Related papers: Parametric Hierarchical Matrix Approximations to K…

Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time…

Information hierarchies are organizational structures that often used to organize and present large and complex information as well as provide a mechanism for effective human navigation. Fortunately, many statistical and computational…

When analyzing real-world data it is common to work with event ensembles, which comprise sets of observations that collectively constrain the parameters of an underlying model of interest. Such models often have a hierarchical structure,…

Hierarchical Clustering is a popular unsupervised machine learning method with decades of history and numerous applications. We initiate the study of differentially private approximation algorithms for hierarchical clustering under the…

This paper introduces a dynamic, error-bounded hierarchical matrix (H-matrix) compression method tailored for Physics-Informed Neural Networks (PINNs). The proposed approach reduces the computational complexity and memory demands of…

Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. "Structure" can be understood as symmetry and a range of symmetries are expressed by hierarchy. Such symmetries directly…

We consider fast kernel summations in high dimensions: given a large set of points in $d$ dimensions (with $d \gg 3$) and a pair-potential function (the {\em kernel} function), we compute a weighted sum of all pairwise kernel interactions…

Hypergraphs serve as an effective tool widely adopted to characterize higher-order interactions in complex systems. The most intuitive and commonly used mathematical instrument for representing a hypergraph is the incidence matrix, in which…

In this paper, we describe the hyper-parameter search problem in the field of machine learning and present a heuristic approach in an attempt to tackle it. In most learning algorithms, a set of hyper-parameters must be determined before…

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…

Modern large-scale scientific applications consist of thousands to millions of individual tasks. These tasks involve not only computation but also communication with one another. Typically, the communication pattern between tasks is sparse…

Traditional heterogeneous parallel algorithms, designed for heterogeneous clusters of workstations, are based on the assumption that the absolute speed of the processors does not depend on the size of the computational task. This assumption…

Conditional kernel mean embeddings are nonparametric models that encode conditional expectations in a reproducing kernel Hilbert space. While they provide a flexible and powerful framework for probabilistic inference, their performance is…

We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…

This paper presents an efficient method to perform Structured Matrix Approximation by Separation and Hierarchy (SMASH), when the original dense matrix is associated with a kernel function. Given points in a domain, a tree structure is first…

In this paper we propose a new framework for analyzing the performance of preprocessing algorithms. Our framework builds on the notion of kernelization from parameterized complexity. However, as opposed to the original notion of…

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,…

This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…

Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…

In this work, we discuss low-parametric approaches for approximating SimRank matrices, which estimate the similarity between pairs of nodes in a graph. Although SimRank matrices and their computation require a significant amount of memory,…