Related papers: Novel technique based on L\'eja Points Approximati…
We consider the approximation of $B^T (A+sI)^{-1} B$ where $A\in\mathbb{R}^{n\times n}$ is large, symmetric positive definite, and has a dense spectrum, and $B\in\mathbb{R}^{n\times p}$, $p\ll n$. Our target application is the computation…
System logs are some of the most important information for the maintenance of software systems, which have become larger and more complex in recent years. The goal of log-based anomaly detection is to automatically detect system anomalies…
High dimensional data and systems with many degrees of freedom are often characterized by covariance matrices. In this paper, we consider the problem of simultaneously estimating the dimension of the principal (dominant) subspace of these…
This paper studies the estimation of a large covariance matrix. We introduce a novel procedure called ChoSelect based on the Cholesky factor of the inverse covariance. This method uses a dimension reduction strategy by selecting the pattern…
We study the problem of computing the maximum likelihood estimator (MLE) of multivariate log-concave densities. Our main result is the first computationally efficient algorithm for this problem. In more detail, we give an algorithm that, on…
In this paper, we consider the estimation of a change-point for possibly high-dimensional data in a Gaussian model, using a k-means method. We prove that, up to a logarithmic term, this change-point estimator has a minimax rate of…
Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g.,…
This paper is concerned with the problem of approximating the determinant of A for a large sparse symmetric positive definite matrix A. It is shown that an efficient solution of this problem is obtained by using a sparse approximate inverse…
Due to their importance in both data analysis and numerical algorithms, low rank approximations have recently been widely studied. They enable the handling of very large matrices. Tight error bounds for the computationally efficient…
Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic…
Hutchinson's method estimates the trace of a matrix function $f(D)$ stochastically using samples $\tau^Hf(D)\tau$, where the components of the random vectors $\tau$ obey an isotropic probability distribution. Estimating the trace of the…
This paper studies the estimation of large precision matrices and Cholesky factors obtained by observing a Gaussian process at many locations. Under general assumptions on the precision and the observations, we show that the sample…
We present an acceleration of the well-established Krylov-Ritz methods to compute the sign function of large complex matrices, as needed in lattice QCD simulations involving the overlap Dirac operator at both zero and nonzero baryon…
The L1-regularized maximum likelihood estimation problem has recently become a topic of great interest within the machine learning, statistics, and optimization communities as a method for producing sparse inverse covariance estimators. In…
In this paper numerical methods for solving stochastic differential equations with Markovian switching (SDEwMSs) are developed by pathwise approximation. The proposed family of strong predictor-corrector Euler-Maruyama methods is designed…
We show that Laplacian and symmetric diagonally dominant (SDD) matrices can be well approximated by linear-sized sparse Cholesky factorizations. We show that these matrices have constant-factor approximations of the form $L L^{T}$, where…
Matrix determinants play an important role in data analysis, in particular when Gaussian processes are involved. Due to currently exploding data volumes, linear operations - matrices - acting on the data are often not accessible directly…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
The L infinity star discrepancy is a measure for how uniformly a point set is distributed in a given space. Point sets of low star discrepancy are used as designs of experiments, as initial designs for Bayesian optimization algorithms, for…
The likelihood functions for discretely observed nonlinear continuous-time models based on stochastic differential equations are not available except for a few cases. Various parameter estimation techniques have been proposed, each with…