Statistics Archives for Academic Year 2021

The Importance of Being Correlated: Implications of Dependence in Joint Spectral Inference across Multiple Networks

When: Thu, September 9, 2021 - 3:30pm
Where: Kirwan Hall 1308
Speaker: Vincent Lyzinski (UMD) -
Abstract: Spectral inference on multiple networks is a rapidly-developing subfield of graph statistics. Recent work has demonstrated that joint, or simultaneous, spectral embedding of multiple independent networks can deliver more accurate estimation than individual spectral decompositions of those same networks. Such inference procedures typically rely heavily on independence assumptions across the multiple network realizations, and even in this case, little attention has been paid to the induced network correlation in such joint embeddings. Here, we present a generalized omnibus embedding methodology and provide a detailed analysis of this embedding across both independent and correlated networks, the latter of which significantly extends the reach of such procedures. We describe how this omnibus embedding can itself induce correlation, leading us to distinguish between inherent correlation -- the correlation that arises naturally in multisample network data -- and induced correlation, which is an artifice of the joint embedding methodology. We show that the generalized omnibus embedding procedure is flexible and robust, and prove both consistency and a central limit theorem for the embedded points. We examine how induced and inherent correlation can impact inference for network time series data, and we provide network analogues of classical questions such as the effective sample size for more generally correlated data. Further, we show how an appropriately calibrated generalized omnibus embedding can detect changes in real biological networks that previous embedding procedures could not discern, confirming that the effect of inherent and induced correlation can be subtle and transformative, with import in theory and practice.

Probabilistic Record Linkage in Data Integration

When: Thu, September 23, 2021 - 3:30pm
Where: Kirwan Hall 1308
Speaker: Takumi Saegusa (UMD) -
Abstract: There is a growing interest in using multiple-frame surveys in recent years in order to save survey costs and reduce different types of nonsampling errors. Following the pioneering work by Hartley, methods and theories have been developed. A key underlying assumption of current papers on multiple-frame surveys is known domain membership of each unit of the finite population. But this assumption is hardly met in practice. The effect of violation of this critical assumption on finite population inference is not fully understood. We first investigate the effect of misspecification of the domain membership on estimation and variance estimation. We then exploit the recent development of probabilistic record linkage techniques in adjusting for biases due to domain membership misspecification in the finite population inference. We study the properties of the proposed estimators and the associated variance estimators analytically and through Monte Carlo simulations.

Extended Residual Coherence with a Financial Application

When: Thu, September 30, 2021 - 3:30pm
Where: Kirwan Hall 1308
Speaker: Xuze Zhang (UMD) -
Abstract: Nonlinear phenomena in random processes can be modeled by a class of nonlinear polynomial functionals relating input and output. Residual coherence, a variation of the well-known measure of linear coherence, is a graphical tool to detect and select potential second-order interactions as functions of a single time series and its lags. An extension of residual coherence is made to account for interaction terms of multiple time series. The method is applied to analyzing the relationship between the implied market volatility of stock market and commodity market.