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.
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:2608. 10857v1 Announce Type: new Abstract: Determining the complexity, or Intrinsic Dimension (ID), of data is fundamental to efficient and interpretable representation learning.
arXiv:2606. 25188v1 Announce Type: new Abstract: Efficient uncertainty quantification (UQ) is essential for trustworthy large-scale learning.
arXiv:2608. 15121v1 Announce Type: cross Abstract: Sufficient dimension reduction (SDR) seeks the minimal subspace of the predictors that captures the full conditional distribution of the response, which is known as the central subspace (CS).
arXiv:2607. 16725v1 Announce Type: cross Abstract: Conditional generative modeling remains a challenging problem in semi-supervised settings where labeled data is scarce but unlabeled samples are abundant.
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.
arXiv:2511. 18945v4 Announce Type: replace Abstract: We propose a fully data-driven approach to designing mutual information (MI) estimators.
arXiv:2607. 19600v1 Announce Type: cross Abstract: The shape of a planar curve is the geometric information that remains once translation, rotation, scale and reparametrisation are removed and is of interest in many health applications, e.
arXiv:2608. 09523v1 Announce Type: new Abstract: Deep neural network (DNN) training with stochastic gradient descent (SGD) and its variants achieves strong empirical performance, yet classical optimization theory does not fully explain this success.
arXiv:2506. 13139v3 Announce Type: replace-cross Abstract: Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data and rely on overparameterized models, where classical low-dimensional intuitions break down.
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.