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.
By Marcos Matabuena, Xiaokai Luo, Oscar Hernan Madrid Padilla
arXiv:2606. 25188v1 Announce Type: new Abstract: Efficient uncertainty quantification (UQ) is essential for trustworthy large-scale learning.
By Kun Jin, James Harrison, Jiawei Li, Sihan Liu, Jiayi Liu, Randolph Linderman, Yuening Li, Arnab Bhadury, Sourabh Prakash Bansod, Liang Liu, Jasper Snoek
arXiv:2606. 04767v1 Announce Type: new Abstract: The robustness of deep neural networks is crucial for safety-critical deployments, yet existing evaluation methods are often attack-dependent and lack interpretability.
By Chong Zhang, Xiang Li, Jia Wang, Qiufeng Wang, Xiaobo Jin
arXiv:2608.24518v1 Announce Type: new
Abstract: Uncertainty Quantification (UQ) plays a vital role in enhancing the reliability of deep learning model predictions, especially in scenarios with high-d...
By Leonhard F. Feiner, Manuel Nickel, Martin Menten, Laurin Lux, Rickmer Braren, Daniel Rueckert, Georgios Kaissis, Raphael Rehms, Johannes Paetzold
arXiv:2607. 04647v1 Announce Type: cross Abstract: Scalable Bayesian inference for generalized linear mixed models (GLMMs) provides uncertainty-aware analysis of correlated longitudinal data, but existing scalable approaches largely assume low-dimensional tabular predictors and do not directly accommodate high-dimensional modalities such as images and text.
By Yuankang Zhao, Youngsoo Baek, Felipe A. Medeiros, Samuel Berchuck, Matthew M. Engelhard
arXiv:2607. 10068v1 Announce Type: new Abstract: Implicit neural representations (INRs) offer compact encoding of volumes, but as lossy approximators, inevitably have prediction errors.
By Zhimin Li, Jake D. Balla, Joshua A. Levine