Related papers: Semi-Supervised Deep Sobolev Regression: Estimatio…

Deep learning demands a huge amount of well-labeled data to train the network parameters. How to use the least amount of labeled data to obtain the desired classification accuracy is of great practical significance, because for many…

We establish in this work approximation results of deep neural networks for smooth functions measured in Sobolev norms, motivated by recent development of numerical solvers for partial differential equations using deep neural networks. {Our…

In deep neural nets, lower level embedding layers account for a large portion of the total number of parameters. Tikhonov regularization, graph-based regularization, and hard parameter sharing are approaches that introduce explicit biases…

Sufficient dimension reduction is a powerful tool to extract core information hidden in the high-dimensional data and has potentially many important applications in machine learning tasks. However, the existing nonlinear sufficient…

Parameter reduction can enable otherwise infeasible design and uncertainty studies with modern computational science models that contain several input parameters. In statistical regression, techniques for sufficient dimension reduction…

Learning representations that capture both intrinsic data geometry and target-relevant structure remains a fundamental challenge, particularly in settings where data reduction must balance compression with predictive fidelity. While…

The inverse problem of supervised reconstruction of depth-variable (time-dependent) parameters in a neural ordinary differential equation (NODE) is considered, that means finding the weights of a residual network with time continuous…

We present a theoretically well-founded deep learning algorithm for nonparametric regression. It uses over-parametrized deep neural networks with logistic activation function, which are fitted to the given data via gradient descent. We…

Semi-supervised semantic segmentation aims to learn from a small amount of labeled data and plenty of unlabeled ones for the segmentation task. The most common approach is to generate pseudo-labels for unlabeled images to augment the…

Purpose: To develop a strategy for training a physics-guided MRI reconstruction neural network without a database of fully-sampled datasets. Theory and Methods: Self-supervised learning via data under-sampling (SSDU) for physics-guided deep…

Deep Neural Networks (DNNs) provide state-of-the-art solutions in several difficult machine perceptual tasks. However, their performance relies on the availability of a large set of labeled training data, which limits the breadth of their…

Deep learning approaches for semantic segmentation rely primarily on supervised learning approaches and require substantial efforts in producing pixel-level annotations. Further, such approaches may perform poorly when applied to unseen…

Recent theoretical studies proved that deep neural network (DNN) estimators obtained by minimizing empirical risk with a certain sparsity constraint can attain optimal convergence rates for regression and classification problems. However,…

Large-scale machine learning models are often trained by parallel stochastic gradient descent algorithms. However, the communication cost of gradient aggregation and model synchronization between the master and worker nodes becomes the…

Semi-supervised learning leverages unlabeled data to enhance model performance, addressing the limitations of fully supervised approaches. Among its strategies, pseudo-supervision has proven highly effective, typically relying on one or…

In this paper, we study nonparametric estimation of instrumental variable (IV) regressions. While recent advancements in machine learning have introduced flexible methods for IV estimation, they often encounter one or more of the following…

We propose Sobolev-regularized Maximum Mean Discrepancy (SrMMD) gradient flow, a regularized variant of maximum mean discrepancy (MMD) gradient flow based on a gradient penalty on the witness function. The proposed regularization mitigates…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

Semi-supervised learning algorithms reduce the high cost of acquiring labeled training data by using both labeled and unlabeled data during learning. Deep Convolutional Networks (DCNs) have achieved great success in supervised tasks and as…

We study source-free unsupervised domain adaptation (SFUDA) for semantic segmentation, which aims to adapt a source-trained model to the target domain without accessing the source data. Many works have been proposed to address this…