6.008 Tutorial Videos

1. Probabilities of Events
• Probability of events
  • Basic Review of Probability
  • Sample Space
  • Coin Flip Example, Part 1
  • Coin Flip Example, Part 2
  • Coin Flip Example, Part 3
  • Two Children Example
  • Sample Space and Probability
  • Conditioning on Events
  • Conditioning: Chain Rule
  • Total Probability
  • Bayes Rule
  • Independence of Events
2. Discrete Random Variables
• Discrete Random Variables and Information Measures
  • Terminology and Introduction of Random Variables
  • Random Variables Example
  • Product Rule for Random Variables
  • Expected Value
  • Linearity of Expectations, Example 1
  • Linearity of Expectations, Example 2
  • Linearity of Expectations, Example 3
  • Indicator Random Variables
  • Geometric Distribution, Intro
  • Geometric Distribution, Problem 1
  • Geometric Distribution, Problem 2
  • Geometric Distribution, Problem 3
  • Shannon Information Content
  • Shannon Entropy (Version 1)
  • Shannon Entropy (Version 2)
  • Information Divergence
• Joint Distributions, Marginalization, Joint Information
  • Relating Two Random Variables
  • Marginalization of Two Random Variables
  • Marginalization of Many Random Variables
  • Joint Information Measures
  • Joint Entropy
• Conditioning, Bayes Rule, Conditional Information
  • Relating Conditioning on Events to Random Variables
  • Conditioning
  • Toward More General Conditioning
  • Random Variables Conditioned on Events
  • Bayes Rule for Random Variables
  • Conditional Entropy
• Independence Structure, Mutual Information
  • Independent Random Variables
  • Conditional Independence (1)
  • Conditional Independence (2)
  • Conditional Independence (3)
  • Mutual vs. Pairwise Independence
  • Explaining Away
  • Mutual Information
3. Decision Making
• Decision-making, Most Probable Configurations, MAP Rule
  • Decisions Intro
  • Maximum Likelihood
  • Maximum Likelihood 2
  • Medical Diagnosis Risk
  • Medical Diagnosis Tree
  • MAP estimation
4. Graphical Models and Decision Making
• Graphical Models, Message-Passing, Hidden Markov Models
  • Introduction to Inference in Graphical Models
  • Graphical Models Overview
  • Hidden Markov Model Ingredients
  • The Sum Product Algorithm
• HMM Marginalization: Forward-Backward Algorithm
  • Formulating Hidden Markov Models
  • Forward Messages in Hidden Markov Models
  • Backward Messages in Hidden Markov Models
• HMM Most Probable Configuration: Viterbi Algorithm
  • Most Probable Configuration
  • The Viterbi Algorithm
5. Model Learning
• Parameter Estimation, Maximum Likelihood Method
  • Introduction to Learning Probabilistic Models
  • Parameter Estimation
  • Maximum Likelihood Method 1
  • Maximum Likelihood Method 2
  • Bayesian Parameter Learning
  • Parameter Learning For Finite Random Variables
  • Parameter Estimation Example 1: Boxes and Balls
  • Parameter Estimation Example 2: German Tanks
• Model learning, Naive Bayes Models and HMMs
  • Introduction to Naive Bayes Model
  • Naive Bayes Model Training
  • Naive Bayes Model Prediction
  • Laplace Smoothing in Naive Bayes Models
• Learning structure in graphical models
  • Parameter Learning in Trees
  • The Chow Liu Algorithm
6. Asymptotics
• Markov and Chebyshev Bounds, Law of Large Numbers
  • Markov And Chebyshev Bounds
  • Bounds Example 1
  • Bounds Example 2
  • Weak Law of Large Numbers
• Typical Sets, Compression, and Hashing
  • Introduction to Typical Sets
  • Typical Set Alternative Notation
  • Typical Set of Fair Coin
  • Typical Set of Biased Coin
  • Example on Typical Set of Biased Coin
7. Sampling
• Markov Chains and Random Walks
  • Markov Chains
• Markov Chain Monte Carlo and Gibbs Sampling
  • Monte Carlo Methods
  • Ising Model: Intro
  • Ising Model: Inference
  • Metropolis Hastings
  • Metropolis Hastings Example: Ising Model
  • Gibbs Sampling
  • Gibbs Sampling Example: Ising Model
8. Continuous Random Variables
• Continuous Distributions
  • Gaussian Distributions
  • Derived Distributions
  • Derived Distributions Example 1
  • Derived Distributions Example 2
  • Derived Distributions Example 3

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