Iterative Methods and High-Dimensional Statistics
summary
Proposes a Hamiltonian composite sampler that expands parameter space to make composite Langevin sampling stable and matches structured targets (box constraints, finite sums), claiming provable closeness to the original density and practical alternation schemes. For list-decodable mean estimation, gives a concise polynomial-time algorithm that is information-theoretically near-optimal, then speeds it to nearly linear time with polylog KPCA via new fast SDP reductions and specialized high‑moment regret bounds; implementations report the approach works end‑to‑end.
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chapters (10)
- 0:00Intro
- 0:50My research goal
- 1:42Techniques
- 3:07Composite logconcave sampling
- 4:23Idea 1: Proximal methods
- 6:03Idea II: Hamiltonian methods
- 7:22List-decodable mean estimation
- 9:02Applications
- 9:17Idea I: geometry of mixture models
- 10:15Idea II: novel fast SDP solvers
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