Related papers: Efficient computation of matrix-vector products wi…
We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, "compression," of an arbitrary dense symmetric positive definite (SPD) matrix. For many applications, GOFMM enables an approximate…
The spatial error model (SEM) is a type of simultaneous autoregressive (SAR) model for analysing spatially correlated data. Markov chain Monte Carlo (MCMC) is one of the most widely used Bayesian methods for estimating SEM, but it has…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
Data assimilation is a method that combines observations (that is, real world data) of a state of a system with model output for that system in order to improve the estimate of the state of the system and thereby the model output. The model…
A fast algorithm for the approximate multiplication of matrices with decay is introduced; the Sparse Approximate Matrix Multiply (SpAMM) reduces complexity in the product space, a different approach from current methods that economize…
We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a…
Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…
Approximate matrix multiplication with limited space has received ever-increasing attention due to the emergence of large-scale applications. Recently, based on a popular matrix sketching algorithm -- frequent directions, previous work has…
We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…
We describe spatio-temporal random processes using linear mixed models. We show how many commonly used models can be viewed as special cases of this general framework and pay close attention to models with separable or product-sum…
Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…
We demonstrate a new, hybrid symbolic-numerical method for the automatic synthesis of all families of translation operators required for the execution of the Fast Multipole Method (FMM). Our method is applicable in any dimensionality and to…
Recent work shows that inference for Gaussian processes can be performed efficiently using iterative methods that rely only on matrix-vector multiplications (MVMs). Structured Kernel Interpolation (SKI) exploits these techniques by deriving…
We study the approximation of integrals $\int_D f(\boldsymbol{x}^\top A) \mathrm{d} \mu(\boldsymbol{x})$, where $A$ is a matrix, by quasi-Monte Carlo (QMC) rules $N^{-1} \sum_{k=0}^{N-1} f(\boldsymbol{x}_k^\top A)$. We are interested in…
Recursive adaptive filtering methods are often used for solving the problem of simultaneous state and parameters estimation arising in many areas of research. The gradient-based schemes for adaptive Kalman filtering (KF) require the…
Accurate estimation and forecasting of energy consumption are important for power-system operation, planning, and demand-side management. In practice, however, complete and timely measurements may not always be available, and the observed…
As nowadays Machine Learning (ML) techniques are generating huge data collections, the problem of how to efficiently engineer their storage and operations is becoming of paramount importance. In this article we propose a new lossless…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
Various Neural Networks employ time-consuming matrix operations like matrix inversion. Many such matrix operations are faster to compute given the Singular Value Decomposition (SVD). Previous work allows using the SVD in Neural Networks…
Learning by integrating multiple heterogeneous data sources is a common requirement in many tasks. Collective Matrix Factorization (CMF) is a technique to learn shared latent representations from arbitrary collections of matrices. It can be…