Riemannian Geometry and Statistical Machine Learning

دانشگاه آزاد اسلامی اصفهان(خوراسگان)

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" Riemannian Geometry and Statistical Machine Learning "

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	150610
Doc. No	:	ET22402
Main Entry	:	Guy Lebanon
Title Proper	:	Riemannian Geometry and Statistical Machine Learning
Note	:	This document is digital این مدرک بصورت الکترونیکی می باشد
Abstract	:	Statistical machine learning algorithms deal with the problem of selecting an appropriatestatistical model from a model space O based on a training set xipz1 c X or (xi, yi)b,",l cX x y. In doing so they either implicitly or explicitly make assumptions on the geometriesof the model space O and the data space X. Such assumptions are crucial to the success ofthe algorithms as different geometries are appropriate for different models and data spaces.By studying these assumptions we are able to develop new theoretical results that enhance ourunderstanding of several popular learning algorithms. Furthermore, using geometrical reasoningwe are able to adapt existing algorithms such as radial basis kernels and linear margin classifiersto non-Euclidean geometries. Such adaptation is shown to be useful when the data space doesnot exhibit Euclidean geometry. In particular, we focus in our experiments on the space of textdocuments that is naturally associated with the Fisher information metric on correspondingmultinomial models....-...,..tested for theQ1 PC1 bus cardBoth these projects mere sofixare des elopment efforts tonards contributing to dlfferentaspects of Roboucs and lZ1echatronics projects m the Controls and Roboucs Group..
Subject	:	Electericl tess
	:	برق
electronic file name	:	TL45613.pdf
Title and statement of responsibility and	:	Riemannian Geometry and Statistical Machine Learning [Thesis]