The course provides an advanced introduction to
machine learning with emphasis on the Bayesian perspective.
The course is intended for Master's students in physics
as well as AI/computer science students with sufficient mathematical
background. For AI/computer science students it is highly recommended
to take the
course Statistical machine learning prior to this course.
For physics and math students, this course is the followup of the bachelor course Inleiding Machine Learning
Course material: All machine learning material is summarized in these slides.pdf
Format: The course will be weekly sessions, mainly taught by me. Emphasis is on learning the material through written and computer exercises.
Presentation schedule: Note that the schedule may change during the course. Detailed breakdown of the chapters to be presented will be discussed during the course.
Exercises between brackets are important to understand and have solution in the book. They do not count towards the grade.
Week  Topic  Chapter MacKay/Material  Weekly exercises  Computer exercises (hand in before end of course)  
1  36  Probability, entropy and inference  Chapter 2 Exercises 2.4, 2.6 + continued, 2.7, 2.8 to be discussed in the class. 
Exercises: 2.10, 2.14, 2.16ab, 2.18, 2.19, 2.26  
2  37  More about inference Model comparison and Occam's raisor 
Chapter 3, Chapter 28 Exercises: 3.3, 3.4, 3.15 to be discussed in the class. 
Exercises: 3.1, 3.2, 3.5, 3.6, (3.7 if you like) 3.8, 3.9 Exercises: 28.1, 28.2 only for model H_1, (28.3 if you like) 

3  38  Gaussians, Gaussian mixtures, EM, Laplace method  Chapter 20, 21, 22, 24, 27  21.3, 22.4, (22.5), 22.6, 22.7, 22.8a, (22.12), 22.13  
3  39  Gaussians, Gaussian mixtures, EM, Laplace method  Chapter 20, 21, 22, 24, 27  21.3, 22.4, (22.5), 22.6, 22.7, 22.8a, (22.12), 22.13  
4  40  Monte Carlo Methods (1)  29.129.5  29.3 The computer simulations of 29.13, reproducing figs 29.20 29.15 

5  41  Markov processes, ergodicity Monte Carlo Methods (2), HMC MCMC for Perceptron posterior 
29.6,30.1, 30.3 38,39,41 
An example of Baysian inference in perceptron learning using MCMC methods. The files (Matlabfiles and instructions) needed to do this exercise can be found here: [mcmc_mackay.tar.gz].  
42  no class   
6  43  Ising model  31  31.1, 31.3. Extra exercises 29,31  Exercise to compare simulated annealing with iterative improvement on Ising model see: simulated_annealing.zip 
7  44  Variational inference  Chapter 33  Write a computer algorithm that reproduces fig. 33.4 Exercise 33.4  
8  45  Boltzmann Machines and Mean Field theory  Chapter 43 handouts chapter 12 
handouts chapter 2 exercises 1a, 2, 3 
Write a computer program to implement the Boltzmann machine learning rule as given on pg. 21 of chapter 2 . Use N=10 neurons and generate random binary patterns. Use these data to compute the clamped statistics (x_i x_j)_c and (x_i)_c. Use K=200 learning steps. In each learning step use T=500 steps of sequential stochastic dynamics to compute the free statistics (x_i x_j) and (x_i). Test the convergence by plotting the size of the change in weights versus iteration. A much more efficient learning method can be obtained by using the mean field theory and the linear response correction. Build a classifier for the MNIST data based on the Boltzmann Machine as described in 2.5.1 
9  46  Supervised learning: Perceptrons and MultiLayered Perceptrons 
handouts chapter 3 (HKP 5 and 6) 
handouts chapter 3, Ex. 2,3

Write a multilayered perceptron learning algorithm to classify two of the MNIST classes (for instance the 3's against the 7s). Optimize the architecture by varying the number of hidden units and hidden layers. Test different learning methods, such as naive gradient descent, momentum and conjugate gradient descent. Assess the quality of the solution with results reported in the literature. 
10  47  MLPs, Deep networks Sparse regression, Lasso 
Sparse regression computer exercise
 
11  48  Sparse regression. Variational Garrote 

12  49  Discrete time control dynamic programming Bellman equation 
Bertsekas 25, 1314, 18, 2132 (2nd ed.) Bertsekas 25, 1012, 1627, 3032 (1nd ed.) Kappen ICML tutorial 1.2 
Ex: Carry out the calculations needed to verify that J0(1)=2.7 and
J0(2)=2.818 in Bertsekas Example 3.2 on pg. 23 in Copies 1b extra exercise 1, 2a,b  
13  50 
Continuous time control HamiltonJacobiBellman Equation Pontryagin Minimum Principle Stochastic differential equations Stochastic optimal control LQ examples, Portfolio management 
Kappen ICML tutorial 1.3,1.4 
extra exercise 2c,3 

14  51 
Path integral control theory 
Kappen ICML tutorial 1.6 Thijssen, Kappen Kappen, Ruiz 
extra exercise 4 and 5 

15  2  Overview of research at SNN Machine learning  
16  3 
Presentation computer exercises

Examination:
There will be no final examination. The grade will be based on
take home computer exercises