Mathematical foundations

Statistical machine learning and signal processing are topics in applied mathematics, which are based upon many abstract mathematical concepts. Defining these concepts clearly is the most important first step in this book. The purpose of this chapter is to introduce these foundational mathematical c...

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Bibliographic Details
Published inMachine Learning for Signal Processing
Main Author Little, Max A
Format Book Chapter
LanguageEnglish
Published Oxford Oxford University Press 13.08.2019
Oxford University Press, Incorporated
Subjects
graphs
probability and stochastic processes
Abstract algebra
data compression and information theory
vector spaces
metrics
convexity
computational complexity
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ISBN9780198714934
0198714939
DOI10.1093/oso/9780198714934.003.0001

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Summary:Statistical machine learning and signal processing are topics in applied mathematics, which are based upon many abstract mathematical concepts. Defining these concepts clearly is the most important first step in this book. The purpose of this chapter is to introduce these foundational mathematical concepts. It also justifies the statement that much of the art of statistical machine learning as applied to signal processing, lies in the choice of convenient mathematical models that happen to be useful in practice. Convenient in this context means that the algebraic consequences of the choice of mathematical modeling assumptions are in some sense manageable. The seeds of this manageability are the elementary mathematical concepts upon which the subject is built.
ISBN:9780198714934
0198714939
DOI:10.1093/oso/9780198714934.003.0001