Public defence in Computer Science, M.Sc. Alejandro Catalina

Title of the doctoral thesis: Robust Bayesian Inference: variable and structure selection and variational inference

Doctoral student: Alejandro Catalina
Opponent: Associate Professor Justin Domke, University of Massachusetts, USA
Custos: Prof. Aki Vehtari, Aalto University School of Science, Department of Computer Science

Thesis available for public display 10 days prior to the defence at: https://aaltodoc.aalto.fi/doc_public/eonly/riiputus/

Bayesian inference serves as a fundamental framework for statistical analysis, enabling the incorporation of prior knowledge and uncertainties into the modeling process. In complex scenarios, exact inference is often infeasible, requiring the development of efficient computational methods for robust Bayesian model assessment and variable selection. 

The doctoral thesis explores novel computational approaches for assessing and refining Bayesian models, with a specific focus on variable and structure selection and variational inference techniques. By leveraging advanced algorithms and robust statistical methodologies, this thesis aims to streamline the process of model evaluation in variational inference and improving the accuracy of variable selection in high-dimensional and complex problems. 

The first part of the thesis studies and develops variable and structure selection in the context of generalized multilevel and additive models and families of models beyond the exponential family. The thesis proposes unifying improvements to enable variable selection in such models, showing that variable and structure selection is possible in these complex models, while maintaining predictive performance. 

The second part of the thesis focuses on assessing model quality and convergence in variational inference problems. The thesis presents advancements for improving the stability and robustness of the estimates and for diagnosing potential pathologies in the solutions. The thesis shows that these can lead to improved quality in estimating target distributions and also to identifying bad behaving solutions. 

These methods aid in bringing a safer and more robust usage of statistical methods to real world problems. The algorithms developed in this thesis are implemented as part of open source software packages and are immediately available to use by researchers and practitioners worldwide.

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Doctoral theses in the School of Science: https://aaltodoc.aalto.fi/handle/123456789/52