Large-Scale Multiple Testing of Composite Null Hypotheses Under Heteroskedasticity

Heteroskedasticity poses several methodological challenges in designing valid and powerful procedures for simultaneous testing of composite null hypotheses. In particular, the conventional practice of standardizing or re-scaling heteroskedastic test statistics in this setting may severely affect the power of the underlying multiple testing procedure. Additionally, when the inferential parameter of interest is correlated with the variance of the test statistic, methods that ignore this dependence may fail to control the type I error at the desired level. We propose a new Heteroskedasticity Adjusted Multiple Testing (HAMT) procedure that avoids data reduction by standardization, and directly incorporates the side information from the variances into the testing procedure. Our approach relies on an improved nonparametric empirical Bayes deconvolution estimator that offers a practical strategy for capturing the dependence between the inferential parameter of interest and the variance of the test statistic. We develop theory to show that HAMT is asymptotically valid and optimal for FDR control. Simulation results demonstrate that HAMT outperforms existing procedures with substantial power gain across many settings at the same FDR level. The method is illustrated on an application involving the detection of engaged users on a mobile game app

A Locally Adaptive Shrinkage Approach to False Selection Rate Control in High-Dimensional Classification

The uncertainty quantification and error control of classifiers are crucial in many high-consequence decision-making scenarios. We propose a selective classification framework that provides an indecision option for any observations that cannot be classified with confidence. The false selection rate (FSR), defined as the expected fraction of erroneous classifications among all definitive classifications, provides a useful error rate notion that trades off a fraction of indecisions for fewer classification errors. We develop a new class of locally adaptive shrinkage and selection (LASS) rules for FSR control in the context of high-dimensional linear discriminant analysis (LDA). LASS is easy-to-analyze and has robust performance across sparse and dense regimes. Theoretical guarantees on FSR control are established without strong assumptions on sparsity as required by existing theories in high-dimensional LDA. The empirical performances of LASS are investigated using both simulated and real data

A Unified and Optimal Multiple Testing Framework based on rho-values

Multiple testing is an important research direction that has gained major attention in recent years. Currently, most multiple testing procedures are designed with p-values or Local false discovery rate (Lfdr) statistics. However, p-values obtained by applying probability integral transform to some well-known test statistics often do not incorporate information from the alternatives, resulting in suboptimal procedures. On the other hand, Lfdr based procedures can be asymptotically optimal but their guarantee on false discovery rate (FDR) control relies on consistent estimation of Lfdr, which is often difficult in practice especially when the incorporation of side information is desirable. In this article, we propose a novel and flexibly constructed class of statistics, called rho-values, which combines the merits of both p-values and Lfdr while enjoys superiorities over methods based on these two types of statistics. Specifically, it unifies these two frameworks and operates in two steps, ranking and thresholding. The ranking produced by rho-values mimics that produced by Lfdr statistics, and the strategy for choosing the threshold is similar to that of p-value based procedures. Therefore, the proposed framework guarantees FDR control under weak assumptions; it maintains the integrity of the structural information encoded by the summary statistics and the auxiliary covariates and hence can be asymptotically optimal. We demonstrate the efficacy of the new framework through extensive simulations and two data applications

Harnessing The Collective Wisdom: Fusion Learning Using Decision Sequences From Diverse Sources

Learning from the collective wisdom of crowds enhances the transparency of scientific findings by incorporating diverse perspectives into the decision-making process. Synthesizing such collective wisdom is related to the statistical notion of fusion learning from multiple data sources or studies. However, fusing inferences from diverse sources is challenging since cross-source heterogeneity and potential data-sharing complicate statistical inference. Moreover, studies may rely on disparate designs, employ widely different modeling techniques for inferences, and prevailing data privacy norms may forbid sharing even summary statistics across the studies for an overall analysis. In this paper, we propose an Integrative Ranking and Thresholding (IRT) framework for fusion learning in multiple testing. IRT operates under the setting where from each study a triplet is available: the vector of binary accept-reject decisions on the tested hypotheses, the study-specific False Discovery Rate (FDR) level and the hypotheses tested by the study. Under this setting, IRT constructs an aggregated, nonparametric, and discriminatory measure of evidence against each null hypotheses, which facilitates ranking the hypotheses in the order of their likelihood of being rejected. We show that IRT guarantees an overall FDR control under arbitrary dependence between the evidence measures as long as the studies control their respective FDR at the desired levels. Furthermore, IRT synthesizes inferences from diverse studies irrespective of the underlying multiple testing algorithms employed by them. While the proofs of our theoretical statements are elementary, IRT is extremely flexible, and a comprehensive numerical study demonstrates that it is a powerful framework for pooling inferences.Comment: 29 pages and 10 figures. Under review at a journa

Chiral magneto-phonons with tunable topology in anisotropic quantum magnets

We propose a mechanism to obtain chiral phonon-like excitations from the bond-dependent magnetoelastic couplings in the absence of out-of-plane magnetization and magnetic fields. We provide a systematic way to understand the hybrid excitation by its phononic analog, and thus we dub it magneto-phonon. We recognize that the system is equivalent to the class D of topological phonons, and show the tunable chirality and topology by an in-plane magnetic field in the example of a triangular lattice ferromagnet. As a possible experimental probe, we evaluate the phonon magnetization and the thermal Hall conductivity. Our study gives a new perspective on tunable topological and chiral excitations without Dzyaloshinskii-Moriya or Raman spin interactions, which suggests possible applications of spintronics and phononics in various anisotropic magnets and/or Kitaev materials

Upper branch thermal Hall effect in quantum paramagnets

Inspired by the persistent thermal Hall effects at finite temperatures in various quantum paramagnets, we explore the origin of the thermal Hall effects from the perspective of the upper branch parts by invoking the dispersive and twisted crystal field excitations. It is shown that the upper branches of the local energy levels could hybridize and form the dispersive bands. The observation is that, upon the time-reversal symmetry breaking by the magnetic fields, these upper branch bands could acquire a Berry curvature distribution and contribute to the thermal Hall effect in the paramagnetic regime. As a proof of principle, we consider the setting on the kagom\'e lattice with one ground state singlet and an excited doublet, and show this is indeed possible. We expect this effect to be universal and has no strong connection with the underlying lattice. Although the thermal Hall signal can be contributed from other sources such as phonons and their scattering in the actual materials, we discuss the application to the Mott systems with the large local Hilbert spaces

Double exchange, itinerant ferromagnetism and topological Hall effect in moir\'{e} heterobilayer

Motivated by the recent experiments and the wide tunability on the MoTe$_2$/WSe$_2$ moir\'{e} heterobilayer, we consider a physical model to explore the underlying physics for the interplay between the itinerant carriers and the local magnetic moments. In the regime where the MoTe$_2$ is tuned to a triangular lattice Mott insulator and the WSe$_2$ layer is doped with the itinerant holes, we invoke the itinerant ferromagnetism from the double exchange mechanism for the itinerant holes on the WSe$_2$ layer and the local moments on the MoTe$_2$ layer. Together with the antiferromagnetic exchange on the MoTe$_2$ layer, the itinerant ferromagnetism generates the scalar spin chirality distribution in the system. We further point out the presence of spin-assisted hopping in addition to the Kondo coupling between the local spin and the itinerant holes, and demonstrate the topological Hall effect for the itinerant electrons in the presence of the non-collinear spin configurations. This work may improve our understanding of the correlated moir\'{e} systems and inspire further experimental efforts