Schedule

Jump to: [Unit 1: Discrete] - [Unit 2: Regression] - [Unit 3: MCMC] - [Unit 4: Mixtures] - [Unit 5: Time Series]

Deadlines

unit HW due CP due in-class quiz
0 Thu Jan 26 n/a Mon Feb 06
1 Thu Feb 09 Thu Feb 16 Wed Feb 22
2 Thu Feb 23 Thu Mar 02 Wed Mar 08
3 Thu Mar 09 Thu Mar 16 Wed Mar 29
4 Thu Apr 06 Thu Apr 13 Mon Apr 24
5 Thu Apr 20 Thu Apr 27 Mon May 01


Unit 1: Foundations for Discrete Data

Key ideas: Probability fundamentals, Point estimation strategies (ML and MAP), Posterior estimation, conjugacy

Models: Beta-Bernoulli models for binary data, Dirichlet-multinomial models for count data

Prerequisite Practice: HW0, which covers joint, conditional, and marginal distributions; Bayes rule; independence

Math Homework: HW1, which covers Beta-Bernoulli models, point estimation & posterior estimation; conjugacy

Coding Practical: CP1 which covers text modeling with unigram distributions

Date Assigned Do Before Class Class Content Optional
Wed 01/18 day00
out:
- HW0
Notes:
Readings:
- Course syllabus

Course Overview & Probability Refresher

Slides:
- Course Overview
Math/Concept Exercises:
- day00 Exercises
- Solutions to day00
- Motivation for Probabilistic ML:
- Ghahramani Nature 2015
- Bishop 'Model-Based ML' 2013
Mon 01/23 day01  
Notes:
- day01.pdf
Videos:
- day01-A part1: Random Vars and Probability
- day01-A part2: Joint, Conditional, Marginal
- day01-A part3: Sum Rule, Product Rule, Bayes Rule
- day01-A part4: Independence
- day01-A part5: Expectations, Mean, Variance
- day01-B: Continuous r.v., PDF, CDF
Readings:
- Bishop PRML Ch. 1 Sec. 1.1, 1.2
--- Focus on 1.2.1, 1.2.2, and 1.2.3

Probability Refresher

Slides:
- day01 Highlights
Math/Concept Exercises:
- day01A Exercises: disc. r.v.
- day01B Exercises: cont. r.v.
- Solutions to day01A
- Solutions to day01B
- MathForML Ch. 6 Sec. 6.1 and 6.2
Wed 01/25 day02
due on Thu:
- HW0
Notes:
- day02.pdf
Videos:
- day02 part1: Bernoulli Distribution
- day02 part2: Models for Coin Flips
- day02 part3: ML Estimation for iid Bern
- day02 part4: Pros and Cons of ML
Readings:
- Bishop PRML Ch. 1 Sec. 1.2.3
--- Focus on maximum likelihood vs Bayesian approach
- Bishop PRML Ch. 2 Sec. 2.1
--- Focus on ML estimator Eq. 2.5-2.8

Maximum Likelihood for Binary Data

Slides:
- day02 Highlights
Math/Concept Exercises:
- day02: Exercises
- Solutions to day02
Lab Notebook:
- day02: Bernoulli Lab [colab]
  
Mon 01/30 day03
out:
- HW1
Notes:
- day03.pdf
Videos:
- day03 part1: Gamma functions
- day03 part2: Beta Distributions
- day03 part3: Beta-Bernoulli
- day03 part4: MAP estimation
- day03 part5: Posterior Predictives
Readings:
- Bishop PRML Ch. 2 Sec. 2.1
--- Focus on Beta and Bernoulli distrib.

Beta-Bernoulli models for Binary Data

Slides:
- day03 Highlights
Lab Notebook:
- day03: Beta-Bernoulli Lab [colab]
- day03: Gamma Function Lab [colab]
  
Wed 02/01 day04  
Notes:
- day04.pdf
- day04B.pdf (Lagrange multipliers)
Videos:
- day04 part1: Categorical distributions
- day04 part2: Categorical ML Estim.
- day04 part3: Dirichlet distributions
- day04 part4: Dirichlet-Categorical model
- day04 part5: MAP Estim. for Dir-Cat.
- day04B part1: Lagrange multipliers 1/2
- day04B part1: Lagrange multipliers 2/2
Readings:
- Bishop PRML Ch. 2 Sec. 2.2
--- Focus on Dirichlet distribution
- Bishop PRML Appendix E Lagrange Multipliers

Dirichlet-Categorical models for Count Data

Slides:
- day04 Highlights
Lab Notebook:
- day04: Dirichlet-Categorical Lab [colab]
- For more on Dirichlet, see Frigyik, Kapila, and Gupta 2010


Unit 2: Multivariate Gaussians and Regression

Key ideas: multivariate Gaussian distributions, model selection, Laplace approximation

Models: Bayesian linear regression, Bayesian logistic regression, generalized linear models

Algorithms: gradient descent

Math Homework: HW2

Coding Practical: CP2

Date Assigned Do Before Class Class Content Optional
Mon 02/06 day05  
Notes:
- day05.pdf
Videos:
- day05 part1: Gaussian distribution
- day05 part2: ML Estim. for Gaussians
- day05 part3: Biased vs Unbiased
- day05 part4: Properties of Gaussians
- day05 part5: Covariance
Readings:
- Bishop PRML Ch. 1 Sec. 1.2.4
--- Focus Univariate Gaussians
--- ML estimators of mean and variance
- Bishop PRML Ch. 2 Sec. 2.3.1-2.3.2
--- Skim multivariate Gaussian properties

Univariate Gaussians

Slides:
- day05 Highlights
Lab Notebook:
- day05: Univar. Gaussian Lab [colab]
  
Wed 02/08 day06
due on Thu:
- HW1
Notes:
- day06.pdf
Videos:
- day06 part1: Multivariate Gaussian
- day06 part2: Visualizing Covariances
- day06 part3: Marginals of Gaussians are Gaussian
- day06 part4: Conditionals of Gaussians are Gaussian
- day06 part5: Linear-Gaussian models are Joint Gaussian
Readings:
- Bishop PRML Ch. 2 Sec. 2.3.1-2.3.5
--- Focus on multivariate Gaussian properties
- Bishop PRML Ch. 2 Sec. 2.3.5-2.3.6
--- Skim for intuition

Multivariate Gaussians

Slides:
- day06 Highlights
Lab Notebook:
- day06: Multivar. Gaussian Lab [colab]
- Wolfram: Determinants Seen Geometrically
- Immersive Linear Algebra: Determinants
- Immersive Linear Algebra: Eigenvalues and eigenvectors
Mon 02/13 day07  
Notes:
- day07.pdf
Videos:
- day07 part1: Probabilistic Linear Regression
- day07 part2: ML Estim.
- day07 part3: Posterior Estim.
- day07 part4: MAP Estim.
Readings:
- Bishop PRML Ch. 3 Sec. 3.1
--- Focus on ML estimator for linear regression
- Bishop PRML Ch. 3 Sec. 3.3
--- Focus on posterior distribution

Bayesian Linear Regression: Estimation

Slides:
- day07 Highlights
Lab Notebook:
- day07: Linear Regr. Lab [colab]
- Bishop PRML Ch. 3 Sec. 3.2
--- Bias/Variance tradeoff
Wed 02/15 day08
due on Thu:
- CP1
Notes:
- day08.pdf
Videos:
- day08 part1: Posterior predictive
- day08 part2: Marginal likelihood (Evidence)
- day08 part3: Model selection
- day08 part4: Hyperparameters
Readings:
- Bishop PRML Ch. 3 Sec. 3.3
--- Focus on predictive distribution
- Bishop PRML Ch. 3 Sec. 3.4 and 3.5
--- Focus on model selection and hyperparameter estimation

Bayes Linear Regression: Prediction & Model Selection

Slides:
- day08 Highlights
Math/Concept Exercises:
- day08 Exercises
- Solutions to day08
  
Wed 02/22 day09  
Notes:
- day09.pdf
Videos:
- day09 part1: Discriminative vs Generative models
- day09 part2: Generalized linear models
- day09 part3: Sigmoid function
- day09 part4: Logistic Regression: ML and MAP estimation
- day09 part5: 2nd-order gradient methods for Linear + Logistic
Readings:
- Bishop PRML Ch. 4 Sec. 4.3
--- Focus on linear models for binary and multi-class classification

Generalized Linear Models

Slides:
- day09 Highlights
- Bishop PRML Ch. 4 Sec. 4.2
--- Skim for Understanding generative classification
THU 02/22 day10
due on Thu:
- HW2
Notes:
- day10.pdf
Videos:
- day10 part1: Bayes Logistic Regression
- day10 part2: Laplace approximation in 1-dim and M-dims
- day10 part3: Laplace approx. for Logistic Regr.
- day10 part4: Predictive posteriors for Logistic Regr.
Readings:
- Bishop PRML Ch. 4 Sec. 4.4
--- Try to understand the Laplace approximation
- Bishop PRML Ch. 4 Sec. 4.5
--- Bayesian Logistic Regression

Bayesian Logistic Regression: Posterior and Prediction

Slides:
- day10 Highlights
Lab Notebook:
- day10: Logistic Regr. Lab [colab]
  
Mon 02/27  
Notes:
Videos:

Recap of Unit 2

Slides:
- Unit 2 Review Highlights
Math/Concept Exercises:
- Practice Quiz 2
- Solutions to Practice Quiz 2
  


Unit 3: Sampling and Markov Chain Monte Carlo

Key ideas: Markov chains, revisibility, ergodicity, detailed balance, probabilistic programming

Models: Bayesian logistic regression, general directed graphical models

Algorithms: Metropolis-Hastings algorithm, Gibbs sampling

Math Homework: HW3

Coding Practical: CP3

Date Assigned Do Before Class Class Content Optional
Wed 03/02 day11
due on Thu:
- CP2
Notes:
- day11.pdf
Videos:
- day11 part1: Monte Carlo estimates of expectations
- day11 part2: Graphical models and ancestral sampling
- day11 part3: MCMC Intro, Stationary Distributions, Ergodicity
- day11 part4: Sampling via Inverting the CDF
- day11 part5: Transformations of Sampled Variables
Readings:
- Bishop PRML Ch. 11 Sec. 11.1
--- Focus on basic methods using transformed uniform r.v. in 11.1.1
--- Skim rejection sampling in 11.1.2
--- Skim importance sampling in 11.1.4
- Bishop PRML Ch. 11 Sec. 11.2
--- Focus on the overview section and 11.2.1 Markov chains

Sampling Methods and Markov Chain Monte Carlo

Slides:
- day11 Highlights
Math/Concept Exercises:
- day11 exercises
- day11 solutions
- Sec 11.1 - 11.3 of Art Owen's MCMC Chapter
--- More technical treatment of stationary distributions
Mon 03/06 day12  
Notes:
- day12.pdf
Videos:
- day12 part1: Markov Transitions via Accept/Reject
- day12 part2: Random Walk Proposals
- day12 part3: Detailed Balance
- day12 part4: Metropolis and Metropolis-Hastings
Readings:
- Bishop PRML Ch. 11 Sec. 11.2.2
--- Focus on Metropolis-Hastings

Random Walks and Metropolis-Hastings Algorithm

Slides:
- day12 Highlights
Math/Concept Exercises:
- day12 exercises
- day12 solutions
Lab Notebook:
- day12: MCMC [colab]
  
Wed 03/08 day13
due on Thu:
- HW3
Notes:
- day13.pdf
Videos:
- day13 part1: Overview of Sampling Vectors
- day13 part2: Pro/con: Gibbs vs. Random Walk
- day13 part3: Gibbs Sampling Algorithm
- day13 part4: Proof: Why Gibbs sampling works
Readings:
- Sec. 11.3 'Gibbs sampling' Bishop PRML Ch. 11

Gibbs Sampling

Slides:
- day13 Highlights
Lab Notebook:
- day13: Gibbs Sampling for MVGaussian [colab]
  
Mon 03/13 day14  
Videos:
- Prob. Prog. with PyMC3 by Dr. C. Fonnesbeck
Readings:
- Salvatier et al. PeerJ CS 2016
--- Read thru Case Study 1

Probabilistic Programming

Slides:
- day14 Highlights
Lab Notebook:
- day14: Demo of PyMC4 [colab]
- Bonus Demo of PyStan [colab]
- Carpenter et al. 2015
--- Skim, focus on examples
Wed 03/15
due on Thu:
- CP3
  

Recap Unit 3 & Project Launch

Slides:
- Unit 3 Recap
- Project Overview
Math/Concept Exercises:
- PracticeQuiz3
- PracticeQuiz3 solutions
  
Mon 03/20     <<-- SPRING BREAK -->>  
Wed 03/22     <<-- SPRING BREAK -->>  


Unit 4: Clustering, Mixture Models, and E-M

Key ideas: coordinate ascent optimization, expectation-maximization (E-M) methods, local optima, entropy, KL divergence

Models: Mixture models with Gaussian emissions

Algorithms: k-means, EM for GMMs, gradient descent for GMMs

Math Practice: HW4

Coding Practice: CP4

Date Assigned Do Before Class Class Content Optional
Mon 03/27 due Mon: Project Team Form
Notes:
- day15.pdf
Videos:
- kmeans part1: Clustering overview
- kmeans part2: K-means problem & cost function
- kmeans part3: K-means algorithm
- kmeans part4: Convergence & local optima
- kmeans part5: How to pick K?
Readings:
- Bishop PRML Ch. 9 Sec. 9.1

K-Means clustering

Slides:
- K-Means Highlights
Math/Concept Exercises:
- day15 exercises
- day15 solutions
  
Wed 03/29
out:
- HW4
Notes:
- day16.pdf
Videos:
- gmm part1: Why mixtures?
- gmm part2: GMMs with and without assignments
- gmm part3: Posterior over assignments
- gmm part4: ML for GMMs (plus log-sum-exp trick)
- gmm part5: Problems with ML
Readings:
- Bishop PRML Ch. 9 Sec. 9.2 - 9.2.1
--- GMMs in depth
- Bishop PRML Ch. 2 Sec. 2.3.9
--- Motivation for Gaussian mixtures

Gaussian mixture models

Slides:
- GMM Highlights
  
Mon 04/03  
Notes:
- day17.pdf
Videos:
- day17 part1: Penalized ML for GMM
- day17 part2: Gradient descent for GMM
- day17 part3: Coord. descent for GMMs
- day17 part4: EM for GMM
Readings:
- Bishop PRML Ch. 9 Sec. 9.2.2, 9.3.1, and 9.3.2

How to train GMM

Slides:
- day17 Highlights
  
Wed 04/05 due on Thu: HW4
Notes:
- day18.pdf
Videos:
- day18 part1: GMM recap
- day18 part2: GMMs with assignments
- day18 part3: Expected complete likelihood
- day18 part4: Lower bound of incomplete likelihood
- day18 part5: EM as coord. ascent
Readings:
- Bishop PRML Ch. 9 Sec. 9.3 and 9.4

EM for GMM

Slides:
- EM for GMM Highlights
- Background on entropy: Sec. 1.6 of Bishop PRML Ch. 1
- Background on KL divergence: Sec. 1.6.1 of Bishop PRML Ch. 1

Unit 5: Time series, sequential data, and HMMs

Key ideas: dynamic programming, joint MAP vs. marginal MAP

Models: Hidden markov models

Algorithms: forward-backward algorithm, Viterbi algorithm, variational inference, belief propagation

Math Practice: HW5

Coding Practice: CP5

Date Assigned Do Before Class Class Content Optional
Mon 04/10 due Tue: Initial Report
Notes:
- day19.pdf
Videos:
- day19 part1: Sequential Data in discrete time
- day19 part2: Markov assumption
- day19 part3: Markov model for sequences
- day19 part4: Hidden Markov model
Readings:
- Bishop PRML Ch. 13 Sec. 13.1 Markov models
- Bishop PRML Ch. 13 Sec. 13.2 Hidden Markov models
--- Only the intro before 13.2.1

Markov models and HMM

Slides:
- day19 Highlights
  
Wed 04/12 due on Thu: CP4
Notes:
- day20.pdf
Videos:
- day20 part1: HMM estimation
- day20 part2: Expected log lik for HMM
- day20 part3: M-step
- day20 part4: E-step overview
- day20 part5: E-step: forward/backward alg.
Readings:
- Bishop PRML Ch. 13 Sec. 13.2.1 'Maximum likelihood for the HMM'
- Bishop PRML Ch. 13 Sec. 13.2.2 'Forward-backward algorithm'
- Bishop PRML Ch. 13 Sec. 13.2.4 'Scaling factors'
--- Think about numerical stability of calculations

EM for HMM

Slides:
- EM for HMM Highlights
  
Mon 04/17    
<<-- NO CLASS -->>
- Patriots day
  
Wed 04/19 due on Thu: HW5  
<<-- NO CLASS -->>
- makeup day
  
Fri 04/21    

UNIT 4 REVIEW

Slides:
- Unit 4 Recap
Math/Concept Exercises:
- PracticeQuiz4
- PracticeQuiz4 solutions
  
Mon 04/24 Quiz4 in-class
Notes:
- day21.pdf
Videos:
- day21 part1: Inferring hidden states
- day21 part2: Most likely states problem
- day21 part3: Intuition
- day21 part4: Viterbi algorithm
Readings:
- Bishop PRML Ch. 13 Sec. 13.2.5 'The Viterbi Algorithm'
- Bishop PRML Ch. 13 Sec. 13.2.6 'Extensions to the HMM'

Virterbi for HMM

Slides:
- Viterbi for HMM Highlights
  
Wed 04/26
due on Thu:
- CP5
  

UNIT 5 REVIEW

Slides:
- Unit 5 Recap
Math/Concept Exercises:
- PracticeQuiz5
- PracticeQuiz5 solutions
  
Mon 05/01 Quiz5 in-class  

COURSE RECAP

Slides:
- Course Recap
  
Thu 05/11 due: Final Report