PhD.Dissertation Defense:Soner Aydın

BAYESIAN METHODS FOR TACKLING COMPLEX INFERENTIAL PROBLEMS IN DATA SCIENCE

Soner Aydın
Industrial Engineering, PhD Dissertation, 2024

Thesis Jury

Asst.Prof. Sinan Yıldırım (Thesis Advisor), Prof. Ayşe Berrin Yanıkoğlu , Assoc. Prof. Kemal Kılıç, Prof. Şevket İlker Birbil, Prof. Ozan Kocadağlı

Date & Time: December 20th, 2024 –  11:00 AM

Place: FENS 2072

Keywords : hyperparameter tuning, posterior sampling, differential privacy, local

differential privacy, adaptive online frequency estimation, robust regression

Abstract

Bayesian methods encompass a principled way of modeling, solving and analyzing various estimation and inference problems in data science. In this dissertation, we utilize a variety of Bayesian methods, such as posterior sampling, EM algorithm for mixture models, subsampling for prior probability estimation, to tackle a wide range of inferential problems. These problems include hyperparameter tuning in regularized linear models in supervised learning, robust regression, frequency estimation for dynamic/online datasets under global and local differential privacy frameworks. For each of these problems, we propose new algorithms that can compete with the existing approaches in terms of estimation accuracy, while performing these tasks in a computationally more efficient way via utilizing sampling and subsampling. Along with each algorithm, we also provide both theoretical analyses and numerical experiments that demonstrate their estimation performance.