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Theses

Adaptative Monte-Carlo methods for complex models

Abstract : This thesis lies in the field of Statistical Inference and more precisely in Bayesian Inference, where the goal is to model a phenomenon given some data while taking into account prior knowledge on the model parameters.The availability of large datasets sparked the interest in using complex models for Bayesian Inference tasks that are able to capture potentially complicated structures inside the data. Such a context requires the development and study of adaptive algorithms that can efficiently process large volumes of data when the dimension of the model parameters is high.Two main classes of methods attempt to fulfil this role: sampling-based Monte Carlo methods and optimisation-based Variational Inference methods. By relying on the optimisation literature and more recently on Monte Carlo methods, the latter have made it possible to construct fast algorithms that overcome some of the computational hurdles encountered in Bayesian Inference.Yet, the theoretical results and empirical performances of Variational Inference methods are often impacted by two factors: one, an inappropriate choice of the objective function appearing in the optimisation problem and two, a search space that is too restrictive to match the target at the end of the optimisation procedure.This thesis explores how we can remedy the two issues mentioned above in order to build improved adaptive algorithms for complex models at the intersection of Monte Carlo and Variational Inference methods.In our work, we suggest selecting the alpha-divergence as a more general class of objective functions and we propose several ways to enlarge the search space beyond the traditional framework used in Variational Inference. The specificity of our approach in this thesis is then that it derives numerically advantageous adaptive algorithms with strong theoretical foundations, in the sense that they provably ensure a systematic decrease in the alpha-divergence at each step. In addition, we unravel important connections between the sampling-based and the optimisation-based methodologies.
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https://tel.archives-ouvertes.fr/tel-03500921
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Submitted on : Wednesday, December 22, 2021 - 5:38:08 PM
Last modification on : Monday, December 27, 2021 - 9:24:09 AM
Long-term archiving on: : Wednesday, March 23, 2022 - 6:45:27 PM

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Kamélia Daudel. Adaptative Monte-Carlo methods for complex models. Statistics [math.ST]. Institut Polytechnique de Paris, 2021. English. ⟨NNT : 2021IPPAT024⟩. ⟨tel-03500921⟩

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