142 citations · 214 across the 30 of their papers we have counts for
38 papers
Revisiting column subset selection through the lens of submodularity
Ilse C. F. Ipsen, Arvind K. Saibaba
The problem is to select k columns with maximal volume from a real mxn matrix X. We show that the logarithm of the volume is a set submodular function on columns of X, and for full…
Numerically Stable Cholesky-QR on GPU via Mixed-Precision Randomized Preconditioning
James E. Garrison, Chao Chen, Ilse C. F. Ipsen
Cholesky-QR is among the fastest algorithms for computing the thin QR factorization of tall-and-skinny matrices on GPUs, relying entirely on BLAS-3 operations. However, it is numer…
THE ROLE OF FOURIER ANALYSIS IN TWO DIMENSIONAL TOMOGRAPHY
Andre Mas, Fatma Terzioglu, Ilse C. F. Ipsen
We highlight the important role of the Fourier transform in deriving inversion formulas for the integral transforms of tomographic imaging. We demonstrate this principle by derivin…
Perturbation Analysis for Preconditioned Normal Equations in Mixed Precision
James E. Garrison, Ilse C. F. Ipsen
For real matrices of full column-rank, we analyze the conditioning of several types of normal equations that are preconditioned by a randomized preconditioner computed in lower pre…
Many (most?) column subset selection criteria are NP hard for a few columns
Ilse C. F. Ipsen, Arvind K. Saibaba
We consider a variety of criteria for selecting k representative columns from a real mxn matrix A, when sufficiently few columns are required, i.e., 1<= k<= min{rank(A), m/3}. The…
Stochastic Trace Optimization of Parameter Dependent Matrices Based on Statistical Learning Theory
Arvind K. Saibaba, Ilse C. F. Ipsen
We consider matrices that depend, possibly nonlinearly, on a parameter from a compact parameter space . We…
Solution of Least Squares Problems with Randomized Preconditioned Normal Equations
Ilse C. F. Ipsen
We consider the solution of full column-rank least squares problems by means of normal equations that are preconditioned, symmetrically or non-symmetrically, with a randomized prec…
Stochastic Rounding 2.0, with a View towards Complexity Analysis
Petros Drineas, Ilse C. F. Ipsen
Stochastic Rounding is a probabilistic rounding mode that is surprisingly effective in large-scale computations and low-precision arithmetic. Its random nature promotes error cance…
Stable Rank and Intrinsic Dimension of Real and Complex Matrices
Ilse C. F. Ipsen, Arvind K. Saibaba
The notion of `stable rank' of a matrix is central to the analysis of randomized matrix algorithms, covariance estimation, deep neural networks, and recommender systems. We compare…
A randomized preconditioned Cholesky-QR algorithm
James E. Garrison, Ilse C. F. Ipsen
We a present and analyze rpCholesky-QR, a randomized preconditioned Cholesky-QR algorithm for computing the thin QR factorization of real mxn matrices with rank n. rpCholesky-QR ha…
Stochastic Rounding Implicitly Regularizes Tall-and-Thin Matrices
Gregory Dexter, Christos Boutsikas, Linkai Ma +2
Motivated by the popularity of stochastic rounding in the context of machine learning and the training of large-scale deep neural network models, we consider stochastic nearness ro…
Small singular values can increase in lower precision
Christos Boutsikas, Petros Drineas, Ilse C. F. Ipsen
We perturb a real matrix of full column rank, and derive lower bounds for the smallest singular values of the perturbed matrix, in terms of normwise absolute perturbations. Our…
Statistical Properties of the Probabilistic Numeric Linear Solver BayesCG
Tim W. Reid, Ilse C. F. Ipsen, Jon Cockayne +1
We analyse the calibration of BayesCG under the Krylov prior, a probabilistic numeric extension of the Conjugate Gradient (CG) method for solving systems of linear equations with s…
Robust Parameter Identifiability Analysis via Column Subset Selection
Katherine J. Pearce, Ilse C. F. Ipsen, Mansoor A. Haider +2
We advocate a numerically reliable and accurate approach for practical parameter identifiability analysis: Applying column subset selection (CSS) to the sensitivity matrix, instead…
Precision-aware Deterministic and Probabilistic Error Bounds for Floating Point Summation
Eric Hallman, Ilse C. F. Ipsen
We analyze the forward error in the floating point summation of real numbers, for computations in low precision or extreme-scale problem dimensions that push the limits of the prec…
Monte Carlo Methods for Estimating the Diagonal of a Real Symmetric Matrix
Eric Hallman, Ilse C. F. Ipsen, Arvind Saibaba
For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds…
Deterministic and Probabilistic Error Bounds for Floating Point Summation Algorithms
Eric Hallman, Ilse C. F. Ipsen
We analyse the forward error in the floating point summation of real numbers, from algorithms that do not require recourse to higher precision or better hardware. We derive informa…
SEAGLE: A Scalable Exact Algorithm for Large-Scale Set-Based GxE Tests in Biobank Data
Jocelyn T. Chi, Ilse C. F. Ipsen, Tzu-Hung Hsiao +5
The explosion of biobank data offers immediate opportunities for gene-environment (GxE) interaction studies of complex diseases because of the large sample sizes and the rich colle…
Probabilistic Iterative Methods for Linear Systems
Jon Cockayne, Ilse C. F. Ipsen, Chris J. Oates +1
This paper presents a probabilistic perspective on iterative methods for approximating the solution of a nonsingular linear system $\mathbf{A} \math…
BayesCG As An Uncertainty Aware Version of CG
Tim W. Reid, Ilse C. F. Ipsen, Jon Cockayne +1
The Bayesian Conjugate Gradient method (BayesCG) is a probabilistic generalization of the Conjugate Gradient method (CG) for solving linear systems with real symmetric positive def…
Multiplicative Perturbation Bounds for Multivariate Multiple Linear Regression in Schatten -Norms
Jocelyn T. Chi, Ilse C. F. Ipsen
Multivariate multiple linear regression (MMLR), which occurs in a number of practical applications, generalizes traditional least squares (multivariate linear regression) to multip…
Probabilistic Error Analysis for Inner Products
Ilse C. F. Ipsen, Hua Zhou
Probabilistic models are proposed for bounding the forward error in the numerically computed inner product (dot product, scalar product) between of two real -vectors. We derive…
Probabilistic Linear Solvers: A Unifying View
Simon Bartels, Jon Cockayne, Ilse C. F. Ipsen +1
Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, e…
A Projector-Based Approach to Quantifying Total and Excess Uncertainties for Sketched Linear Regression
Jocelyn T. Chi, Ilse C. F. Ipsen
Linear regression is a classic method of data analysis. In recent years, sketching -- a method of dimension reduction using random sampling, random projections, or both -- has gain…