CS 57800 Statistical Machine Learning, Fall 2026

Description: This graduate course develops the mathematical foundations of statistical machine learning, with statistical reasoning and probabilistic inference as recurring themes. Modern AI systems can often produce predictions or implement standard learning algorithms automatically. The harder questions are what those predictions mean, whether they are supported by the available data, which assumptions and approximations they rely on, and when they may fail. Accordingly, this offering is theory-focused: rather than presenting a catalog of methods, it develops a mathematical account of four questions that recur throughout modern machine learning:

• Generalization: What conclusions about an unknown population are justified by finitely many samples, and what cannot be learned without additional assumptions?
• Inference: How can predictions, latent structure, and marginal probabilities be computed or approximated in structured probabilistic models?
• Generation: How can we sample from a complicated learned distribution, and how do estimation, mixing, and discretization errors affect the result?
• Reliability: How are learning guarantees affected by approximation, distribution shift, privacy constraints, objective misspecification, or adversarial modification?

These questions organize the course into six connected units: statistical learning theory; unsupervised and latent-variable learning; probabilistic inference and statistical physics; diffusion-model theory; modern neural-network theory; and trustworthy machine learning. Students will also read selected research papers to see how these ideas are applied, tested, and extended in current research.

Time/Location: MWF 1:30 PM - 2:20 PM at LWSN B155

Instructor: Ruizhe Zhang Office hours: M 10:30 AM - 11:30 AM at DSAI 1119B

Teaching Assistants: Shreya Nasa (Office hours: Th 9:00 AM - 10:00 AM at DSAI B061), Yucheng Zhang (Office hours: Th 3:00 PM - 3:30 PM at DSAI B061)

Course policy: See syllabus for detailed overview.

Suggested projects list: See [link].