相关论文: Improved variants of the Hutch++ algorithm for tra…

This paper studies an optimization problem on the sum of traces of matrix quadratic forms in $m$ semi-orthogonal matrices, which can be considered as a generalization of the synchronization of rotations. While the problem is nonconvex, the…

Matrix completion tackles the task of predicting missing values in a low-rank matrix based on a sparse set of observed entries. It is often assumed that the observation pattern is generated uniformly at random or has a very specific…

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…

A zeroth-order Hessian estimator aims to recover the Hessian matrix of an objective function at any given point, using minimal finite-difference computations. This paper studies zeroth-order Hessian estimation for low-rank Hessians, from a…

We introduce a novel algorithm that leverages stochastic sampling techniques to compute the perturbative triples correction in the coupled-cluster (CC) framework. By combining elements of randomness and determinism, our algorithm achieves a…

Approximating a function $f(x)$ on $[-1,1]$ based on $N+1$ samples is a classical problem in numerical analysis. If the samples come with heteroskedastic noise depending on $x$ of variance $\sigma(x)^2$, an $O(N\log N)$ algorithm for this…

Trotter and linear-combination-of-unitary (LCU) are two popular Hamiltonian simulation methods. We propose Hamiltonian simulation algorithms using LCU to compensate Trotter error, which enjoy both of their advantages. By adding few gates…

We show that, for finite-sum minimization problems, incorporating partial second-order information of the objective function can dramatically improve the robustness to mini-batch size of variance-reduced stochastic gradient methods, making…

We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…

The CUR matrix decomposition and the Nystr\"{o}m approximation are two important low-rank matrix approximation techniques. The Nystr\"{o}m method approximates a symmetric positive semidefinite matrix in terms of a small number of its…

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…

Covariance matrix estimates are an essential part of many signal processing algorithms, and are often used to determine a low-dimensional principal subspace via their spectral decomposition. However, exact eigenanalysis is computationally…

We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…

Motivated by the need for efficient estimation of conditional expectations, we consider a least-squares function approximation problem with heavily polluted data. Existing methods that are effective in the small-noise regime are suboptimal…

We describe a new method to map the requested error tolerance on an H-matrix approximation to the block error tolerances. Numerical experiments show that the method produces more efficient approximations than the standard method for kernels…

Randomized compilation protocols have recently attracted attention as alternatives to traditional deterministic Trotter-Suzuki methods, potentially reducing circuit depth and resource overhead. These protocols determine gate application…

Assessing sampling uncertainty in extremum estimation can be challenging when the asymptotic variance is not analytically tractable. Bootstrap inference offers a feasible solution but can be computationally costly especially when the model…

We derive an estimate of statistical error in calculating the trace of a large matrix by using random vector, and show that {\em random phase vector} gives the results with the smallest statistical error for a given basis set. This result…

Hidden Markov models (HMMs) are popular models to identify a finite number of latent states from sequential data. However, fitting them to large data sets can be computationally demanding because most likelihood maximization techniques…

Hamiltonian Monte-Carlo (HMC) and its auto-tuned variant, the No U-Turn Sampler (NUTS) can struggle to accurately sample distributions with complex geometries, e.g., varying curvature, due to their constant step size for leapfrog…