相关论文: Improved variants of the Hutch++ algorithm for tra…
Stochastic computing is a paradigm in which logical operations are performed on randomly generated bit streams. Complex arithmetic operations can be executed by simple logic circuits, resulting in a much smaller area footprint compared to…
In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…
In this paper, we propose a novel bootstrap algorithm that is more efficient than existing methods for approximating the distribution of the factor-augmented regression estimator for a rotated parameter vector. The regression is augmented…
An algorithm for solving nonconvex smooth optimization problems is proposed, analyzed, and tested. The algorithm is an extension of the Trust Region Algorithm with Contractions and Expansions (TRACE) [Math. Prog. 162(1):132, 2017]. In…
A survey of a variety of computational procedures for finding the mean first passage times in Markov chains is presented. The author recently developed a new accurate computational technique, an Extended GTH Procedure, Hunter (Special…
In this work, we present the tree tensor network Nystr\"om (TTNN), an algorithm that extends recent research on streamable tensor approximation, such as for Tucker and tensor-train formats, to the more general tree tensor network format,…
We introduce an algorithm for estimating the trace of a matrix function $f(\mathbf{A})$ using implicit products with a symmetric matrix $\mathbf{A}$. Existing methods for implicit trace estimation of a matrix function tend to treat…
Randomized algorithms in numerical linear algebra have proven to be effective in ameliorating issues of scalability when working with large matrices, efficiently producing accurate low-rank approximations. A key remaining challenge,…
${\cal H}^2$-matrix constitutes a general mathematical framework for efficient computation of both partial-differential-equation and integral-equation-based operators. Existing linear-complexity ${\cal H}^2$ matrix-matrix product (MMP)…
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…
In recent years, the fervent demand for computational power across various domains has prompted hardware manufacturers to introduce specialized computing hardware aimed at enhancing computational capabilities. Particularly, the utilization…
A new, fast second-order method is proposed that achieves the optimal $\mathcal{O}\left(|\log(\epsilon)|\epsilon^{-3/2}\right)$ complexity to obtain first-order $\epsilon$-stationary points. Crucially, this is deduced without assuming the…
This article proposes a biconvex modification to convex biclustering in order to improve its performance in high-dimensional settings. In contrast to heuristics that discard a subset of noisy features a priori, our method jointly learns and…
Learning-based low rank approximation algorithms can significantly improve the performance of randomized low rank approximation with sketch matrix. With the learned value and fixed non-zero positions for sketch matrices from learning-based…
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…
We present a cache-oblivious adaptation of matrix multiplication to be incorporated in the parallel TU decomposition for rectangular matrices over finite fields, based on the Morton-hybrid space-filling curve representation. To realise…
Finding a good approximation of the top eigenvector of a given $d\times d$ matrix $A$ is a basic and important computational problem, with many applications. We give two different quantum algorithms that, given query access to the entries…
Recently, randomized algorithms for low-rank approximation of quaternion matrices have received increasing attention. However, for large-scale problems, existing quaternion orthonormalizations are inefficient, leading to slow rangefinders.…
Monte Carlo matrix trace estimation is a popular randomized technique to estimate the trace of implicitly-defined matrices via averaging quadratic forms across several observations of a random vector. The most common approach to analyze the…
Precision matrix, which is the inverse of covariance matrix, plays an important role in statistics, as it captures the partial correlation between variables. Testing the equality of two precision matrices in high dimensional setting is a…