The paper develops theory for deep neural network (DNN) estimators under dependent data. It establishes nonasymptotic probability bounds on the theoretical and empirical ∼2-errors of nonparametric sieve estimators for a general class of estimation problems with possibly nonstationary β-mixing data in unbounded sets. The theory is then applied to fully connected and convolutional DNN estimators without weight bounds or sparsity restrictions, deriving results for H"older smooth functions under nonstationary, subgaussian, β-mixing data with exponential or polynomial decay, and achieving the nonparametric minimax rate up to logarithmic factors in several regression settings.
By Chad Brown
arXiv:2608. 08204v1 Announce Type: cross Abstract: This work proposes deep nonparametric Instrumental variable quantile regression (IVQR), a two-stage estimator that combines conditional diffusion modeling with a kernel-smoothed conditional moment formulation.
By Xingdong Feng, Xinhong Jiang, Yuling Jiao, Lican Kang, Junwei Liu
arXiv:2606. 05599v1 Announce Type: new Abstract: This paper establishes a theoretical framework for the uniform convergence of smoothly activated deep neural network (DNN) estimators.
By Yizhe Ding, Runze Li, Jia Liu, Lingzhou Xue
The paper introduces BROT, a two‑step approach for estimating optimal transport maps. First, it computes the unregularized OT plan, then fits a deep neural network to the resulting barycentric targets using least‑squares regression. The authors prove that, under standard regularity conditions, BROT achieves the minimax convergence rate when the true OT map is Lipschitz, and demonstrate its effectiveness on synthetic data, images, and downstream tasks such as single‑cell perturbation prediction and unsupervised domain adaptation.
By Kunwoong Kim, Insung Kong, Yongdai Kim
arXiv:2609. 01166v1 Announce Type: cross Abstract: The present research is devoted to the nonparametric estimation of a density-dependent drift coefficient in a multivariate McKean--Vlasov diffusion from independent observations at a common time, as well as the stationary density.
By Denis Belomestny, Ekaterina Morozova
arXiv:2609. 25605v1 Announce Type: cross Abstract: 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.
By Kexuan Li