Benedict H. W. Wong | Searcharxiv

arXiv2026

Understanding Circulant Permutation to Extend the CMinHash Estimator

CMinHash promises a new direction for designing MinHash algorithms with reduced variance and storage space via circulant permutations. However, the original variance analysis is difficult to extend to other MinHash estimators. We present a new approach that gives explicit and easily comparable approximate variance expressions, and use it to analyze the Minner estimator. Numerical experiments show that our variance expression matches the empirical mean square error (MSE) of estimates. Our work thereby demonstrates how to apply circulant permutation to other MinHash estimators and compute their approximate variance.

stat.ML↗

arXiv2026

It's all In the (Exponential) Family: An Equivalence between Maximum Likelihood Estimation and Control Variates for Sketching Algorithms

Maximum likelihood estimators (MLE) and control variate estimators (CVE) have been used in conjunction with known information across sketching algorithms and applications in machine learning. We prove that under certain conditions in an exponential family, an optimal CVE will achieve the same asymptotic variance as the MLE, giving a fixed point algorithm for the MLE. Experiments show the fixed point algorithm is faster and numerically stable compared to other root finding algorithms for the MLE for the bivariate Normal distribution, and we expect this to hold across distributions satisfying these conditions. We show how this algorithm leads to reproducibility for algorithms using MLE / CVE, and demonstrate how the algorithm leads to finding the MLE when the CV weights are known.

stat.ML↗

arXiv2018

A general approach to detect gene (G)-environment (E) additive interaction leveraging G-E independence in case-control studies

It is increasingly of interest in statistical genetics to test for the presence of a mechanistic interaction between genetic (G) and environmental (E) risk factors by testing for the presence of an additive GxE interaction. In case-control studies involving a rare disease, a statistical test of no additive interaction typically entails a test of no relative excess risk due to interaction (RERI). It is also well known that a test of multiplicative interaction exploiting G-E independence can be dramatically more powerful than standard logistic regression for case-control data. Likewise, it has recently been shown that a likelihood ratio test of a null RERI incorporating the G-E independence assumption (RERI-LRT) outperforms the standard RERI approach. In this paper, the authors describe a general, yet relatively straightforward approach to test for GxE additive interaction exploiting G-E independence. The approach which relies on regression models for G and E is particularly attractive because, unlike the RERI-LRT, it allows the regression model for the binary outcome to remain unrestricted. Therefore, the new methodology is completely robust to possible mis-specification in the outcome regression. This is particularly important for settings not easily handled by RERI-LRT, such as when E is a count or a continuous exposure with multiple components, or when there are several auxiliary covariates in the regression model. While the proposed approach avoids fitting an outcome regression, it nonetheless still allows for straightforward covariate adjustment. The methods are illustrated through an extensive simulation study and an ovarian cancer empirical application.

stat.ME↗