DFNN: A Deep Fr\'echet Neural Network Framework for Learning Metric-Space-Valued Responses
Read the original on arXiv Statistics ML →The Flow has not summarised this story yet — read it at arXiv Statistics ML.
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The paper introduces a deep learning framework for regression with random objects in metric spaces, bypassing restrictive manifold or Euclidean embedding assumptions. It provides statistical consistency, convergence rates, and conditions that mitigate the curse of dimensionality for hierarchically compositional regression functions. Extensive simulations and two digital health case studies with distribution-valued outcomes demonstrate competitive predictive performance over existing methods.
arXiv:2606. 06957v1 Announce Type: cross Abstract: Predicting outputs that are located in non-Euclidean spaces, such as probability distributions, networks, and symmetric positive-definite matrices, is becoming increasingly important in modern data analysis, particularly when inputs are high-dimensional.
arXiv:2509. 23544v2 Announce Type: replace-cross Abstract: Many modern applications involve predicting structured, non-Euclidean outputs such as probability distributions, networks, and symmetric positive-definite matrices.
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.
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.
arXiv:2606. 06772v2 Announce Type: replace-cross Abstract: Characterizing the optimization dynamics and statistical performance of over-parameterized deep neural networks (DNNs) remains a central challenge in understanding the remarkable success of deep learning.