In this 77th episode of www.learningmachines101.com , we explain the proper semantic interpretation of the Bayesian Information Criterion (BIC) and emphasize how this semantic interpretation is fundamentally different from AIC (Akaike Information Criterion) model selection methods. Briefly, BIC is used to estimate the probability of the training data given the probability model, while AIC is used to estimate out-of-sample prediction error. The probability of the training data given the model is called the “marginal likelihood”. Using the marginal likelihood, one can calculate the probability of a model given the training data and then use this analysis to support selecting the most probable model, selecting a model that minimizes expected risk, and support Bayesian model averaging. The assumptions which are required for BIC to be a valid approximation for the probability of the training data given the probability model are also discussed.
LM101-026: How to Learn Statistical Regularities (Rerun)
LM101-025: How to Build a Lunar Lander Autopilot Learning Machine
LM101-024: How to Use Genetic Algorithms to Breed Learning Machines
LM101-023: How to Build a Deep Learning Machine
LM101-022: How to Learn to Solve Large Constraint Satisfaction Problems
LM101-021: How to Solve Large Complex Constraint Satisfaction Problems (Monte Carlo Markov Chain)
LM101-020: How to Use Nonlinear Machine Learning Software to Make Predictions
LM101-019 (Rerun): How to Enhance Intelligence with a Robotic Body (Embodied Cognition)
LM101-018: Can Computers Think? A Mathematician's Response (Rerun)
LM101-017: How to Decide if a Machine is Artificially Intelligent (Rerun)
LM101-016: How to Analyze and Design Learning Rules using Gradient Descent Methods
LM101-015: How to Build a Machine that Can Learn Anything (The Perceptron)
LM101-014: How to Build a Machine that Can Do Anything (Function Approximation)
LM101-013: How to Use Linear Machine Learning Software to Make Predictions (Linear Regression Software)
LM101-012: How to Evaluate the Ability to Generalize from Experience (Cross-Validation Methods)
LM101-008: How to Represent Beliefs Using Probability Theory
LM101-011: How to Learn About Rare and Unseen Events (Smoothing Probabilistic Laws)
LM101-010: How to Learn Statistical Regularities (MAP and maximum likelihood estimation)
LM101-009: How to Enhance Intelligence with a Robotic Body (Embodied Cognition)
LM101-007: How to Reason About Uncertain Events using Fuzzy Set Theory and Fuzzy Measure Theory
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