Probabilistic Machine Learning for Scientific Discovery

As machine learning is increasingly applied in science and engineering, there is a growing need for methods that can model complex data assumptions, quantify uncertainty, and make reliable predictions and decisions. Probabilistic machine learning provides a principled framework for addressing these challenges. This course covers foundational and recent developments in probabilistic machine learning, including generative modeling, uncertainty quantification, sampling, and optimization. We will also survey research papers and their applications to scientific domains, such as chemistry, materials science, and physics. The course culminates in a research project inspired by a scientific application of probabilistic machine learning.

The requirements are in-class paper presentations, weekly reader reports, and several homework assignments. All written work should be prepared in LaTeX and should be your own words (not from AI or another person). Written assignments will also be a chance to practice your writing skills; see below for additional resources.

Participation — 20%

You will present one or more papers in class, depending on enrollment. Presentations should include some background and an introduction to the key methodological or scientific problem, a breakdown of the approach, a summary of results, and future research questions. If you are not presenting, you are expected to participate in paper discussions.

Homework — 20%

There will be several short homework assignments throughout the course.

Readings — 20%

Each week, you will hand in a (at most) 2 page reader report on the readings. Provide a 1--2 sentence summary of the readings, the main points from the paper(s), any limitations or extensions you see for the paper(s), and your impressions of the readings. Reader reports will be due in class each Thursday.

Final project — 40%

This will involve developing and using probabilistic machine learning, motivated by a real-world scientific problem (e.g., astrophysics, biology, chemistry, engineering, or neuroscience). The project will be broken down into Proposal (10%), Final Report (15%), and Final Presentation (15%).

Textbooks

• Murphy. Probabilistic Machine Learning: An Introduction.
• Murphy. Probabilistic Machine Learning: Advanced Topics.
• Bishop. Deep Learning.
• Nocedal and Wright. Numerical Optimization.
• Garnett. Bayesian Optimization.
• Hennig, Osborne, and Kersting. Probabilistic Numerics.
• Gelman et al. Bayesian Data Analysis.

Research

• Mitzenmacher. How to Read a Paper.
• Gopen and Swan. The Science of Scientific Writing.
• McConnell. Defining Effective Scientific Presentations.