Probabilistic Machine Learning (Spring 2025)
Homeworks
- Assignment 1
- Assignment 2
- Assignment 3
- Q2: To implement collapsed-Gibbs sampler, refer to Normal-Wishart (Section 8) on Kevin Murphy’s Conjugate Bayesian Analysis of the Gaussian distribution.
- Q3: Refer to Chapter 8 of PML2 regarding the details of Kalman filter.
- Problem 1 solution; notebook for Q1; notebook for Q2.
- Problem 2 solution; notebook for Q1; reproduced figure 2
Course Schedule
Jan 21: Overview; condensed PDF slides; Python primer.
Jan 23: Probability and Bayes; condensed PDF slides; sampling.ipynb.
Jan 28 Part 1: Optimization and Sampling; condensed PDF slides; optimization.ipynb.
Jan 28 Part 2: Directed Graphical Models; condensed PDF slides.
Jan 30: Hidden Markov models and forward pass (PML2 9.1-9.2); forward.ipynb.
Feb 4: HMM backward pass and parameter estimation (PML2 9.1-9.2); Kalman filter (PML2 8.1-8.2). forward_backward.ipynb.
Feb 6: Intro to phylogenetics; Felsenstein.ipynb.
Feb 11: EM algorithm and Gaussian mixture model. GMM.ipynb.
Feb 13: Factor graph and sum-product algorithm.
Feb 18: Sequential Importance Sampling and Bootstrap Particle Filter. smc.ipynb.
Feb 20: Discussion of On-line inference for hidden Markov models via particle filters. Slides.
Feb 25: Markov chain Monte Carlo methods. Slides.
Feb 27: Discussion of Markov Chain Sampling Methods for Dirichlet Process Mixture Models. Slides.
Mar 4: Discussion of HW1 and HW2.
Mar 6: Hamiltonian Monte Carlo. Slides.
Mar 11-13: Spring break (no classes).
Mar 18: Variational Inference basics: KL divergence, mean-field VI, coordinate ascent VI with Gaussian mixture model example. Notes.
Mar 20: Class cancelled.
Mar 25: Stochastic VI: REINFORCE, Reparameterization trick, variational auto-encoder with MNIST example. Slides; VAE notebook.
Mar 27: SVI with Pyro. Slides; Bayesian linear regression example.
Apr 1: Discussion.
Paper presentations
Apr 3: Strong and Precise Modulation of Human Percepts via Robustified ANNs.
Apr 8: Efficient Training of Probabilistic Neural Networks for Survival Analysis.
Apr 10: Physics-informed machine learning.
Apr 15: Probabilistic Forecasting for Dynamical Systems with Missing or Imperfect Data.
Apr 17: Invariant Face and Object Recognition in the Visual System.
Apr 22: Machine Learning in Genome-Wide Association Studies.
Apr 24: Detecting single-nucleotide polymorphism by single-nucleotide polymorphism interactions in rheumatoid arthritis using a two- step approach with machine learning and a Bayesian threshold least absolute shrinkage and selection operator (LASSO) model.
Apr 30: Class cancelled.
May 1: A Task-Optimized Neural Network Replicates Human Auditory Behavior, Predicts Brain Responses, and Reveals a Cortical Processing Hierarchy.