טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentEyal Lebanony
SubjectTime Series Modeling using Bayesian Networks
DepartmentDepartment of Electrical Engineering
Supervisor Full Professor Meir Ron


Abstract

   The modeling of time series is a basic task in many areas of science. It is used for example in biology, speech processing, pattern recognition, financial forecasting as well as many other areas.

   Inferring models from observations and studying their properties is an attempt to link observations together in a coherent pattern. The inferred model is used for understanding the process that created the observations, and can help in forecasting future observations. For example, if we are interested in enhancing a speech signal corrupted by noise and transmission distortion, we can use the signal model to design a system, which will optimally remove the noise and transmission disorder. Sometimes signal models are potentially capable of letting one learn about the signal source without having the source available. Using models helps solving efficiently the basic tasks in time series analysis: classification, segmentation, state estimation, noise filtering and prediction. 

   This work first reviews the difficulties in time series modeling and the way to compare between different models in order to select the best one for a given series at a low complexity price. The family of linear models is described in detail. The advantage of these models is in their simplicity but the linearity assumption is not justified in many real problems. The thesis explains the advantage of models that can be generalized to the form of Bayesian networks. The Hidden Markov Model, which is a member of this family, is described in detail with other variants of this model. The Mixture of Experts model is a Bayesian network model, which uses a gating network to divide the given sequence between linear autoregression experts. Each expert specializes in a different linear problem. In this way, non linear problems can be solved efficiently. This model seems promising for solving difficult problems.

   Finally, comparison results from implementation of linear and nonlinear models on several synthetic data sets and benchmark time series are introduced.