contrast to general probabilistic inference, forecasting is rendered tractable in these models when we assume noncontemporaneous intercausal dependence. We investigate the role of noise models in the forecasting methodology. We develop methods to induce the dynamic structure of the model from the time series. These methods exploit the dynamic nature of the domain. We apply the methodology to the difficult problem of predicting outcome in critically-ill patients. The nonlinear, dynamic behavior of the critical- care domain highlights the need for a synthesis of probability forecasting and uncertain reasoning.

Keywords: Forecasting, Bayesian reasoning, dynamic network models, time series, probabilistic inference.

Reference: P. Dagum, P., A. Galper, E. Horvitz, A. Seiver, Uncertain reasoning and forecasting, International Journal of Forecasting 11(1):73-87, March 1995.

Author Email: dagum@smi.stanford.edu, galper@smi.stanford.edu, horvitz@microsoft.com, seiver@smi.stanford.edu