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Recently, there has been growing concern about heavy‐tailed and skewed noise in biological data. We introduce RobustPALMRT, a flexible permutation framework for testing the association of a covariate of interest adjusted for control covariates. RobustPALMRT controls type I error rate for finite‐samples, even in the presence of heavy‐tailed or skewed noise. The new framework expands the scope of state‐of‐the‐art tests in three directions. First, our method applies to robust and quantile regressions, even with the necessary hyper‐parameter tuning. Second, by separating model‐fitting and model‐evaluation, we discover that performance improves when using a robust loss function in the model‐evaluation step, regardless of how the model is fit. Third, we allow fitting multiple models to detect specialized features of interest in a distribution. To demonstrate this, we introduce DispersionPALMRT, which tests for differences in dispersion between treatment and control groups. We establish theoretical guarantees, identify settings where our method has greater power than existing methods, and analyze existing immunological data on Long‐COVID patients. Using RobustPALMRT, we unveil novel differences between Long‐COVID patients and others even in the presence of highly skewed noise. 

Conformal prediction (CP) is an important tool for distribution-free predictive uncertainty quantification. Yet, a major challenge is to balance computational efficiency and prediction accuracy, particularly for multiple predictions. We propose Leave-One-Out Stable Conformal Prediction (LOO-StabCP), a novel method to speed up full conformal using algorithmic stability without sample splitting. By leveraging leave-one-out stability, our method is much faster in handling a large number of prediction requests compared to existing method RO-StabCP based on replace-one stability. We derived stability bounds for several popular machine learning tools: regularized loss minimization (RLM) and stochastic gradient descent (SGD), as well as kernel method, neural networks and bagging. Our method is theoretically justified and demonstrates superior numerical performance on synthetic and real-world data. We applied our method to a screening problem, where its effective exploitation of training data led to improved test power compared to state-of-the-art method based on split conformal. 

The joint analysis of imaging‐genetics data facilitates the systematic investigation of genetic effects on brain structures and functions with spatial specificity. We focus on voxel‐wise genome‐wide association analysis, which may involve trillions of single nucleotide polymorphism (SNP)‐voxel pairs. We attempt to identify underlying organized association patterns of SNP‐voxel pairs and understand the polygenic and pleiotropic networks on brain imaging traits. We propose abi‐cliquegraph structure (ie, a set of SNPs highly correlated with a cluster of voxels) for the systematic association pattern. Next, we develop computational strategies to detect latent SNP‐voxelbi‐cliquesand an inference model for statistical testing. We further provide theoretical results to guarantee the accuracy of our computational algorithms and statistical inference. We validate our method by extensive simulation studies, and then apply it to the whole genome genetic and voxel‐level white matter integrity data collected from 1052 participants of the human connectome project. The results demonstrate multiple genetic loci influencing white matter integrity measures on splenium and genu of the corpus callosum.