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.

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.