- 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.
- 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.
- 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.
(pdf), (code), (poster)
- 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.
- 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.
- 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.