Nonparametric Regression

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Nonparametric regression studies how to estimate an unknown relationship between inputs and outcomes while allowing its shape to be determined by data and assumptions such as smoothness or additivity. Common approaches include kernel and spline smoothing, Gaussian processes and reproducing-kernel methods, tree ensembles, and neural networks; researchers also develop online, functional, and distributional variants for specialized data. A central theoretical goal is to match minimax rates, which quantify the best possible prediction accuracy under a given smoothness class, while adapting to unknown structure and handling dependence, missingness, or distribution shift. The main tension is that flexible models can achieve strong guarantees under suitable conditions, but high dimension, computational cost, and reliable uncertainty estimates remain difficult.

Latest papers

45 papers7 papers in the last four weeks, down 30% on the four weeks before. 0.0% of all new papers.

Federated Nonparametric Regression with Heterogeneous Clients
Oct 23, 2026Xiaoran Jiang, Anand N. VidyashankarFederated Learning Nonparametric Regression
Deep Learning for Random Objects in Metric Spaces: Beyond Manifold Assumptions
Oct 22, 2026Marcos Matabuena, Xiaokai Luo, Oscar Hernan Madrid PadillaNonparametric Regression Distributional Regression
Mohamed bin Zayed University of Artificial Intelligence · University of Notre Dame · Department of Statistics at University of California, Los Angeles
Making Tensor Decoupling More Robust and Less Parametric
Oct 12, 2026Maxime Rochkoulets, Joppe De Jonghe, Mariya IshtevaTensor Decomposition Nonparametric Regression
Department of Computer Science, KU Leuven, Belgium · Department of Computer Science, NUMA, KU Leuven, 2440 Geel, Belgium
Distributional Regression for Arbitrary Response Variables Using ReLU Neural Networks
Oct 12, 2026Junpeng Ren, Carlos Misael Madrid Padilla, Oscar Hernan Madrid PadillaDistributional Regression Conditional Distribution Estimation
Department of Statistics and Data Science, University of California, Los Angeles, Los Angeles, CA, USA · Department of Statistics and Data Science, Washington University in St Louis, St. Louis, MO, USA
Energy-Guided Learning for Heat Equation with Noisy Source: Optimal Estimation and Generalization Bounds
Oct 10, 2026Zixiang Zhou, Xiaohui Chen, Shanghua TengPhysics-Informed ML PDE Solving
Department of Mathematics, University of Southern California · Thomas Lord Department of Computer Science, University of Southern California · Computing and Mathematical Sciences, California Institute of Technology
RoBART: Bayesian Additive Regression Trees with Tree-Specific Rotations
Oct 7, 2026Jeongung Heo, Seonghyun JeongPosterior Contraction Nonparametric Regression
Yonsei University
Minimax Additive Regression under Unknown Dependent Designs
Sep 30, 2026Baptiste Ferrere, Fabrice Gamboa, Jean-Michel LoubesNonparametric Regression Minimax Estimation
Université de Toulouse EDF R&D · Université de Toulouse ANITI
Domain Adaptation with Target Information via Doubly-Anchored Distributionally Robust Optimization
Sep 26, 2026David Kepplinger, Anand N. VidyashankarDomain Adaptation Distributionally Robust Optimization
Department of Statistics George Mason University Fairfax, VA 22030, USA
Nonparametric In-Context Learning under Growing Geometric Complexity: Minimax Optimality and Local Geometry-Adaptivity of Transformers
Sep 25, 2026Jaehee Seo, Jisu KimIn-Context Learning Transformer
Department of Statistics Seoul National University, Korea
Optimal Tradeoffs Between Network Size and Parameter Magnitude in Neural Approximation and Minimax Regression
Sep 22, 2026Baicheng Li, Zuowei Shen, Haizhao Yang +1Neural Network Optimization Nonparametric Regression
Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA. · Department of Mathematics, National University of Singapore, Singapore 119076. · Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China.
Generalized Deep Regression for Repeated Measurements
Sep 22, 2026Kexuan LiNeural Network Generalization ReLU Neural Networks
Bristol Myers Squibb
Riemannian Simultaneous Inference for Tangent Vector Field Regression
Sep 18, 2026Xiaotian Chang, Yangdi Jiang, Qirui HuNonparametric Regression
Division of Mathematical Sciences, Nanyang Technological University. · School of Statistics and Data Science, Shanghai University of Finance and Economics.
A Smoothed Discrepancy Principle for Random Feature Methods and Neural Networks
Sep 17, 2026Mike Nguyen, Nicole MückeEarly Stopping Nonparametric Regression
Technical University of Braunschweig
MiNCE: Nonparametric, Strongly Consistent Confidence Envelopes for Band-Limited Functions and their Smoothed Spectra
Sep 8, 2026Balázs Csanád Csáji, Bálint HorváthConfidence Region Estimation Nonparametric Regression
HUN-REN SZTAKI: Institute for Computer Science and Control, Budapest, Hungary · Institute of Mathematics, Eötvös Loránd University (ELTE), Budapest, Hungary
Optimal estimation for Functional Linear Regression with Noisy Discretized Data
Sep 8, 2026Sixtine SphabmixayNonparametric Regression Minimax Estimation
Université Paris Cité, CNRS, MAP5, F-75006 Paris, France
Distributed Lag Neural Additive Models
Sep 7, 2026Calle Helmersson, Shivang Pandey, Leonardo Olivetti +1Nonparametric Regression Neural Network Interpretability
Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden · Department of Global Public Health, Karolinska Institutet, Stockholm, Sweden · Swedish Centre for Impacts of Climate Extremes (climes), Uppsala University, Uppsala, Sweden +4
Functional Attentive Interpretable Regression
Sep 5, 2026Haixu Wang, Tianyu Guan, Jiguo CaoNonparametric Regression
Department of Mathematics and Statistics, University of Calgary · Department of Mathematics and Statistics, York University · Department of Statistics and Actuarial Science, Simon Fraser University
Efficient Regression Models for Scan Statistics
Aug 23, 2026Gazi Abdur Rakib, Tristan Ashton, Ryan A. Loomis +4Time-Series Anomaly Detection Nonparametric Regression
University of Utah & CosmicAI · National Radio Astronomy Observatory & CosmicAI
Transfer Learning in Nonparametric Regression with Deep ReLU Networks
Aug 20, 2026Junpeng Ren, Carlos Misael Madrid Padilla, Yanzhen Chen +1Transfer Learning Nonparametric Regression
Department of Statistics and Data Science, University of California, Los Angeles, California, USA · Department of Statistics and Data Science, Washington University in St. Louis, Missouri, USA · Department of Information Systems, Business Statistics and Operations Management, Hong Kong University of Science and Technology, Hong Kong, China.
A Deep Learning Model for Spatially Clustered Data via Differentiable Cluster Assignment
Aug 15, 2026Kexuan Li, Weidong MaNonparametric Regression Clustering
Bristol Myers Squibb · University of Pennsylvania, Department of Biostatistics
Conditional Diffusion for Nonparametric Instrumental Variable Quantile Regression
Aug 8, 2026Xingdong Feng, Xinhong Jiang, Yuling Jiao +2Quantile Regression Nonparametric Regression
School of Statistics and Data Science, Institute of Data Science and Statistics, Shanghai University of Finance and Economics, Shanghai 200433, China · School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China · School of Artificial Intelligence, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan, 430072, China +1
Verifiable Regularity Criterion for Conditional Expectation Operators and Conditional Mean Embeddings with Applications to Nonparametric Regression, Bayesian Inverse Problems, and Koopman Operators
Aug 6, 2026Maximiliano Hertel, Ilja Klebanov, Manuel Schaller +1Nonparametric Regression
Optimization-based Control Group, Institute of Mathematics, Technische Universität Ilmenau, Germany · Department of Mathematics and Computer Science, Freie Universität Berlin, Germany · Faculty of Mathematics, Chemnitz University of Technology, Germany
The Noise Premium in Adversarial Training for Kernel Regression
Jul 30, 2026Yiling Xie, Xiaoming HuoAdversarial Training Kernel Regression
Department of Decision Analytics and Operations, City University of Hong Kong · H. Milton Stewart School of Industrial and Systems Engineering Georgia Institute of Technology
Automatic knot selection in smooth additive models
Jul 23, 2026Nicolás Carrizosa, Vanesa Guerrero, María DurbánNonparametric Regression
Department of Statistics, Operations Research and Mathematics Education, Universidad de Oviedo · Department of Statistics, Universidad Carlos III de Madrid
Adaptive deep nonparametric regression from dependent data under covariate shift
Jul 22, 2026William Kengne, Ehud Mossa OckegnaQuantile Regression Covariate Shift
Université Jean Monnet, ICJ UMR5208, CNRS, Ecole Centrale de Lyon, INSA Lyon, Universite Claude Bernard Lyon 1, 42000 Saint-Étienne, France
Black-Box Assisted Regression: Phase Transitions and Minimax Optimality
Jun 24, 2026Yan ZhouResidual Learning Nonparametric Regression
School of Mathematics and Statistics, Changsha University of Science and Technology.
Generalized nonparametric regression in reproducing kernel Hilbert spaces: Consistency and rates of convergence
Jun 22, 2026Ioannis KalogridisNonparametric Regression Reproducing Kernel Hilbert Spaces
School of Mathematics and Statistics, University of Glasgow, United Kingdom
Posterior Contraction of Lévy Adaptive B-spline Regression in Besov Spaces
May 19, 2026Jeunghun Oh, Sewon Park, Jaeyong LeeBayesian Inference Posterior Contraction
Department of Statistics, Seoul National University. · Department of Statistics, Sookmyung Women’s University.
Shallow ReLU $^s$ Networks in $L^p$ -Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalization
May 18, 2026Weizhao Li, Fanghui Liu, Lei ShiShallow Neural Networks Nonparametric Regression
School of Mathematical Sciences Fudan University Shanghai, China · School of Mathematical Sciences Institute of Natural Sciences and MOE-LSC2026 Shanghai Jiao Tong University Shanghai, China · School of Mathematical Sciences Shanghai Key Laboratory for Contemporary Applied Mathematics25 Fudan University Shanghai, China
On Uniform Error Bounds for Kernel Regression under Non-Gaussian Noise
May 10, 2026Johannes Teutsch, Oleksii Molodchyk, Marion Leibold +2Kernel Regression Uncertainty Quantification
Chair of Automatic Control Engineering, Department of Computer Engineering, Technical University of Munich, 80333 Munich, Germany · Institute of Control Systems, Hamburg University of Technology, 21073 Hamburg, Germany · Department of Electrical and Computer Engineering, National University of Singapore, 117583 Singapore

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Federated Nonparametric Regression with Heterogeneous Clients

Xiaoran Jiang, Anand N. Vidyashankar

Federated Learning Nonparametric Regression Heterogeneous Federated Learning

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Whether a federated predictor benefits an individual client depends on both population heterogeneity and estimation uncertainty. We study this question for Nadaraya--Watson regression in a triangular array with potentially different fitting and evaluation distributions. Each client transmits local kernel summaries, allowing the server to construct a covariate-density-weighted federated estimator without centralizing individual observations. A client combines its fitted local predictor with the federated predictor through a prescribed weight, and gain is the paired reduction in squared prediction loss on an independent audit observation. Exact identities characterize both the gain of the realized fitted pair and its repeated-fitting mean. We also establish pointwise inference for the federated estimator. A two-stage analysis of client gains separates fitting variability from audit variability, retains the covariance created when a client's observations enter both its local estimator and the common server estimator, and yields fixed-block simultaneous inference across clients. Robustness is examined under two perturbation models. A Kullback--Leibler neighborhood provides a variance-sensitive lower certificate in a regular positive-gain-variance regime, while an

L_2

neighborhood yields an exact least-favorable regression direction and robust value. Exact-model, vanishing-variance, and exact-zero-direction boundaries are kept separate because their scalar inputs are nonregular. The framework thus distinguishes decisions about a realized fitted pair from claims about the learning procedure under repeated fitting.