Related papers: Avoiding matrix exponentials for large transition …
Recent work in machine learning community proposed multiple methods for performing lossy compression (quantization) of large matrices. This quantization is important for accelerating matrix multiplication (main component of large language…
Efficient methods for computing with matrices over finite fields often involve randomised algorithms, where matrices with a certain property are sought via repeated random selection. Complexity analyses for these algorithms require…
We present a new algorithm for computing the Lyapunov exponents spectrum based on a matrix differential equation. The approach belongs to the so called continuous type, where the rate of expansion of perturbations is obtained for all times,…
In this work, an approximate family of implicit multiderivative Runge-Kutta (MDRK) time integrators for stiff initial value problems is presented. The approximation procedure is based on the recent Approximate Implicit Taylor method (Baeza…
We propose an efficient algorithmic framework for time domain circuit simulation using exponential integrator. This work addresses several critical issues exposed by previous matrix exponential based circuit simulation research, and makes…
This review covers recent results concerning the estimation of large covariance matrices using tools from Random Matrix Theory (RMT). We introduce several RMT methods and analytical techniques, such as the Replica formalism and Free…
Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of $N$ interacting auxiliary chains targeting tempered…
Fast matrix-by-matrix multiplication (hereafter MM) is a highly recognized research subject. The record upper bound 3 of 1968 on the exponent of the complexity MM decreased below 2.38 by 1987, applies to celebrated problems in many areas of…
The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…
In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…
The training process of neural networks is known to be time-consuming, and having a deep architecture only aggravates the issue. This process consists mostly of matrix operations, among which matrix multiplication is the bottleneck. Several…
In the following article we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment (DA) model which has a likelihood…
In this paper, we introduce a powerful technique based on Leave-one-out analysis to the study of low-rank matrix completion problems. Using this technique, we develop a general approach for obtaining fine-grained, entrywise bounds for…
In this paper we show how to calculate explicitly the exponential of certain matrices, which are evolution operators governing the interaction of the four level system of atoms and the radiation, etc. We present a consistent method in terms…
We establish $L^2$-exponential convergence rate for three popular piecewise deterministic Markov processes for sampling: the randomized Hamiltonian Monte Carlo method, the zigzag process, and the bouncy particle sampler. Our analysis is…
We consider the rank minimization problem from quadratic measurements, i.e., recovering a rank $r$ matrix $X \in \mathbb{R}^{n \times r}$ from $m$ scalar measurements $y_i=a_i^{\top} XX^{\top} a_i,\;a_i\in \mathbb{R}^n,\;i=1,\ldots,m$. Such…
In the present paper, we propose Krylov-based methods for solving large-scale differential Sylvester matrix equations having a low rank constant term. We present two new approaches for solving such differential matrix equations. The first…
This paper develops a new exponential forgetting algorithm that can prevent so-called the estimator windup problem, while retaining fast convergence speed. To investigate the properties of the proposed forgetting algorithm, boundedness of…
Nonnegative tensors arise very naturally in many applications that involve large and complex data flows. Due to the relatively small requirement in terms of memory storage and number of operations per step, the (shifted) higher-order power…