# Advanced machine learning - autumn 2021

## Course information

• Half semester course (6 ec). Course code NWI-NM048B
• Format: Lectures, excercises, computer exercises, student presentations
• For: Master and PhD students in physics or mathematics
• Teacher lectures: Bert Kappen
• Teacher Practicals: Eduardo Dominguez and Federico Stella

This course covers advanced topics in machine learning. The course is intended for Master's students in physics and mathematics. This course is the follow-up of the course Machine Learning

Format: The course will be weekly sessions. Emphasis is on learning the material through mathematical derivation and computer exercises.

Course material: The course uses the following material:

 Week Topic Material Exercises 1 45 Monte Carlo Methods (1) Sampling means and variance, uniform sampling, sampling from multi variate Gaussian, importance sampling, rejection sampling MK chapter 29.1-29.5BRML chapter 27 BRML exercise 27.1. Box-Muller method (3)MK exercise 29.3. Show diffusion scales as sqrt(T) (1)MK exercise 29.13. Importance sampling of one Gaussian with another (only the computer simulations, reproducing figs 29.20) (3) 2 46 Monte Carlo Methods (2)Markov processes, ergodicity, Metropolis Hasting algorithm, Gibbs sampling, Hamilton Monte Carlo MK chapter 29.6 MK chapter 30.1, 30.3 handouts chapter 1 MK exercise 29.15. Gibbs sampling of posterior over mu, sigma given data (5). Hint: It is recommended to sample beta = 1/sigma^2 rather than sigma^2. But be aware that such a transformation affects the prior that you assume. For instance, if you assume a flat prior over sigma^2, this transforms to a non-flat prior over beta. For this exercise choose the prior over beta as 1/beta. This choice corresponds to a so-called non-informative prior that is flat in the log(sigma) domain. See also slides lecture 3 where we consider the variational approximation for this problem. (5) MCMC exercises (10) 3 47 The Ising modelPhase transitions, critical slowing down, frustration, transfer matrix method discrete optimization with simulated annealing. MK chapter 31 Further reading: HKP appendix A, Sandvik 2018 section 5 SoKal 1999: Critical slowing down Aarts and Korst, Simulated Annealing and Boltzmann Machines 1989 MK exercise 31.1. Relation entropy and free energy (2) Simulated annealing exercise on spin glass (10) 4 48 Deterministic approximate inference for Bayesian posterior Laplace approximation Variational approximation MK chapter 33.1, 33.4, 33.5Further reading: Barber Bishop 1998, Ensemble Learning in Bayesian Neural Networks Consider again the perceptron learning problem of Mackay chapter 39 and 41, for which we computed the posterior by sampling in week 2. This time, compute p(t=1|x,D,alpha) using the Laplace approximation and reproduce Mackay figure 41.11b.(7) 5 49 Deterministic approximate inference for the Ising model Mean field approximation Linear response correction, TAP SK model Belief propagation MK 33.2, 33.3, BRML chapter 28.7 Further reading: Kappen, Spanjers, Mean field theory for asymmetric neural networks (1999), Physical Review E, 61:56585663. MF and BP in Ising model exercise (10) 6 50 Deterministic approximate inference for the Ising model Convergence of BP, Factor graph version of BP, max-product BP, Applications of BP for compressed sensing and clustering Further reading: Mooij, Kappen. Sufficient conditions for convergence of the sum-product algorithm (2007). IEEE Information Theory, 53:44224437 7 51 The statistical physics approach to machine learning The replica symmetric solution for the SK model The cavity method Analysis of compressed sensing and random satisfiability using replica method and message passing algorithms Further reading: Sherrington, D. and Kirkpatrick, S. (1975). Solvable model of Spin-Glass. Physical review letters, 35:17921796. Kappen, H.J. An introduction to stochastic neural networks, in: Handbook of biological physics 2001, 517-552. pdf Reproduce the phase plot of the SK model in the replica symmetric approximation replica_SK.pdf (7) 8 5 The Boltzmann Machine MK chapter 43 handouts chapter 1-2 Boltzmann Machine Learning (10) Here are the salamander retina data. 9 6 Student presentations Dirk, Ilja, Luc. Generative Adversarial Networks 10 7 Student presentations Wenhao, Yangchu, Casper. Autoregessive variational inference 11 8 Student presentations Andrea, Santiago Markov processes on speech recognition and biological sequences Lauren, Caroline, KasperRecurrent neural networks for speech recognition 12 10 Student presentations Steffen, Rao, Stijn Dimension reduction methods Niels, Tomas, ThaliaGaussian processes 13 11 Student presentations Dirren, Olivier, MatthijnsDimension reduction methods Maksim, Mats, Bruno Model comparison 14 12 Student presentations Shakeeb, Andre, Leo Neural data analysis and anaestesia Research overview Quantum Machine Learning Atomic BMs Approximate quantum inference Medical expert system (Promedas) Disaster Victim Identification (Bonaparte)

Each exercise counts for a number of points, indicated between brackets. The total number of points for the exercises is 68. For each exercise, hand in the code that can be run stand-alone. For the large (10 point) exercises, write a report:

All assignments of lectures 1-6 should be handed in before the end of January 2022. The assignments of lecture 7-9 should be handed in before end March 2022.

In addition to the exercises, your group should prepare a 45 minute presentation on a modern topic in machine learning. There are 8 suggestions for
student presentations but your group can also suggest another topic. The topic of your group presentation and preferred time slot (max 4 presentations per week, in weeks 5 to 10 in 2022) should be sent to me before the end of the year. The student presentation counts for 20 points.