Related papers: Multilevel Evaluation of Multidimensional Integral…

Recently, Su and Cook proposed a dimension reduction technique called the inner envelope which can be substantially more efficient than the original envelope or existing dimension reduction techniques for multivariate regression. However,…

This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…

We present an error-neural-modeling-based strategy for approximating two-dimensional curvature in the level-set method. Our main contribution is a redesigned hybrid solver [Larios-C\'ardenas and Gibou, J. Comput. Phys. (May 2022),…

Obtainable computational efficiency is evaluated when using an Adaptive Mesh Refinement (AMR) strategy in time accurate simulations governed by sets of conservation laws. For a variety of 1D, 2D, and 3D hydro- and magnetohydrodynamic…

We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…

The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator.…

We propose a compact and effective framework to fuse multimodal features at multiple layers in a single network. The framework consists of two innovative fusion schemes. Firstly, unlike existing multimodal methods that necessitate…

We introduce a novel diffusion-based spectral algorithm to tackle regression analysis on high-dimensional data, particularly data embedded within lower-dimensional manifolds. Traditional spectral algorithms often fall short in such…

Random Reshuffling (RR) is an algorithm for minimizing finite-sum functions that utilizes iterative gradient descent steps in conjunction with data reshuffling. Often contrasted with its sibling Stochastic Gradient Descent (SGD), RR is…

Multi-degree splines are piecewise polynomial functions having sections of different degrees. They offer significant advantages over the classical uniform-degree framework, as they allow for modeling complex geometries with fewer degrees of…

Learning implicit representations has been a widely used solution for surface reconstruction from 3D point clouds. The latest methods infer a distance or occupancy field by overfitting a neural network on a single point cloud. However,…

For low-dimensional data sets with a large amount of data points, standard kernel methods are usually not feasible for regression anymore. Besides simple linear models or involved heuristic deep learning models, grid-based discretizations…

In this paper we present a second-order and continuous interpolation algorithm for cell-centered adaptive-mesh-refinement (AMR) grids. Continuity requirement poses a non-trivial problem at resolution changes. We develop a classification of…

Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…

In practice, encoding invariances into models improves sample complexity. In this work, we study this phenomenon from a theoretical perspective. In particular, we provide minimax optimal rates for kernel ridge regression on compact…

Deep convolutional neural networks (ConvNets) of 3-dimensional kernels allow joint modeling of spatiotemporal features. These networks have improved performance of video and volumetric image analysis, but have been limited in size due to…

The last decade has witnessed the breakthrough of deep neural networks (DNNs) in many fields. With the increasing depth of DNNs, hundreds of millions of multiply-and-accumulate (MAC) operations need to be executed. To accelerate such…

This paper proposes and analyzes a communication-efficient distributed optimization framework for general nonconvex nonsmooth signal processing and machine learning problems under an asynchronous protocol. At each iteration, worker machines…

In this paper, we introduce two robust, nonparametric methods for multiple change-point detection in the variability of a multivariate sequence of observations. We demonstrate that changes in ranks generated from data depth functions can be…

In scientific machine learning, regression networks have been recently applied to approximate solution maps (e.g., potential-ground state map of Schr\"odinger equation). In this paper, we aim to reduce the generalization error without…