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!!!
LM101-085:Ch7:How to Guarantee your Batch Learning Algorithm Converges
LM101-084: Ch6: How to Analyze the Behavior of Smart Dynamical Systems
LM101-083: Ch5: How to Use Calculus to Design Learning Machines
LM101-082: Ch4: How to Analyze and Design Linear Machines
LM101-081: Ch3: How to Define Machine Learning (or at Least Try)
LM101-080: Ch2: How to Represent Knowledge using Set Theory
LM101-079: Ch1: How to View Learning as Risk Minimization
LM101-078: Ch0: How to Become a Machine Learning Expert
LM101-077: How to Choose the Best Model using BIC
LM101-076: How to Choose the Best Model using AIC and GAIC
LM101-075: Can computers think? A Mathematician's Response (remix)
LM101-074: How to Represent Knowledge using Logical Rules (remix)
LM101-073: How to Build a Machine that Learns to Play Checkers (remix)
LM101-072: Welcome to the Big Artificial Intelligence Magic Show! (Remix of LM101-001 and LM101-002)
LM101-071: How to Model Common Sense Knowledge using First-Order Logic and Markov Logic Nets
LM101-070: How to Identify Facial Emotion Expressions in Images Using Stochastic Neighborhood Embedding
LM101-069: What Happened at the 2017 Neural Information Processing Systems Conference?
LM101-068: How to Design Automatic Learning Rate Selection for Gradient Descent Type Machine Learning Algorithms
LM101-067: How to use Expectation Maximization to Learn Constraint Satisfaction Solutions (Rerun)
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