My top picks, with links if you want to tag along:
- Ledoux and Talagrand (available from Talagrand’s webpage). Specifically, the chapters on Rademacher and Gaussian sums, symmetrization and contraction properties, and tail bounds for sums of random vectors. Also the bits on scalar martingale arguments.
- Sourav Chatterjee’s thesis and its matrix counterpart. He came up with a beautiful approach for deriving concentration inequalities from exchangeable pairs which generalizes nicely to the matrix case.
- Plan and Vershynin’s works on one-bit compressed sensing, tessellation for dimension reduction, and sparse logistic regression. I’ve said it before and I’ll say it again: I’m not interested in compressed sensing per se. But the concentration and geometric techniques they use are both beautiful and useful, and I’m interesting in learning them.
- Robust computation of linear models, or How to find a needle in a haystack. Robust PCA is more interesting than compressed sensing, but again I’m most interested in the tools here.
- Candes et al.’s paper on subspace clustering. Interesting problem and interesting geometric tools.