This is the first of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. In this paper, cumulants are proved to coincide with morphisms of homotopy algebras. The sequel paper outlines how the framework presented here can assist in the development of homotopy probability theory, allowing the principles of deri...

Probability theory is the study of uncertainty. Through this class, we will be relying on concepts from probability theory for deriving machine learning algorithms. These notes attempt to cover the basics of probability theory at a level appropriate for CS 229. The mathematical theory of probability is very sophisticated, and delves into a branch of analysis known as measure theory. In these no...

This is the second of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. This paper outlines how the framework can assist in the development of homotopy probability theory, where a vector space of random variables is replaced by a chain complex of random variables. This allows the principles of derived mathe...

1 Construction of measures 3 1.

These notes are intended to give a solid introduction to Probability Theory with a reasonable level of mathematical rigor. Results are carefully stated, and many are proved. Numerous examples and exercises are included to illustrate the applications of the ideas. Many important concepts are already evident in simple situations and the notes include a review of elementary probability theory. c ©...