Algorithm for Learning from a Random Walk Oracle

Xiaolin Yang

Defense Date

7-23-2009

Graduation Date

Summer 1-1-2009

Availability

Campus Only

Submission Type

thesis

Degree Name

MS

Department

Computational Mathematics

School

McAnulty College and Graduate School of Liberal Arts

Committee Chair

Jeffrey C. Jackson

Committee Member

Donald L. Simon

Keywords

Computational Learning, Fourier Analysis, Random Walk Oracle

Abstract

Learning Disjunctive Normal Form and Threshold of Parity functions are well-studied problems in computational learning theory. Under different learning models we can achieve different time complexities with respect to the size of the input. In this thesis, I consider using an oracle whose power lies in between membership and example oracles, the random walk oracle. I first study a heuristic algorithm for estimating the sum of squares of Fourier coefficients. Then I propose a new algorithm for learning under a random walk oracle and compare the performance of this algorithm with an algorithm previously proposed by Jackson and Wimmer. The performance of these two algorithms is evaluated empirically based on experiments on linear threshold functions, a special case of TOP. Finally, I prove a theorem showing how to efficiently generate a richer subclass of TOP functions from linear threshold functions, which could allow for broader testing of these algorithms.

Format

PDF

Language

English

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