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Fundamentals of Machine Learning$
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Thomas P. Trappenberg

Print publication date: 2019

Print ISBN-13: 9780198828044

Published to Oxford Scholarship Online: January 2020

DOI: 10.1093/oso/9780198828044.001.0001

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Basic probability theory

Basic probability theory

Chapter:
(p.121) 6 Basic probability theory
Source:
Fundamentals of Machine Learning
Author(s):

Thomas P. Trappenberg

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198828044.003.0006

The discussion provides a refresher of probability theory, in particular with respect to the formulations that build the theoretical language of modern machine learning. Probability theory is the formalism of random numbers, and this chapter outlines what these are and how they are characterized by probability density or probability mass functions. How such functions have traditionally been characterized is covered, and a review of how to work with such mathematical objects such as transforming density functions and how to measure differences between density function is presented. Definitions and basic operations with multiple random variables, including the Bayes law, are covered. The chapter ends with an outline of some important approximation techniques of so-called Monte Carlo methods.

Keywords:   probability theory, probability density function, random variables, Bayesian formula, Monte Carlo

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