Computational Statistics seminars

A major challenge for causal inference from time-series data is the trade-off between computational feasibility and accuracy. Motivated by process motifs for lagged covariance in an autoregressive model with slow mean-reversion, we propose to infer networks of causal relations via pairwise edge measure (PEMs) that one can easily compute from lagged correlation matrices. Motivated by contributions of process motifs to covariance and lagged variance, we formulate two PEMs that correct for confounding factors and for reverse causation. To demonstrate the performance of our PEMs, we consider network interference from simulations of linear stochastic processes, and we show that our proposed PEMs can infer networks accurately and efficiently. Specifically, for slightly autocorrelated time-series data, our approach achieves accuracies higher than or similar to Granger causality, transfer entropy, and convergent crossmapping -- but with much shorter computation time than possible with any of these methods. Our fast and accurate PEMs are easy-to-implement methods for network inference with a clear theoretical underpinning. They provide promising alternatives to current paradigms for the inference of linear models from time-series data, including Granger causality, vector-autoregression, and sparse inverse covariance estimation.

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.