Nonparametric Regression

Nonparametric regression aims to estimate an unknown function from data without making strong assumptions about its form, focusing on achieving optimal prediction accuracy and understanding the underlying function's properties. Current research emphasizes developing efficient algorithms, including those based on kernel methods, neural networks (especially deep and shallow ReLU networks), and tensor neural networks, often incorporating techniques like regularization, adversarial training, and active learning to improve performance and generalization. These advancements are significant for various fields, enabling more accurate modeling of complex relationships in data and facilitating robust statistical inference in scenarios where parametric assumptions are unrealistic or inappropriate.

Papers

September 28, 2023

Selective Nonparametric Regression via Testing
Fedor Noskov, Alexander Fishkov, Maxim Panov
Novel Regression Level Test Nonparametric Regression Selective Prediction Selective Regression

September 26, 2023

Free Discontinuity Regression: With an Application to the Economic Effects of Internet Shutdowns
Florian Gunsilius, David Van Dijcke
Application Proficiency Nonparametric Regression Functional Theory Regression Function Inherent Discontinuity Digital Economy Discontinuity Discrimination

July 8, 2023

Sup-Norm Convergence of Deep Neural Network Estimator for Nonparametric Regression by Adversarial Training
Masaaki Imaizumi
Adversarial Training Nonparametric Regression Superlinear Convergence Deep Neural Network Estimator

June 27, 2023

Wasserstein Generative Regression
Shanshan Song, Tong Wang, Guohao Shen, Yuanyuan Lin, Jian Huang
Value Function Generative Framework Conditional Distribution Nonparametric Regression

June 14, 2023

Nonparametric regression using over-parameterized shallow ReLU neural networks
Yunfei Yang, Ding-Xuan Zhou
Neural Network Shallow Neural Network Wide Neural Network Nonparametric Regression Shallow ReLU Rate Maximization

April 25, 2023

Positive definite nonparametric regression using an evolutionary algorithm with application to covariance function estimation
Myeongjong Kang
Application Proficiency Evolutionary Algorithm Nonparametric Regression Positive Emotional Language Covariance Function Positive Definiteness Kernel Based Surrogate

April 4, 2023

Optimal rates of approximation by shallow ReLU$^k$ neural networks and applications to nonparametric regression
Yunfei Yang, Ding-Xuan Zhou
Neural Network Average Approximation Gradient Norm Shallow Neural Network Nonparametric Regression Optimal Rate Shallow ReLU Approximation Rate

March 19, 2023

Skeleton Regression: A Graph-Based Approach to Estimation with Manifold Structure
Zeyu Wei, Yen-Chi Chen
Estimation Task Low Dimensional Manifold Nonparametric Regression Graph Based Approach Manifold Dimension Skeleton Extraction Regression Framework

March 2, 2023

Sparse-penalized deep neural networks estimator under weak dependence
William Kengne, Modou Wade
Nonparametric Regression Sparse Deep Deep Neural Network Estimator

October 28, 2022

Nonparametric Probabilistic Regression with Coarse Learners
Brian Lucena
Conditional Density Nonparametric Regression Probabilistic Regression Nonparametric Approach Base Classifier

July 17, 2022

Nonparametric regression with modified ReLU networks
Aleksandr Beknazaryan, Hailin Sang
Empirical Risk Minimization ReLU Network Nonparametric Regression Smooth Function Weighted Network

June 27, 2022

Benign overfitting and adaptive nonparametric regression
Julien Chhor, Suzanne Sigalla, Alexandre B. Tsybakov
Linear Estimator Benign Overfitting Nonparametric Regression Average Smoothness Square Loss Rate Maximization

May 30, 2022

Testing for Geometric Invariance and Equivariance
Louis G. Christie, John A. D. Aston
Inter Part Equivariance Level Test Cyclic Symmetry Dynamical Invariant Equivariant Model Nonparametric Regression Topological Invariance

May 6, 2022

Optimally tackling covariate shift in RKHS-based nonparametric regression
Cong Ma, Reese Pathak, Martin J. Wainwright
Covariate Shift Kernel Hilbert Space Kernel Ridge Regression Nonparametric Regression

April 20, 2022

Deep Learning meets Nonparametric Regression: Are Weight-Decayed DNNs Locally Adaptive?
Kaiqi Zhang, Yu-Xiang Wang
Neural Network Deep Learning Nonparametric Regression Deep ReLU Network Heterogeneous Curvature

February 6, 2022

A new similarity measure for covariate shift with applications to nonparametric regression
Reese Pathak, Cong Ma, Martin J. Wainwright
Financial Application Estimation Task Covariate Shift Similarity Measure Nonparametric Regression Target Distribution

December 7, 2021

Phase transitions in nonparametric regressions
Ying Zhu
Phase Transition Nonparametric Regression Regression Function Minimax Rate

November 4, 2021

Label Ranking through Nonparametric Regression
Dimitris Fotakis, Alkis Kalavasis, Eleni Psaroudaki
Random Forest Robust Regression Nonparametric Regression Noisy Input Training Label