Isotropy and Log-Concave Polynomials

Explore the concept of isotropy and log-concave polynomials in this 20-minute IEEE conference talk. Delve into accelerated sampling techniques and high-precision counting of matroid bases. Learn about discrete and continuous distributions, log-concave generating polynomials, and Determinantal Point Processes (DPPs). Discover a new approach combining instant mixing and hierarchical walk, and understand negative dependence properties. Gain insights into converting to isotropic position and consider open questions in this field presented by Nima Anari from Stanford and Michal Derezinski from UC-Berkeley.

Syllabus

Intro
Sampling from discrete distributions
Isotropy for continuous distributions
Isotropy for discrete distributions
Main results
Log-concave generating polynomials
Prior work: Log-concave polynomials
Determinantal Point Processes (DPPs)
Prior work: Sampling from DPP
Distortion-free intermediate sampling beyond DPPS
New approach: Instant mixing + Hierarchical walk
Techniques: Negative dependence properties
Negative dependence for intermediate sampling
Converting to isotropic position
Conclusions and open questions
References