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: www.learningmachines101.com and www.statisticalmachinelearning.com for more information!!!

This 85th episode of Learning Machines 101 discusses formal convergence guarantees for a broad class of machine learning algorithms designed to minimize smooth non-convex objective functions using batch learning methods. In particular, a broad class of unsupervised, supervised, and reinforcement machine learning algorithms which iteratively update their parameter vector by adding a perturbation based upon all of the training data. This process is repeated, making a perturbation of the parameter vector based upon all of the training data until a parameter vector is generated which exhibits improved predictive performance. The magnitude of the perturbation at each learning iteration is called the “stepsize” or “learning rate” and the identity of the perturbation vector is called the “search direction”. Simple mathematical formulas are presented based upon research from the late 1960s by Philip Wolfe and G. Zoutendijk that ensure convergence of the generated sequence of parameter vectors. These formulas may be used as the basis for the design of artificially intelligent smart automatic learning rate selection algorithms. The material in this podcast is designed to provide an overview of Chapter 7 of my new book “Statistical Machine Learning” and is based upon material originally presented in Episode 68 of Learning Machines 101! Check out: www.learningmachines101.com for the show notes!!!

In this episode of Learning Machines 101, we review Chapter 6 of my book “Statistical Machine Learning” which introduces methods for analyzing the behavior of machine inference algorithms and machine learning algorithms as dynamical systems. We show that when dynamical systems can be viewed as special types of optimization algorithms, the behavior of those systems even when they are highly nonlinear and high-dimensional can be analyzed. Learn more by visiting: www.learningmachines101.com and www.statisticalmachinelearning.com .