Related papers: Conditional regularized halfspace depth for sparse…

Depth completion aims to recover dense depth maps from sparse depth measurements. It is of increasing importance for autonomous driving and draws increasing attention from the vision community. Most of existing methods directly train a…

Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity term and an…

Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the…

Constructing sparse, effective reduced-order models (ROMs) for high-dimensional dynamical data is an active area of research in applied sciences. In this work, we study an efficient approach to identifying such sparse ROMs using an…

Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. In this paper, we propose a novel nonparametric covariance function estimation…

Regression aims at estimating the conditional mean of output given input. However, regression is not informative enough if the conditional density is multimodal, heteroscedastic, and asymmetric. In such a case, estimating the conditional…

This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…

Approximate inference via information projection has been recently introduced as a general-purpose approach for efficient probabilistic inference given sparse variables. This manuscript goes beyond classical sparsity by proposing efficient…

Depth completion is an important vision task, and many efforts have been made to enhance the quality of depth maps from sparse depth measurements. Despite significant advances, training these models to recover dense depth from sparse…

This paper describes a hierarchical learning strategy for generating sparse representations of multivariate datasets. The hierarchy arises from approximation spaces considered at successively finer scales. A detailed analysis of stability,…

We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…

High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…

Set representations are the foundation of various set-based approaches in state estimation, reachability analysis and fault diagnosis. In this paper, we investigate spectrahedral shadows, a class of nonlinear geometric objects previously…

Convolutional neural networks are designed for dense data, but vision data is often sparse (stereo depth, point clouds, pen stroke, etc.). We present a method to handle sparse depth data with optional dense RGB, and accomplish depth…

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…

Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…

The optimization problems with a sparsity constraint is a class of important global optimization problems. A typical type of thresholding algorithms for solving such a problem adopts the traditional full steepest descent direction or…

We introduce SubGD, a novel few-shot learning method which is based on the recent finding that stochastic gradient descent updates tend to live in a low-dimensional parameter subspace. In experimental and theoretical analyses, we show that…

Consider a structured dataset of features, such as $\{\textrm{SEX}, \textrm{INCOME}, \textrm{RACE}, \textrm{EXPERIENCE}\}$. A user may want to know where in the feature space observations are concentrated, and where it is sparse or empty.…

Statistical depth functions are a standard tool in nonparametric statistics to extend order-based univariate methods to the multivariate setting. Since there is no universally accepted total order for fuzzy data (even in the univariate…