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How to Predict Sequences with Bayes, MDL, and Experts
Published on Feb 25, 20074106 Views
Chapter list
How to Predict Sequences with00:03
Overview01:39
Table of Contents07:40
Philosophical Issues: Contents08:34
Philosophical Issues: Abstract08:42
On the Foundations of Machine Learning08:48
Example 1: Probability of Sunrise Tomorrow09:54
Example 2: Digits of a Computable Number13:20
Example 3: Number Sequences14:36
Occam's Razor to the Rescue16:35
Foundations of Induction17:12
Problem Setup18:03
Dichotomies in Machine Learning19:30
Sequential/online predictions22:12
Bayesian Sequence Prediction: Contents24:42
Bayesian Sequence Prediction: Abstract25:22
Uncertainty and Probability25:52
Frequency Interpretation: Counting27:39
Objective Interpretation: Uncertain Events28:35
Subjective Interpretation: Degrees of Belief29:31
Bayes' Famous Rule30:49
Example: Bayes' and Laplace's Rule33:36
Example: Bayes' and Laplace's Rule36:28
Exercise 1: Envelope Paradox40:22
Exercise 2: Con¯rmation Paradox42:32
Notation: Strings & Probabilities44:40
The Bayes-Mixture Distribution »45:46
Relative Entropy48:09
Proof of the Entropy Bound50:45
Posterior Convergence52:11
Sequential Decisions55:13
Loss Bounds57:07
Proof of Instantaneous Loss Bounds01:00:55
Generalization: Continuous Probability Classes M01:03:01
Bayesian Sequence Prediction: Summary01:10:46