Related papers: Fast Hyperbolic Wavelet Regression meets ANOVA

Wavelets are well known for data compression, yet have rarely been applied to the compression of neural networks. This paper shows how the fast wavelet transform can be used to compress linear layers in neural networks. Linear layers still…

The lack of smoothness is a common feature of weak solutions of nonlinear hyperbolic equations and is a crucial issue in their approximation. This has motivated several efforts to define appropriate indicators, based on the values of the…

Reconstructing both objects and hands in 3D from a single RGB image is complex. Existing methods rely on manually defined hand-object constraints in Euclidean space, leading to suboptimal feature learning. Compared with Euclidean space,…

Hyperbolic space is a geometry that is known to be well-suited for representation learning of data with an underlying hierarchical structure. In this paper, we present a novel hyperbolic distribution called \textit{pseudo-hyperbolic…

We study the performances of an adaptive procedure based on a convex combination, with data-driven weights, of term-by-term thresholded wavelet estimators. For the bounded regression model, with random uniform design, and the nonparametric…

High-dimensional vector autoregressive (VAR) models provide a flexible framework for characterizing dynamic dependence in multivariate spatio-temporal systems, but their unrestricted estimation becomes infeasible when multiple variables are…

Matrix-variate time series data are increasingly popular in economics, statistics, and environmental studies, among other fields. This paper develops regularized estimation methods for analyzing high-dimensional matrix-variate time series…

Shallow Water Moment Equations are reduced-order models for free-surface flows that employ a vertical velocity expansion and derive additional so-called moment equations for the expansion coefficients. Among desirable analytical properties…

Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings…

We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…

It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…

In this paper, we present a mathematical study of wave scattering by a hard elastic obstacle embedded in a soft elastic body in three dimensions. Our contributions are threefold. First, we characterize subwavelength resonances using the…

In this paper we deal with the regression problem in a random design setting. We investigate asymptotic optimality under minimax point of view of various Bayesian rules based on warped wavelets and show that they nearly attain optimal…

Learning dynamical models from data plays a vital role in engineering design, optimization, and predictions. Building models describing dynamics of complex processes (e.g., weather dynamics, or reactive flows) using empirical knowledge or…

Latest diffusion-based methods for many image restoration tasks outperform traditional models, but they encounter the long-time inference problem. To tackle it, this paper proposes a Wavelet-Based Diffusion Model (WaveDM). WaveDM learns the…

Kernel matrices are crucial in many learning tasks such as support vector machines or kernel ridge regression. The kernel matrix is typically dense and large-scale. Depending on the dimension of the feature space even the computation of all…

In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an $N$th-order $(I_1\times I_2\times \cdots \times I_N)$ data tensor $\underline{\mathbf{X}}$ from a…

For many inverse parameter problems for partial differential equations in which the domain contains only well-separated objects, an asymptotic solution to the forward problem involving 'polarization tensors' exists. These are functions of…

Recent years have witnessed an upsurge of interest in employing flexible machine learning models for instrumental variable (IV) regression, but the development of uncertainty quantification methodology is still lacking. In this work we…

We combine Newton's variational method with ideas from eigenvector continuation to construct a fast & accurate emulator for two-body scattering observables. The emulator will facilitate the application of rigorous statistical methods for…