统计学

How many key-value associations can a $d\times d$ linear memory store? We show that the answer depends not only on the $d^2$ degrees of freedom in the memory matrix, but also on the retrieval criterion. In an isotropic Gaussian model for…

Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…

Uncertainty quantification for individual treatment effects (ITEs) is a daunting challenge in causal inference. Motivated by recent advances in conformal prediction, several works aim to construct distribution-free prediction sets for ITEs…

Hypergraphs model higher-order interactions, but realistic hypergraph generation remains difficult because incidence, hyperedge-size heterogeneity, and overlap structure are not faithfully captured by pairwise reductions. We propose \HEDGE,…

Regionalization aims to partition a spatial domain into contiguous regions that share similar characteristics, enabling more effective spatial analysis, policy making, and resource management. Existing approaches for spatial regionalization…

We propose a high-dimensional white noise test that captures serial correlations within and across component series without specifying an alternative model. The test statistic is a U-statistic based on sample autocovariances. Under the…

Sea surface temperature (SST) is a fundamental determinant of global climate dynamics and economic activity. Reliable projections of future SST patterns depend critically on a rigorous characterization of the underlying spatial random…

The standard constraint-based paradigm for causal discovery with incomplete data -- impute first, test second -- is frequently miscalibrated: any consistent conditional independence (CI) test rejects a true null with probability approaching…

Protecting confidential data while preserving utility is particularly challenging when data sets contain outlying observations. Existing latent space anonymization methods, such as spectral anonymization (SA), rely on principal component…

Large-scale population-level datasets, such as the UK Biobank and the All of Us Research Program, often lack covariates needed for a specific analysis, such as genetic or lifestyle measures, while related studies measure them. This creates…

High-dimensional neuroimaging and spatiotemporal blocks often contain structured missingness from acquisition artifacts, preprocessing failures, and sensor dropout. Multiple imputation propagates uncertainty, but fully conditional…

Causal discovery methods such as LiNGAM identify causal structure from observational data by assuming mutually independent disturbances. This assumption is fragile: shared volatility, common scale effects, or other forms of dependence can…

The role of the microbiome in disease pathogenesis is an emerging field with strong evidence suggesting that dysbiosis is associated with precancerous and cancerous states. Microbiome data present substantial challenges for causal mediation…

We introduce a simple yet powerful framework for training large language models. In contrast to the standard autoregressive next-token prediction based on an exact prefix, we propose a perturbation-based procedure that first transforms the…

We provide a theoretical analysis of Adam under non-stationary stochastic objectives, separating two regimes: Euclidean tracking under adaptive strong monotonicity of the Adam-preconditioned mean-gradient operator, and high-probability…

Many machine learning problems involve data supported on curved spaces such as spheres, rotation groups, hyperbolic spaces, and general Riemannian manifolds, where Euclidean geometry can distort distances, averages, and the resulting…

Zero-inflated outcomes, where responses are zero with positive probability and otherwise continuous, are common in biomedical, environmental, and social science studies. We propose a conformal prediction based framework that provides…

In phase I dose escalation studies for dual-agent combinations, at least one drug often has an established monotherapy dose. Consequently, substantial prior clinical safety data often exist for one or more monotherapies, allowing the study…

Fine particulate matter (PM$_{2.5}$) concentration data are positive, right-skewed series that arise naturally in environmental monitoring and are well described by the Birnbaum-Saunders (BS) distribution. In this paper, we propose a…

We study contextual dynamic pricing under a semiparametric demand model in which the purchase probability is $1-F(p-m(\mathbf{x}))$, where $m(\mathbf{x})$ captures mean utility as a function of product features and buyer covariates, and $F$…