Video: Information Theory Basics

Ryan AdamsVideo

Information theory is a fascinating topic that informs many of the ways we think about structure in data. This video provides a brief overview of some of the concepts, inspired by the lectures of my PhD advisor, the late David MacKay. This is part of a series of videos for COS 302: Mathematics for Numerical Computation and Machine Learning, replacing lectures after the course went remote due to the COVID-19 pandemic.

Video: The Gaussian Distribution

Ryan AdamsVideo

It’s difficult to overstate the centrality of the Gaussian distribution to machine learning, statistics, and many other natural sciences. This video talks about some of the reasons this distribution is special. This is part of a series of videos for COS 302: Mathematics for Numerical Computation and Machine Learning, replacing lectures after the course went remote due to the COVID-19 pandemic.

Video: Useful Inequalities and Limit Theorems

Ryan AdamsVideo

This video talks about Chebyshev, Markov, Jensen, and friends. This is part of a series of videos for COS 302: Mathematics for Numerical Computation and Machine Learning, replacing lectures after the course went remote due to the COVID-19 pandemic.

Video: Dependence and Independence

Ryan AdamsVideo

To do interesting things with joint distributions, they need to have dependence structure. This is part of a series of videos for COS 302: Mathematics for Numerical Computation and Machine Learning, replacing lectures after the course went remote due to the COVID-19 pandemic.

Video: Basics of Joint Probability

Ryan AdamsVideo

From a modeling point of view, joint probability distributions are where the action is. They let you posit latent structure and reason about conditional probability. This video gives an overview of the basics of joint random variables. This is part of a series of videos for COS 302: Mathematics for Numerical Computation and Machine Learning, replacing lectures after the course went remote due to the COVID-19 pandemic.

Video: Some Useful Probability Distributions

Ryan AdamsVideo

There are some distributions that come up over and over again in machine learning and statistics. In this video, I give an overview of some distributions to be aware of. This is part of a series of videos for COS 302: Mathematics for Numerical Computation and Machine Learning, replacing lectures after the course went remote due to the COVID-19 pandemic.

Video: Probability Density and Mass Functions

Ryan AdamsVideo

Probability mass functions and probability density functions are key objects for reasoning about uncertainty. This video by Ari Seff gives an introduction. This is part of a series of videos for COS 302: Mathematics for Numerical Computation and Machine Learning, replacing lectures after the course went remote due to the COVID-19 pandemic.

Video: Probability Spaces and Random Variables

Ryan AdamsVideo

Probability is a big part of many aspects of machine learning, and this video looks at some of the basic formalisms for it. This is part of a series of videos for COS 302: Mathematics for Numerical Computation and Machine Learning, replacing lectures after the course went remote due to the COVID-19 pandemic.

Video: Why is Probability Important to Machine Learning?

Ryan AdamsVideo

Probability is a big part of many aspects of machine learning, but this may not be totally obvious from the outset. In this video we take a look at different ways that probability informs ML. This is part of a series of videos for COS 302: Mathematics for Numerical Computation and Machine Learning, replacing lectures after the course went remote due to the COVID-19 pandemic.

Video: Why is the Gradient the Direction of Steepest Ascent

Ryan AdamsVideo

We often talk about the gradient of a scalar function as being the direction of steepest ascent. Rather than taking that for granted, let’s convince ourselves that it is true. This is part of a series of videos for COS 302: Mathematics for Numerical Computation and Machine Learning, replacing lectures after the course went remote due to the COVID-19 pandemic.