CS 274A: Syllabus and Schedule, Winter 2025

Note: dates and topics may change slightly during the quarter, but the overall syllabus should remain largely the same.

• Week 1: January 6th
  • Probability Review: random variables, conditional and joint probabilities, Bayes rule, law of total probability, factorization. Sets of random variables, the multivariate Gaussian model. Conditional independence and graphical models.


• Week 2: January 13th
  • Learning from Data: Concepts of models and parameters. Definition of the likelihood function and the principle of maximum likelihood.
  • Maximum Likelihood Learning: Maximum likelihood for Gaussian models, binomial, multivariate and other parametric models.


• Week 3: January 20th
  • No lecture on Monday (university holiday)
  • Sequence Models: Learning from sequential data. Markov models and related approaches. Connections with language models.


• Week 4: January 27th
  • Lectures cancelled
  
  
• Week 5: Feb 3rd
  • Bayesian Learning: General principles of Bayesian estimation: prior densities, posterior densities, Beta-binomial examples.
  • Bayesian Learning: Comparing point estimates (ML, MAP, MPE) and fully Bayesian approaches. Bayesian analysis of multinomial models and Markov models. Bayesian approaches to multi-arm bandits (in homework).
  
  
• Week 6: Feb 10th
  • Bayesian Learning: Bayesian analysis of Gaussian models. Predictive densities. Bayesian model selection. Approximate Bayesian inference: Laplace, variational, and Monte Carlo methods.
  • Regression Learning: Linear and non-linear (e.g., neural network) models. Probabilistic perspectives on regression. Loss functions. Parameter estimation methods for regression.


• Week 7: February 17th
  • No lecture on Monday (university holiday)
  • Midterm Exam during Wednesday's class
  
  
• Week 8: February 24th
  • Regression Learning: Bayesian approaches to regression. The bias-variance trade-off for squared error and regression.
  Classification Learning: Likelihood-based approaches and properties of objective functions. Connections between regression and classification. Logistic regression and neural network classifiers.
  
  
• Week 9: March 3rd
  • Classification Learning: Decision boundaries, discriminant functions, optimal decisions, Bayes error rate.
  • Mixture Models and EM: Finite mixture models. The EM algorithm for learning Gaussian mixtures.
  
  
• Week 10: March 10th
  • Mixture Models and EM: Properties of the EM algorithm. Relation of K-means clustering to Gaussian mixture modeling. Mixtures for discrete and non-vector data.
  • Additional topics: (time-permitting) latent variable models, temporal models
  
  
• Finals Week:
  • Final exam, Wed March 19th, 10:30am - 12:30pm