Topics on statistical inference with model uncertainty

Statistical inference is a method of data analysis used for drawing conclusions about underlying probability distributions in a statistical model and making decisions based on inferred knowledge. Classically, the theory of statistical inference was developed for the purposes of hypothesis testing and estimation of model parameters. With the advent of machine learning, several new challenging data-driven inference problems have been emerging, in which knowledge of underlying models available to the decision-maker is incomplete or ambiguous. In this dissertation, we explore and study broadly three problems in the area of statistical inference under model uncertainty. In these problems, the uncertainty arises due to the fact that either partial or no knowledge of ground truth data distributions is assumed. We approach these problems using techniques from statistics, optimization, and information theory, to understand their fundamental limits and develop theory-based algorithms with guarantees. These three problems lie in diverse sub-fields, namely, sequential controlled sensing for composite multi-hypothesis testing, robust mean estimation, and distributed feature compression. In the problems of controlled sensing and robust mean estimation, our main contributions are optimal algorithms based on statistical analysis, which are guaranteed to achieve information-theoretic limits, and exhibit competitive empirical performance. In the problem of distributed feature compression, our main contribution is a distributed compression scheme for pretrained learning models, which is based on the form of optimal quantizers derived for pretrained linear regressors assuming knowledge of underlying data distribution. In all problems discussed, we demonstrate effectiveness of proposed algorithms through experiments.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Deshmukh, Aditya Omprakash

Contributors dc:contributor

• Veeravalli, Venugopal V
• Moulin, Pierre
• Raginsky, Maxim
• Fellouris, Georgios

• Statistical Inference
• Model Uncertainty
• Information Theory

Statement dc:rights

• Copyright 2024 Aditya Deshmukh

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/124309

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F124309