Related papers: Sketching with Spherical Designs for Noisy Data Fi…
Spherical t-designs are Chebyshev-type averaging sets on the d-sphere S^d which are exact for polynomials of degree at most t. This concept was introduced in 1977 by Delsarte, Goethals, and Seidel, who also found the minimum possible size…
The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…
The unprecedented amount and the excellent quality of lensing data that the upcoming ground- and space-based surveys will produce represent a great opportunity to shed light on the questions that still remain unanswered concerning our…
Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…
Spherical regression, in which both covariates and responses lie on the sphere, arises in many scientific applications and has attracted considerable methodological attention in recent years. Despite this progress, constructing flexible and…
We consider data-based predictive control based on behavioral systems theory. In the linear setting this means that a system is described as a subspace of trajectories, and predictive control can be formulated using a projection onto the…
Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large…
In sketched clustering, a dataset of $T$ samples is first sketched down to a vector of modest size, from which the centroids are subsequently extracted. Advantages include i) reduced storage complexity and ii) centroid extraction complexity…
Probabilistic ideas and tools have recently begun to permeate into several fields where they had traditionally not played a major role, including fields such as numerical linear algebra and optimization. One of the key ways in which these…
Real-world data is typically a noisy manifestation of a core pattern (schema), and the purpose of data mining algorithms is to uncover that pattern, thereby splitting (i.e. decomposing) the data into schema and noise. We introduce SCHENO, a…
Most real-world 3D measurements from depth sensors are incomplete, and to address this issue the point cloud completion task aims to predict the complete shapes of objects from partial observations. Previous works often adapt an…
Cardinality sketches are compact data structures for representing sets or vectors. These sketches are space-efficient, typically requiring only logarithmic storage in the input size, and enable approximation of cardinality (or the number of…
Recently, a novel coded compressed sensing (CCS) approach was proposed in [1] for dealing with the scalability problem for large sensing matrices in massive machine-type communications. The approach is to divide the compressed sensing (CS)…
A hypergraph spectral sparsifier of a hypergraph $G$ is a weighted subgraph $H$ that approximates the Laplacian of $G$ to a specified precision. Recent work has shown that similar to ordinary graphs, there exist $\widetilde{O}(n)$-size…
We consider feature selection for applications in machine learning where the dimensionality of the data is so large that it exceeds the working memory of the (local) computing machine. Unfortunately, current large-scale sketching algorithms…
Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis…
Distributed training is an effective way to accelerate the training process of large-scale deep learning models. However, the parameter exchange and synchronization of distributed stochastic gradient descent introduce a large amount of…
We consider a polynomial reconstruction of smooth functions from their noisy values at discrete nodes on the unit sphere by a variant of the regularized least-squares method of An et al., SIAM J. Numer. Anal. 50 (2012), 1513--1534. As nodes…
Sketches make an intuitive and powerful visual expression as they are fast executed freehand drawings. We present a method for synthesizing realistic photos from scene sketches. Without the need for sketch and photo pairs, our framework…
Pairwise alignment of DNA sequencing data is a ubiquitous task in bioinformatics and typically represents a heavy computational burden. A standard approach to speed up this task is to compute "sketches" of the DNA reads (typically via…