We propose to develop and analyze approximate inference methods for probabilistic models. Probabilistic models are widely used in Machine Learning to solve complex real-world problems and they also form an important research area in Statistics. One of the biggest challenges in probabilistic modelling is to be able to infer marginal probabilities of some random variables in the model, a task which is often formally computationally intractable due to the complexity of the situation modeled. We propose to contribute to the advancement in developing and understanding the properties of approximate inference techniques through three important research objectives. The first objective is to develop and analyze approximate inference techniques for Bayesian Linear Gaussian State-Space based Models (LGSSMs). LGSSMs are used in many application domains and we recently developed a Bayesian approach to a class of models based on LGSSMs using a deterministic approximation technique. We would like to investigate more in dept the properties of the proposed technique and develop other approximation techniques which have different characteristics. The second objective is to perform a theoretical evaluation and a more exhaustive experimental comparison of the the state-of-the-art algorithm for approximate inference in LGSSMs with switching dynamics, and investigate the extension of this approximation technique to other related models. The third objective is to develop inference methods in sequential decision theory, by exploiting the new point-of-view which sees planning problems as inference problems in probabilistic models. We would like to concentrate on Markovian models not yet analyzed, and to apply the resulting methods to solve imitation problems in robotics and to design optimal sequential experiments in bioinformatics and chemoinformatics. This project has the potential to contribute towards technological advances in a large spectrum of applications.
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