(Tentative; we will flexibly change the contents.)
1. Course guidance and introduction to unsupervised learning
2. Principal components analysis (PCA) and SVD, linear autoencoder
3. k-means clustering and Gaussian mixture model, EM algorithms
4. Probbabilistic interpretations of PCA and mixture models
5. Manifold learning (Isomap, Laplacian Eigenmaps, t-SNE, UMAP)
6. Unsupervised learning of dynamical systems
7. Autoencoders
8. Autoregressive generative models
9. Normalizing flows
10. Generative adversarial networks, energy-based models, etc.
11. Diffusion models, score-based models
12, 13 Student presentations