Publications

2021

• H. L. de Kergorlay and D. J. Higham. Consistency of anchor-based spectral clustering, Information and Inference: A Journal of the IMA, to appear, 2021.
• D. J. Higham and H. L. de Kergorlay. Epidemics on hypergraphs: Spectral thresholds for extinction, Proceedings of the Royal Society, Series A, to appear, 2021.
• F. Tudisco and Desmond J. Higham. Node and edge eigenvector centrality for hypergraphs, Communications Physics, to appear, 2021.
• F. Arrigo, D. J. Higham and V. Noferini. A theory for backtrack-downweighted walks, SIAM Journal on Matrix Analysis and Applications, to appear, 2021.
• O. Sheridan-Methven. Nested multilevel Monte Carlo methods and a modified Euler-Maruyama scheme utilising approximate Gaussian random variables suitable for vectorised hardware and low-precisions, PhD thesis, Oxford University.
• N. J. Higham. The mathematics of floating-point arithmetic, LMS Newsletter, 493:35–41, 2021.
• T. Karvonen, C. J. Oates, and M. Girolami. Integration in reproducing kernel Hilbert spaces of Gaussian kernels, Mathematics of Computation, pages 1, June 2021.
• M. Croci, M.B. Giles, M.E. Rognes, and P.E. Farrell. Multilevel quasi Monte Carlo methods for elliptic partial differential equations driven by spatial white noise, to appear in SISC, June 2021.
• M. Zounon, N. J. Higham, C. Lucas and F. Tisseur. Performance Impact of Precision Reduction In Sparse Linear Systems Solvers, MIMS EPrint 2020.20, September 2020, revised June 2021.
• S. A. Niederer, M. S. Sacks, M. Girolami, and K. Willcox. Scaling digital twins from the artisanal to the industrial, Nature Computational Science, 1(5):313–320, May 2021.
• G. Wynne, F. X. Briol, and M. Girolami. Convergence Guarantees for Gaussian Process Means with Misspecified Likelihoods and Smoothness, Journal of Machine Learning Research 22 (123): 1–40, May 2021.
• P. Amestoy, A. Buttari, N. J. Higham, J.-Y. L’Excellent, T. Mary, and B. Vieublé. Five-precision GMRES-based iterative refinement, MIMS EPrint 2021.5, April 2021.
• A. Scillitoe, P. Seshadri and M. Girolami. Uncertainty quantification for data-driven turbulence modelling with Mondrian forests, Journal of Computational Physics, Volume 430, April 2021.
• M. Fasi and N. J. Higham. Matrices with Tunable Infinity-Norm Condition Number and No Need for Pivoting in LU Factorization, SIAM J. Matrix Anal. Appl. 42(1):417–435, March 2021.
• N. J. Higham and X. Liu. A Multiprecision Derivative-Free Schur-Parlett Algorithm for Computing Matrix Functions, MIMS EPrint 2020.19, September 2020; revised March 2021 22 pp. To appear in SIAM J. Matrix Anal. Appl.
• A. Abdelfattah et al. A Survey of Numerical Methods Utilizing Mixed Precision Arithmetic ,Int. J. High Performance Computing Applications, 109434202110033, March 2021.
• M. Girolami, E. Febrianto, G. Yin and F. Cirak. The statistical finite element method (statFEM) for coherent synthesis of observation data and model predictions, Computer Methods in Applied Mechanics and Engineering, Volume 375, March 2021.
• C. Gilmour and D. J. Higham. Modelling burglary in Chicago using a self-exciting point process with isotropic triggering, European Journal of Applied Mathematics, 1-23, to appear, 2021.
• M.B. Giles and O. Sheridan-Methven. Analysis of nested multilevel Monte Carlo using approximate Normal random variable, arXiv pre-print, February 2021.
• M. Fasi and N. J. Higham. Generating Extreme-Scale Matrices with Specified Singular Values or Condition Numbers, SIAM J. Sci. Comput., 43(1):A663–A684, February 2021.
• M. P. Connolly, N. J. Higham and T. Mary. Stochastic Rounding and Its Probabilistic Backward Error Analysis, SIAM J. Sci. Comput., 43(1):A566–A585, February 2021.
• M. Fasi, N. J. Higham, M. Mikaitis and S. Pranesh. Numerical Behavior of NVIDIA Tensor Cores, PeerJ Comput. Sci. 7:e330(1–19), February 2021.
• D. J. Higham, N. J. Higham and S. Pranesh. Random Matrices Generating Large Growth in LU Factorization with Pivoting, SIAM J. Matrix Anal. Appl., 42(1):185–201, February 2021.
• S. Virtanen and M. Girolami. Spatio-Temporal Mixed Membership Models for Criminal Activity,  Journal of the Royal Statistical Society Series A: Statistics in Society, January 2021.
• N. J. Higham and S. Pranesh. Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems, SIAM J. Sci. Comput., 43(1):A258–A277, January 2021.

2020

• M. Jans-Singh, K. Leeming, R. Choudhary, and M. Girolami. Digital twin of an urban-integrated hydroponic farm, Data-Centric Engineering, December 2020.
• M. Dhada, M. Girolami, and A. K. Parlikad. Anomaly detection in a fleet of industrial assets with hierarchical statistical modeling, Data-Centric Engineering, December 2020
• C. Duffin, E. Cripps, T. Stemler, and M. Girolami. Statistical finite elements for misspecified models. Proceedings of the National Academy of Sciences, 118(2):e2015006118, December 2020.
• M. Jans-Singh, K. Leeming, R. Choudhary, and M. Girolami. Digital Twin of an Urban-Integrated Hydroponic Farm, Data-Centric Engineering 1, December 2020.
• E. Carson, N. J. Higham and S. Pranesh. Three-Precision GMRES-based Iterative Refinement for Least Squares Problems, SIAM J. Sci. Comput., 42(6):A4063-A40835, December 2020.
• C. Yui Wong, P. Seshadri, G. T. Parks and M. Girolami. Embedded ridge approximations, Computer Methods in Applied Mechanics and Engineering, Volume 372, December 2020.
• K. Menberg, A. Bidarmaghz, A. Gregory, R. Choudhary, and M. Girolami. Multi-fidelity approach to bayesian parameter estimation in subsurface heat and fluid transport models, Science of The Total Environment, 745, 140846, November 2020.
• R. Sacks, I. Brilakis, E. Pikas, H. Sally Xie, and M. Girolami. Construction with digital twin information systems, Data-Centric Engineering, November 2020.
• A. Haidar, H. Bayraktar, S. Tomov,  J. Dongarra and N. J. Higham. Mixed-Precision Iterative Refinement Using Tensor Cores on GPUs to Accelerate Solution of Linear Systems, Proc. Roy. Soc. London A, 476 (2243):20200110, November 2020.
• M. Croci and M.B. Giles. Effects of round-to-nearest and stochastic rounding in the numerical solution of the heat equation in low precision, arXiv pre-print, October 2020.
• N. J. Higham and T. Mary. Sharper Probabilistic Backward Error Analysis for Basic Linear Algebra Kernels with Random Data, SIAM J. Sci. Comput., 42(5), A3427–A3446, October 2020.
• J. Povala, S. Virtanen, and M. Girolami. Forthcoming 2020. Burglary in London: Insights from Statistical Heterogeneous Spatial Point Processes, Journal of the Royal Statistical Society. Series C (Applied Statistics). Code.
• S. Virtanen and M. Girolami. Dynamic Content Based Ranking. To appear in AISTATS, 2020.
• K. Monterrubio-Gómez, L. Roininen, S. Wade, T. Damoulas, and M. Girolami. Posterior inference for sparse hierarchical non-stationary models, Computational Statistics and Data Analysis, 148, 106954, 2020.
• S.-C. Kuok, K.-V. Yuen, S. Roberts, and M. A. Girolami. Propagative broad learning for nonparametric modeling of ambient effects on structural health indicators, Structural Health Monitoring, 20(4), 1409-1427, May 2020.
• A. Haidar, H. Bayraktar, S. Tomov, J. Dongarra and N. J. Higham. Mixed-Precision Solution of Linear Systems Using Accelerator-Based Computing, Technical Report ICL-UT-20-05, Innovative Computing Laboratory, University of Tennessee, Knoxville, TN, USA, May 2020.
• I. Y. Tyukin, D. J. Higham and A .N. Gorban. On adversarial examples and stealth attacks in artificial intelligence systems, IEEE International Joint Conference on Neural Networks (IJCNN), 2020.
• A. Mantzaris and D. J. Higham. A network model for polarization of political opinion, Chaos: An Interdisciplinary Journal of Nonlinear Science, 30(4), 043109, April 2020.
• F. Arrigo, D. J. Higham and F. Tudisco. A framework for second-order eigenvector centralities and clustering coefficients, Proceedings of the Royal Society, Series A, 476, March 2020.
• F. Arrigo, D. J. Higham and V. Noferini. Beyond non-backtracking: Non-cycling network centrality measures, Proceedings of the Royal Society, Series A, 476, March 2020.
• N. J. Higham and E. Hopkins. A Catalogue of Software for Matrix Functions. Version 3.0, MIMS EPrint 2020.7, March 2020.
• J. Dongarra, L. Grigori N. J. Higham. Numerical Algorithms for High-Performance Computational Science, Phil. Trans. R. Soc. A, 378(2166):1-18, 2020
• A. Barp, F-X. Briol., A. B. Duncan, M. Girolami and L. Mackey. Minimum Stein discrepancy estimators, arXiv:1906.08283. To appear in Neural Information Processing Systems.
• W. Fang and M.B. Giles. Adaptive Euler-Maruyama method for SDEs with non-globally Lipschitz drift, Annals of Applied Probability, 30(2):526-560, 2020
• C. Gilmour and D. J. Higham. Modelling and inferring the triggering function in a self-exciting point process, Proceedings of “Numerical Analysis and Optimization 2020”  Muscat, Springer.

2019

• G. D. Ranasinghe, T. Lindgren, M. Girolami and A. K. Parlikad. A Methodology for Prognostics Under the Conditions of Limited Failure Data Availability ,IEEE Access, vol. 7, pp. 183996-184007, 2019.
• S. Virtanen and M. Girolami. Precision-Recall Balanced Topic Modelling. Thirty-third Conference on Neural Information Processing Systems, NeurIPS 2019.
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• N. J. Higham and T. Mary. A New Approach to Probabilistic Rounding Error Analysis, SIAM J. Sci. Comput., 41(5):A2815-A2835, 2019.
• N. J. Higham. Error Analysis For Standard and GMRES-Based Iterative Refinement in Two and Three-Precisions, MIMS EPrint 2019.19, November 2019.
• F. Arrigo, D. J. Higham and V. Noferini. Non-backtracking PageRank, Journal of Scientific Computing, 80(3), 1419-1437, 2019.
• F. Tudisco and D. J. Higham. A fast and robust kernel optimization method for core-periphery detection in directed and weighted graphs, Applied Network Science, 4(1), 1-13, 2019
• C. F. Higham and D. J. Higham. Deep learning: An introduction for applied mathematicians, SIAM Review, 61, 860–891, 2019.
• F. Tudisco and D. J. Higham. A nonlinear spectral method for core–periphery detection in networks, SIAM Journal on Mathematics of Data Science, 1(2), 269-292, 2019.
• D. J. Higham. Centrality-friendship paradoxes: When our friends are more important than us, Journal of Complex Networks, 7, 515–528, 2019.
• P. Blanchard, N.J. Higham, F. Lopez, T. Mary and S. Pranesh. Mixed Precision Block Fused Multiply-Add: Error Analysis and Application to GPU Tensor Coress, SIAM J. Sci. Comput., 42(3):C124-C141, 2020.
• P. Blanchard, D. J. Higham and N. J. Higham. Accurately Computing the Log-Sum-Exp and Softmax Functions, MIMS EPrint 2019.16, September 2019; revised May 2020. 19 pp. To appear in IMA J. Numer. Anal.
• N. J. Higham and T. Mary. Solving Block Low-Rank Linear Systems by LU Factorization is Numerically Stable, IMA J. Numer. Anal., 1–30. 2021 (Advanced access)
• P. Blanchard, D. J. Higham and N. J. Higham. Accurate Computation of the Log-Sum-Exp and Softmax Functions, MIMS EPrint 2019.16, 2019.
• P. Blanchard, N. J. Higham and T. Mary. A Class of Fast and Accurate Summation Algorithms, SIAM J. Sci. Comput., 42(3):A1541-A1557, 2020.
• O. Hamelijnck, T. Damoulas, K. Wang, M. Girolami, Multi-resolution Multi-task Gaussian Processes. Thirty-third Conference on Neural Information Processing Systems, NeurIPS 2019, arXiv preprint arXiv:1906.08344, 2019.
• W. Y. Chen, A. Barp, F- X. Briol, J. Gorham, M. Girolami, L. Mackey, C. J. Oates. Stein point Markov chain Monte Carlo, International Conference on Machine Learning, PMLR 97:1011-1021, 2019.
• F-X. Briol, C. J. Oates, M. Girolami, M. A. Osborne and D. Sejdinovic. Probabilistic integration: a role in statistical computation? Statistical Science, Vol 34, Number 1, pp1-22, 2019.
• C. J. Oates, J. Cockayne, F-X. Briol and  M. Girolami, Convergence rates for a class of estimators based on Stein’s identity, Bernoulli, Vol. 25, No. 2, 1141-1159.
• N. J. Higham and S. Pranesh. Simulating Low Precision Floating-Point Arithmetic, MIMS EPrint 2019.4, 2019.
• J. Cockayne, C. J. Oates, I. Ipsen and M. Girolami. A Bayesian Conjugate Gradient Method, Bayesian Anal., advance publication, 18 May 2019. doi:10.1214/19-BA1145, 2019.
• H. Anzt, J. Dongarra, G. Flegar, N. J. Higham and E. S. Quintana-Orti. Adaptive Precision in Block-Jacobi Preconditioning for Iterative Sparse Linear System Solvers, Concurrency Computat.: Pract. Exper, 31(6), e4460, 2019.
• N. J. Higham and T. Mary. A new preconditioner that exploits low-rank approximations to factorization error, SIAM J. Sci. Comput., 41(1), A59-A82, 2019.
• W. Fang and M.B. Giles. Multilevel Monte Carlo method for ergodic SDEs without contractivity, Journal of Mathematical Analysis and Applications, 476(1):149-176, 2019.

• D. F. Anderson, D. J. Higham, S. C. Leite and R. J. Williams. On constrained Langevin equations and (bio)chemical reaction networks, Multiscale Modeling and Simulation (SIAM), 17(1), 1-30, 2019.

2018

• M. Fasi and N. J. Higham. An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential, MIMS EPrint 2018.36, 2018.
• A.Haidar, S. Tomov, J. Dongarra and N. J. Higham. Harnessing GPU Tensor Cores for Fast FP16 Arithmetic to Speed up Mixed-Precision Iterative Refinement Solvers, In Proceedings of the International Conference for High Performance Computing, Networking, Storage, and Analysis (p. 47), IEEE Press, 2018.
• M. M. Dunlop, M. A. Girolami, A. M. Stuart and A. L. Teckentrup. How deep are deep Gaussian processes?, The Journal of Machine Learning Research, 19(1), 2100-2145, 2018.
• P. Grindrod and D. J. Higham. High modularity creates scaling laws, Scientific Reports, 8(1), pp.1-9, 2018.
• M. Fasi and N. J. Higham. Multiprecision Algorithms for Computing The Matrix Logarithm, SIAM J. Matrix Anal. Appl., 39(1):472-491, 2018.
• L. Ellam, G. Pavliotis, M. Girolami, A. Wilson, Stochastic modelling of urban structure, Proc. R. Soc. A, rspa.2017.0700, 2018.
• M. Croci, M.B. Giles, M.E. Rognes, P.E. Farrell. Efficient white noise sampling and coupling for multilevel Monte Carlo with non-nested meshes, SIAM/ASA Journal on Uncertainty Quantification, 6(4):1630-1655, 2018.
• M. B. Giles, Multilevel Monte Carlo methods, Acta Numerica, 10.1017/S09624929, 2018.
• M. Fasi and N. J. Higham. Multiprecision Algorithms for Computing the Matrix Logarithm, SIAM J. Matrix Anal. Appl., 39(1), 472–491, 2018.
• E. Carson and N, J. Higham, Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions, SIAM J. Sci. Comput., 40(2), A817–A847, 2018.
• H. Anzt, J. Dongarra, G. Flegar, N. J. Higham and E. S. Quintana-Orti, Adaptive Precision in Block-Jacobi Preconditioning for Iterative Sparse Linear System Solvers, Concurrency Computat.: Pract. Exper., 2018.
• A. Barp, F-X. Briol, A. D. Kennedy and M. Girolami. Geometry and dynamics for Markov chain Monte Carlo, Annual Review of Statistics and Its Applications, Vol. 5:451-471, 2018.

2017

• F-X. Briol, C. J. Oates, J. Cockayne, W. Y. Chen and M. Girolami.  On the sampling problem for kernel quadrature, Proceedings of the 34th International Conference on Machine Learning, PMLR 70:586-595, 2017.
• E. Carson and N. J. Higham. A new analysis of iterative refinement and its application to accurate solution of ill-conditioned sparse linear systems, SIAM J. Sci. Comput., 39(6):A2834-A2856, 2017.
• L. Ellam, H. Strathmann, M. Girolami and I. Murray, A determinant-free method to simulate the parameters of large Gaussian fields, Stat, 6(1), 271-281, 2017.