Computational Statistics seminars

Arka Banerjee introduces k-nearest-neighbor distributions as summaries of cosmological survey data that capture information beyond two-point statistics. They respond to moments of all N-point correlations while retaining a computational cost comparable to two-point measurements. The talk covers auto-correlations and cross-correlations in discrete and continuous datasets, their relationship to other higher-order summaries, and applications that improve detection significance or parameter constraints. It also explores modeling these distributions with methods already successful for two-point functions in real and redshift space.

Locality-sensitive hashing is widely used for high-dimensional nearest-neighbor search. This talk develops another view of hashing as a biased sampling method for density-estimation queries. Given a point set and a query, one may estimate kernel density by summing distance-dependent influence functions, or count points within a chosen radius. A linear scan is costly for large datasets and many queries. The presentation surveys recent methods that preprocess the data and use locality-sensitive hashing to construct unbiased estimators for these problems and their extensions. It covers joint work with Arturs Backurs, Piotr Indyk, Vishnu Natchu, Paris Syminelakis, and Xian (Carrie) Wu.