A Model for Analysis of Computational Learning

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Sattari Javid, Ali | 2017

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 49779 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Daneshgar, Amir
Abstract:
The subject of this thesis is about a certain set of algorithms that try to indirectly solve problems. Instead of a programmer crafting an algorithm to solve a problem, these algorithms learn a solution themselves. These methods are usually studied in the Probably Accurately Correct (PAC) learning model. Although, PAC Learning is a generally accepted model, it falls short to describe certain aspects of learning algorithms. Many learning methods rely on convergence to minimize error, or maximize their fitness, yet the PAC model doesn’t explicitly provide any means to measure these behaviours. In this thesis, we first go through different models related to computational requirements of learning and convergence. We then continue by describing PAC model, and finally proceeded by introducing a new model along with metrics to examine convergence properties of a learning algorithm. We continue by showing that these new metrics doesn’t undermine the generality of PAC model, and a problem is PAC learnable if and only if it’s gradually learnable.This thesis doesn’t provide any actual analysis of existing algorithms, and leaves it for future researchers interested in this field
Keywords:
Machine Learning ; Turing Machine ; Computation Theory ; Computational Method