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We present an efficient and scalable algorithm for performing matrix-vector multiplications ("matvecs") for block Toeplitz matrices. Such matrices, which are shift-invariant with respect to their blocks, arise in the context of solving…
We present a novel algorithm attaining excessively fast, the sought solution of linear systems of equations. The algorithm is short in its basic formulation and, by definition, vectorized, while the memory allocation demands are trivial,…
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
Hyperdimensional Computing (HDC) is a brain-inspired and light-weight machine learning method. It has received significant attention in the literature as a candidate to be applied in the wearable internet of things, near-sensor artificial…
The assumed hardness of the Shortest Vector Problem in high-dimensional lattices is one of the cornerstones of post-quantum cryptography. The fastest known heuristic attacks on SVP are via so-called sieving methods. While these still take…
By the asymptotic oracle property, non-convex penalties represented by minimax concave penalty (MCP) and smoothly clipped absolute deviation (SCAD) have attracted much attentions in high-dimensional data analysis, and have been widely used…
In science and engineering, intelligent processing of complex signals such as images, sound or language is often performed by a parameterized hierarchy of nonlinear processing layers, sometimes biologically inspired. Hierarchical systems…
Quadratic programming is a ubiquitous prototype in convex programming. Many machine learning problems can be formulated as quadratic programming, including the famous Support Vector Machines (SVMs). Linear and kernel SVMs have been among…
Support Vector Machines (SVM), a popular machine learning technique, has been applied to a wide range of domains such as science, finance, and social networks for supervised learning. Whether it is identifying high-risk patients by…
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…
The breakthrough ideas in the modern proximal splitting methodologies allow us to express the set of all minimizers of a superposition of multiple nonsmooth convex functions as the fixed point set of computable nonexpansive operators. In…
We propose an algorithm for clustering high dimensional data. If $P$ features for $N$ objects are represented in an $N\times P$ matrix ${\bf X}$, where $N\ll P$, the method is based on exploiting the cluster-dependent structure of the…
Kernel matrices are ubiquitous in computational mathematics, often arising from applications in machine learning and scientific computing. In two or three spatial or feature dimensions, such problems can be approximated efficiently by a…
This paper proposes a special-purpose system to achieve high-accuracy and high-efficiency machine learning (ML) molecular dynamics (MD) calculations. The system consists of field programmable gate array (FPGA) and application specific…
The balanced hypergraph partitioning problem (HGP) is to partition the vertex set of a hypergraph into k disjoint blocks of bounded weight, while minimizing an objective function defined on the hyperedges. Whereas real-world applications…
The Volterra Tensor Network lifts the curse of dimensionality for truncated, discrete times Volterra models, enabling scalable representation of highly nonlinear system. This scalability comes at the cost of introducing randomness through…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
We study the Weighted Min Cut problem in the Adaptive Massively Parallel Computation (AMPC) model. In 2019, Behnezhad et al. [3] introduced the AMPC model as an extension of the Massively Parallel Computation (MPC) model. In the past…
This paper presents a quantum algorithm for efficiently decoding hypervectors, a crucial process in extracting atomic elements from hypervectors - an essential task in Hyperdimensional Computing (HDC) models for interpretable learning and…
Linear systems with a tensor product structure arise naturally when considering the discretization of Laplace type differential equations or, more generally, multidimensional operators with separable coefficients. In this work, we focus on…