Rethinking Maximum Likelihood Estimation

This thesis is a culmination of my doctoral work which addresses the issue of bias in statistical parameter estimation, with a particular focus on deep generative models. I propose a novel alternative to Maximum Likelihood Estimation, most popular method for estimating parameters, and show how my proposed method mitigates bias, reduces overfitting and the overrepresentation of high frequency events, increases the representation of low frequency data, is more stable in a MAD setting. This thesis details how this method can be solved analytically, used with existing estimators, and implemented in deep learning settings with hypernetworks. Inspired by this method, I propose a new grading scheme that incentives students to report their true beliefs, and show how the proposed method evaluates cognition and metacognition simultaneously. This thesis justifies both methods on the basis of the Bayesian interpretation of probability, and details how such an interpretation works as an extension of logic, defending this interpretation against rival views. Finally, this thesis addresses logic itself (and why Logic is important to Electrical and Computer Engineering), providing the necessary background from Aristotle's axioms to Linear Algebra, to statistical parameter estimation.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Engineering

Grantor

Rice University

Year dc:date.issued

2025

Author dc:creator

• Mayer, Paul Michael

Advisor dc:contributor.advisor

• Baraniuk, Richard G

• Maximum Likelihood Estimation
• Statistics
• Machine Learning
• Parameter Estimation
• Bias

Statement dc:rights

• Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/118486

OAI identifier oai:identifier

oai:repository.rice.edu:1911/118486