LM101-086: Ch8: How to Learn the Probability of Infinitely Many Outcomes

This 86th episode of Learning Machines 101 discusses the problem of assigning probabilities to a possibly infinite set of outcomes in a space-time continuum which characterizes our physical world. Such a set is called an "environmental event". The machine learning algorithm uses information about the frequency of environmental events to support learning. If we want to study statistical machine learning, then we must be able to discuss how to represent and compute the probability of an environmental event. It is essential that we have methods for communicating probability concepts to other researchers, methods for calculating probabilities, and methods for calculating the expectation of specific environmental events. This episode discusses the challenges of assigning probabilities to events when we allow for the case of events comprised of an infinite number of outcomes. Along the way we introduce essential concepts for representing and computing probabilities using measure theory mathematical tools such as sigma fields, and the Radon-Nikodym probability density function. Near the end we also briefly discuss the intriguing Banach-Tarski paradox and how it motivates the development of some of these special mathematical tools. Check out: and for more information!!!

You can listen to LM101-086: Ch8: How to Learn the Probability of Infinitely Many Outcomes online on Radio and Podcast. Open the player on this page to stream the available audio.

LM101-086: Ch8: How to Learn the Probability of Infinitely Many Outcomes is an episode from Learning Machines 101 by Richard M. Golden.

This episode is 35:29 long.

This episode was published on Jul 20, 2021.

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