Probability, Information Theory and Bayesian Inference

Posted in Science on September 07, 2008

Probability, Information Theory and Bayesian Inference

Lecture slides:

  • Probabilistic Machine Learning
  • Why Probabilistic Models for Learning?
  • Probabilities and Ensembles
  • Basic Rules of Probability
  • Expectation and Variance (Moments)
  • Example of Joint Probability - Bigrams
  • An Exercise on Mammographies
  • Solving the Mammography Exercise Writing Down Probabilities
  • Solving the Mammography Exercise Playing with Concrete Numbers
  • Solving the Mammography Exercise Apply Bayes’ Rule
  • Do You Trust Your Doctor?
  • Information, Probability and Entropy
  • Entropy
  • Entropy of a Binary Random Variable
  • Information Between Two Random Variables
  • Kullback-Leibler Divergence
  • Shannon’s Source Coding Theorem
  • What is Probability?
  • Beliefs and Probability
  • Bayesian Learning
  • Bayesian Learning: A Coin Toss Example
  • Priors for Coin Tossing
  • Posterior for Coin Tossing
  • Before and After Observing One Head
  • Making Predictions
  • Some Terminology
  • Learning About a Coin
  • Bayesian Classification
  • Verifying the Prior
  • Observing Some Data
  • Posterior Samples
  • Bayesian Predictions
  • The Evidence or Marginal Likelihood Revisited
  • Bayesian Regression
  • Bayesian Regression - Observe Some Data
  • Bayesian Regression - Posterior Distribution
  • Bayesian Regression - Predictive Distribution

Author: Joaquin Quiñonero Candela, Max Planck Institute For Biological Cybernetics

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