Statistical Methods and Inference

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• Conformal Prediction under Exponential-Tilt Joint Shift

  Seungjin Choi · 28 septembre 2026

  Conformal prediction can lose coverage when the data distribution changes after deployment. We study adaptation using labeled source data and unlabeled target inputs, allowing both the input distribution and its relationship with outcomes to change. We use Exponential Tilt Reweighting Alignment (ExT…

• Missingness-Aware Conformal Prediction Under Cross-Hospital Distribution Shift

  Liang You, Dongwen Ou, Hengyu Shi, Siyuan Dai · 28 septembre 2026

  Clinical measurements are recorded for some patients but not others, at rates that differ across hospitals, and marginal conformal coverage does not ensure coverage within groups defined by missingness. We propose a missingness-aware conformal calibration procedure for mortality prediction under cro…

• Sufficiently Reduced Distributional Regression

  Alexander Henzi, Tiange Liu, Xinwei Shen · 25 septembre 2026

  We propose Sufficiently Reduced Distributional Regression (SRDR), a generative method that combines conditional distribution estimation with nonlinear sufficient dimension reduction (SDR). It builds on a characterization of sufficiency through strictly proper scoring rules: a dimension reduction is …

• Common Covariance Geometry and Certification for Brownian Kernel Ladders

  Mahdi Mohammadigohari · 25 septembre 2026

  A representation-adaptive kernel class produces, on a fixed sample, a union of reproducing-kernel Hilbert-space ellipsoids rather than one ellipsoid. We introduce the minimum-trace common covariance that dominates the unrestricted empirical union generated by Brownian kernel ladders and develop its …

• Conformal Bayes under Continuous Label Shift: Sensitivity Analysis and the Limits of Exact Validity

  Seungjin Choi · 24 septembre 2026

  Conformal Bayes combines Bayesian posterior predictive scores with conformal calibration, but under continuous label shift both the score and calibration weight depend on the unknown response-marginal density ratio. Existing methods typically estimate one shift parameter from pseudo-labels or predic…

• Multitask Regression with Pairwise Fusion

  Xiaodong Li, Zhentao Li · 24 septembre 2026

  We study multitask regression when coefficient sharing can differ by predictor. For a given predictor, many tasks may have the same coefficient while a few differ, and the exceptional tasks need not be the same for another predictor. We describe this structure by two quantities: the number of active…

• CVaR anchor regression protects against rare shifts

  Malte Londschien · 24 septembre 2026

  We study prediction in new environments when training data contain rare, large shifts. Anchor regression penalizes the average of the squared mean residual across environments. It protects against shifts in an ellipsoid determined by the second moment of the training shifts. Covering rare shifts may…

• CS-WCP: Robust Conformal Sets for LLM-Judge Traffic Shifts with Uncertain Group Proportions

  Ibne Farabi Shihab, Fariya Afrin · 24 septembre 2026

  Prediction sets built from an LLM judge can undercover when deployment traffic changes the prevalence of task or policy groups. Weighted conformal prediction is exact under covariate shift when the density ratio is known, but group proportions must usually be estimated from finite unlabeled samples.…

• Tail-Aware Geometry Learning for Conformal Ellipsoids

  Xiang Zhang · 24 septembre 2026

  This paper studies multivariate conformal prediction (CP), a distribution-free uncertainty quantification framework with finite-sample coverage guarantees. The efficiency of multivariate prediction sets hinges critically on the residual geometry encoded by the nonconformity score, while existing min…

• Generalized Deep Regression for Repeated Measurements

  Kexuan Li · 23 septembre 2026

  In this paper, we study the estimation of a marginal regression function from independent units with repeated binary, count, or continuous responses using ReLU deep neural networks. In the model, we assume that the dependence is generated by an unobserved random mean function within each unit. We th…

• The Informational Content in Lepto-Variance and Its Relation to Higher Moments

  Vassilis Polimenis · 23 septembre 2026

  Lepto-regression is defined as the machine learning process of constructing a Regression Tree of a target feature on itself. It is a novel, model-free method potentially revealing information on important sample structure properties. But it is yet not clear what the informational content of lepto-va…

• When Unpaired Sets Support Shared-Corruption Calibration: Moment Geometry and Two-Sample Precision

  Shuheng Cao, Zhenhao Zhang, Ruiqi Chen, Renjie Cao, Siyu Zhang, Zhaoxiang Feng, Lingwei Dang, Haoyang Wu · 23 septembre 2026

  Collections of diverse observations often share one acquisition, processing, geometric, or channel corruption, while only an unpaired clean reference set is available. For a prescribed low-dimensional correction shared across observations, the observed and clean reference sets support inference only…

• PICPIs: Prediction-Interval-Conditional Prediction Intervals

  Xuelin Yang, Baihe Huang, Yilong Hou, Guido Imbens, Michael I. Jordan · 23 septembre 2026

  A classical question in statistics is which observable quantities to condition on when drawing inferences about unobservable targets. For conformal prediction in nonparametric uncertainty quantification, standard marginal validity offers limited resolution at the prediction values on which decisions…

• Locally Private Inference for Riemannian Stochastic Optimization

  Xiaotian Chang, Yangdi Jiang, Qirui Hu · 22 septembre 2026

  We develop inference for manifold-valued population minimizers when each observation belongs to a different participant and only locally private messages reach the analyst. The method releases randomized tangent gradients and combines them through Riemannian stochastic approximation and Polyak-Ruppe…

• Belted Engression: Sufficient Dimension Reduction for Generative Distributional Regression

  Wenxi Tan, Bing Li, Lingzhou Xue · 22 septembre 2026

  Modern conditional generative models face significant challenges when learning complex covariate dependencies. While sufficient dimension reduction (SDR) provides a principled approach to compress these dependencies, traditional SDR frameworks were not formulated for conditional generation. To bridg…

• Tail-Weight Control and Localized Generalization in Nearly Low-Rank Adversarial Classification

  Kunyu Wang, Dehan Wang, Wenjun Chen · 22 septembre 2026

  We study norm-constrained linear classification under Eu clidean adversarial perturbations in a Gaussian model with a low-dimen sional informative subspace and an independent noise tail. For bounded ramp loss, we prove that a principal-space witness with risk below one half forces every near-optimal…

• Riemannian Simultaneous Inference for Tangent Vector Field Regression

  Xiaotian Chang, Yangdi Jiang, Qirui Hu · 21 septembre 2026

  We consider nonparametric tangent vector field regression on a Riemannian manifold without boundary. Because responses at different points lie in different tangent spaces, the proposed kernel estimator first parallel transports nearby responses to the target tangent space and then forms a volume-cor…

• A Smoothed Discrepancy Principle for Random Feature Methods and Neural Networks

  Mike Nguyen, Nicole M\"ucke · 21 septembre 2026

  We study data-driven early stopping for spectral regularisation methods in the classical non-parametric regression setting. Building on the discrepancy principle, we propose a multi-scale stopping rule that applies to general kernel estimators and show that, unlike previous approaches, it achieves f…

• Estimation of multiple mean vectors in high dimension

  Gilles Blanchard (LMO, DATASHAPE), Jean-Baptiste Fermanian (LMO), Hannah Marienwald (TUB) · 18 septembre 2026

  We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived from these samples. We introduce two strategies to find appro…

• Next-token functional estimation

  Milind Nakul, Vidya Muthukumar, Ashwin Pananjady · 18 septembre 2026

  Suppose we observe the first $n$ points of a sequence of random variables having length $n+1$, and wish to estimate a functional of the unobserved final point and the empirical measure of the $n$ observed training points. Such next-token functionals include the probability that the next token is nov…

• Weighted Empirical Risk Minimization for Machine Learning under Long-Range Dependence: Exact Pathwise Rates and Learning-Error Geometry

  Elina Moldavskaya · 11 septembre 2026

  We develop an exact almost-sure learning theory for smooth parametric models trained by regularly weighted empirical risk minimization on long-range dependent data. The training observations are generated from a fixed finite window of a stationary Gaussian sequence, and the sample weights are regula…

• Likelihood-free inference with nuisance parameters through normalizing flows

  Phil Assheton · 10 septembre 2026

  We present a simple decomposition of a neural-network-based normalizing flow that naturally uncovers a pivotal statistic (or something close) in the presence of nuisance parameters, based only on a sample generator from the distribution of interest. We show that the statistic is near-pivotal in the …

• MiNCE: Nonparametric, Strongly Consistent Confidence Envelopes for Band-Limited Functions and their Smoothed Spectra

  Bal\'azs Csan\'ad Cs\'aji, B\'alint Horv\'ath · 10 septembre 2026

  Minimum-norm confidence envelope strategies offer a nonparametric approach to constructing nonasymptotic, simultaneous confidence regions for band-limited functions, exploiting the theory of Reproducing Kernel Hilbert Spaces (RKHS). While the finite-sample coverage guarantees of these envelopes have…

• A Statistical Approach to Estimating Sample Size of Machine Learning Models

  Dat Phan-Trong, Sunil Gupta, Svetha Venkatesh · 10 septembre 2026

  Sample size determination for machine learning (ML) prediction models is challenging because conventional power analysis typically requires the predictor-outcome relationship and effect structure to be specified a priori. Nonlinear ML models learn complex prediction surfaces that do not admit straig…

• Semiparametric Inference for Counterfactual Regression under Intervention-Driven Shift

  Kwangho Kim · 4 septembre 2026

  We study counterfactual regression, which maps features to outcomes under hypothetical scenarios that differ from those observed in the data. This problem is central to decision-making under distribution shift, where treatment patterns may change at deployment. We develop a semiparametric framework …