Related papers: Hybrid hierarchical matrices with adaptive mixed p…

Certification for machine learning is proving that no adversarial sample can evade a model within a range under certain conditions, a necessity for safety-critical domains. Common certification methods for segmentation use a flat set of…

A hierarchical Model Predictive Control (MPC) formulation is presented for coupled discrete-time linear systems with state and input constraints. Compared to a centralized approach, a two-level hierarchical controller, with one controller…

We introduce two practical properties of hierarchical clustering methods for (possibly asymmetric) network data: excisiveness and linear scale preservation. The latter enforces imperviousness to change in units of measure whereas the former…

In this paper, we consider the matrices approximated in H2 format. The direct solution, as well as the preconditioning, of systems with such matrices is a challenging problem. We propose a non-extensive sparse factorization of the H2 matrix…

In this paper we extend the hierarchical model reduction framework based on reduced basis techniques for the application to nonlinear partial differential equations. The major new ingredient to accomplish this goal is the introduction of…

In this work, we develop an optimization framework for problems whose solutions are well-approximated by Hierarchical Tucker (HT) tensors, an efficient structured tensor format based on recursive subspace factorizations. By exploiting the…

There is evidence that the self-assembly of complex molecular systems often proceeds hierarchically, by first building subunits that later assemble in larger entities, in a process that can repeat multiple times. Yet, our understanding of…

Black box variational inference allows researchers to easily prototype and evaluate an array of models. Recent advances allow such algorithms to scale to high dimensions. However, a central question remains: How to specify an expressive…

In this paper we examine the use of low-rank approximations for the handling of radiation boundary conditions in a transient heat equation given a cavity radiation setting. The finite element discretization that arises from cavity radiation…

This article introduces HODLR2D, a new hierarchical low-rank representation for a class of dense matrices arising out of $N$ body problems in two dimensions. Using this new hierarchical framework, we propose a new fast matrix-vector product…

Hierarchical clustering is an effective, interpretable method for analyzing structure in data. It reveals insights at multiple scales without requiring a predefined number of clusters and captures nested patterns and subtle relationships,…

Artificial intelligence (AI) application domains consist of a mix of tensor operations with high and low arithmetic intensities (aka reuse). Hierarchical (i.e. compute along multiple levels of memory hierarchy) and heterogeneous (multiple…

The applicability of agglomerative clustering, for inferring both hierarchical and flat clustering, is limited by its scalability. Existing scalable hierarchical clustering methods sacrifice quality for speed and often lead to over-merging…

Object oriented bounding box tree (OBB-Tree for short) has many applications in collision detection, real-time rendering, etc. It has a wide range of applications. The construction of the hierarchical directed bounding box of the solid mesh…

A robust $hp$-adaptive finite element framework is presented for the investigation of static cracks in materials characterized by complex, pointwise density variations. Within such heterogeneous media, the equilibrium equation governed by…

This contribution presents a hierarchical multigrid approach for the solution of large-scale finite cell problems on both uniform grids and multi-level hp-discretizations. The proposed scheme leverages the hierarchical nature of the basis…

Hierarchical clustering is one of the most powerful solutions to the problem of clustering, on the grounds that it performs a multi scale organization of the data. In recent years, research on hierarchical clustering methods has attracted…

Deploying deep neural networks for risk-sensitive tasks necessitates an uncertainty estimation mechanism. This paper introduces hierarchical selective classification, extending selective classification to a hierarchical setting. Our…

The rapid growth of distributed energy resources (DERs) presents both opportunities and operational challenges for electric grid management. Accurately predicting DER adoption is critical for proactive infrastructure planning, but the…

Large-scale Hierarchical Classification (HC) involves datasets consisting of thousands of classes and millions of training instances with high-dimensional features posing several big data challenges. Feature selection that aims to select…