2021-03-02 meeting notes
Warm-up
Consider the equations $\alpha x^2 + \beta x = \gamma$ and the fixed point iteration $\beta x_{k+1} = \gamma - \alpha x_k^2$.
Write an error iteration. Can you give conditions on the coefficients and the initial error that are sufficient to guarantee convergence?
Logistics
- Reaction paper - March 15
- May do in small groups if you want (up to 3)
- Problem spec and some paper pointers online
- SIAM CSE has lots of relevant talks (and often you can chase down pointers)
- Project proposal - March 22
- Again in small groups (1-3)
- Not required to be the same direction as reaction paper
- Use the discussion board to advertise!
Rand NLA comments
- Sketching vs preconditioning
Matrix data
- Matrix data and (approximate) low-rank structure
- Example data: images, docs, graphs, preferences, joint distributions
- Interpretation: latent factors and bilinear maps
- Supervised learning applications
- Imputation and missing data (e.g. collaborative filtering)
- Guided dimension reduction (e.g. linear discriminant analysis)
- Unsupervised learning applications
- k-means clustering as a matrix factorization (and alternating iteration)
- Latent-space embeddings (e.g. LSI)
- Latent Dirichlet Allocation, NMF, and interepretable topic models
- Example: Linear Discriminant Analysis
- Basic setup
- Key numerical issues (robustness and performance)