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!!!
LM101-066: How to Solve Constraint Satisfaction Problems using MCMC Methods (Rerun)
LM101-065: How to Design Gradient Descent Learning Machines (Rerun)
LM101-064: Stochastic Model Search and Selection with Genetic Algorithms (Rerun)
LM101-063: How to Transform a Supervised Learning Machine into a Policy Gradient Reinforcement Learning Machine
LM101-062: How to Transform a Supervised Learning Machine into a Value Function Reinforcement Learning Machine
LM101-061: What happened at the Reinforcement Learning Tutorial? (RERUN)
LM101-060: How to Monitor Machine Learning Algorithms using Anomaly Detection Machine Learning Algorithms
LM101-059: How to Properly Introduce a Neural Network
LM101-058: How to Identify Hallucinating Learning Machines using Specification Analysis
LM101-057: How to Catch Spammers using Spectral Clustering
LM101-056: How to Build Generative Latent Probabilistic Topic Models for Search Engine and Recommender System Applications
LM101-055: How to Learn Statistical Regularities using MAP and Maximum Likelihood Estimation (Rerun)
LM101-054: How to Build Search Engine and Recommender Systems using Latent Semantic Analysis (RERUN)
LM101-053: How to Enhance Learning Machines with Swarm Intelligence (Particle Swarm Optimization)
LM101-052: How to Use the Kernel Trick to Make Hidden Units Disappear
LM101-051: How to Use Radial Basis Function Perceptron Software for Supervised Learning[Rerun]
LM101-050: How to Use Linear Machine Learning Software to Make Predictions (Linear Regression Software)[RERUN]
LM101-049: How to Experiment with Lunar Lander Software
LM101-048: How to Build a Lunar Lander Autopilot Learning Machine (Rerun)
LM101-047: How Build a Support Vector Machine to Classify Patterns (Rerun)
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