Award Date

May 2018

Degree Type

Thesis

Degree Name

Master of Science in Electrical Engineering (MSEE)

Department

Electrical and Computer Engineering

First Committee Member

Pushkin Kachroo

Second Committee Member

Sahjendra Singh

Third Committee Member

Brendan Morris

Fourth Committee Member

David Costa

Number of Pages

70

Abstract

Hidden Markov models (HMMs) constitute a broad and flexible class of statistical models that are widely used in studying processes that evolve over time and are only observable through the collection of noisy data. Two problems are essential to the use of HMMs: state estimation and parameter estimation. In state estimation, an algorithm estimates the sequence of states of the process that most likely generated a certain sequence of observations in the data. In parameter estimation, an algorithm computes the probability distributions that govern the time-evolution of states and the sampling of data. Although algorithms for the two problems are widely researched, relatively little study has been devoted to understanding the tradeoffs between key design variables of these algorithms from a mathematically rigorous viewpoint. In this thesis, we provide such a study by establishing theorems regarding these tradeoffs. Furthermore, we illustrate the implications of these theorems in practice, highlighting the scope of their applicability and generality. We then suggest directions for future research in this area by bringing attention to the critical assumptions and tools used in the proofs of our theorems.

Keywords

gradient descent; information theory; statistical inference; stochastic processes

Disciplines

Applied Mathematics | Operational Research | Operations Research, Systems Engineering and Industrial Engineering | Statistics and Probability

Language

English


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