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Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the…

Computerized Adaptive Testing (CAT) has proven effective for efficient LLM evaluation on multiple-choice benchmarks, but modern LLM evaluation increasingly relies on generation tasks where outputs are scored continuously rather than marked…

This work addresses the problem of conducting valid inference for additive and linear mixed models after model selection. One possible solution to overcome overconfident inference results after model selection is selective inference, which…

We present a systematic algebraic approach for the weak coupling of Cauchy problems to multiple Lohe tensor models. For this, we identify an admissible Cauchy problem to the Lohe tensor (LT) model with a characteristic symbol consisting of…

Hard-threshold estimators are popular in signal processing applications. We provide a detailed study of using hard-threshold estimators for estimating an unknown deterministic signal when additive white Gaussian noise corrupts observations.…

Lagrangian relaxation stands among the most efficient approaches for solving a Mixed Integer Linear Programs (MILP) with difficult constraints. Given any duals for these constraints, called Lagrangian Multipliers (LMs), it returns a bound…

Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives…

This paper considers the problem of robust hypothesis testing under non-identically distributed data. We propose Wald-type tests for both simple and composite hypothesis for independent but non-homogeneous observations based on the robust…

This study compares statistical properties of ARCH tests that are robust to the presence of the misspecified conditional mean. The approaches employed in this study are based on two nonparametric regressions for the conditional mean. First…

Permutation-based partial-correlation tests guarantee finite-sample Type I error control under any fixed design and exchangeable noise, yet their power can collapse when the permutation-augmented design aligns too closely with the covariate…

Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at…

We develop methods for detector learning which exploit joint training over both weak and strong labels and which transfer learned perceptual representations from strongly-labeled auxiliary tasks. Previous methods for weak-label learning…

This paper discusses estimation and limited information goodness-of-fit test statistics in factor models for binary data using pairwise likelihood estimation and sampling weights. The paper extends the applicability of pairwise likelihood…

This paper considers the optimal modification of the likelihood ratio test (LRT) for the equality of two high-dimensional covariance matrices. The classical LRT is not well defined when the dimensions are larger than or equal to one of the…

In this paper, we obtain a new characterization result for symmetric distributions based on the entropy measure. Using the characterization, we propose a nonparametric test to test the symmetry of a distribution. We also develop the…

Certain cancer types, notably pancreatic cancer, are difficult to detect at an early stage, motivating robust biomarker-based screening. Liquid biopsies enable non-invasive monitoring of circulating biomarkers, but typical machine learning…

A stochastic linear quadratic (LQ) optimal control problem with a pointwise linear equality constraint on the terminal state is considered. A strong Lagrangian duality theorem is proved under a uniform convexity condition on the cost…

Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with…

Despite the non-convexity of most modern machine learning parameterizations, Lagrangian duality has become a popular tool for addressing constrained learning problems. We revisit Augmented Lagrangian methods, which aim to mitigate the…

We propose a novel weakly supervised discriminative algorithm for learning context specific registration metrics as a linear combination of conventional similarity measures. Conventional metrics have been extensively used over the past two…