# Preprints and publications

## Preprints and publications

### 2024

O. Sheridan-Methven, M.B. Giles

**Rounding error using low precision approximate random variables **

SIAM Journal of Scientific Computing to appear 2024

M.B. Giles

**Approximation of an inverse of the incomplete beta function. Proceedings of International Congress on Mathematical Software 2024**

To appear in the Springer series Lecture notes in Computer Science (LNCS)

### 2023

Talia Tseriotou, Ryan Sze-Yin Chan, Adam Tsakalidis, Iman Munire Bilal , Elena Kochkina, **Terry Lyons, **Maria Liakata

**Sig-Networks Toolkit: Signature Networks for Longitudinal Language Modelling **

arXiv:2312.03523

Jason Rader, **Terry Lyons, **Patrick Kidger

**Lineax: unified linear solves and linear least-squares in JAX and Equinox **

arXiv:2311.17283

**Karl Welzel**, Raphael A Hauser

**Approximating Higher-Order Derivative Tensors Using Secant Updates **

SIAM Journal on Optimization (SIOPT), 2024

Wenqing Ouyang, Yang Liu, Andre Milzarek

**Descent Properties of an Anderson Accelerated Gradient Method With Restarting **

Accepted to appear in SIAM Journal on Optimization (SIOPT)

Ahmed Ammar Naseer, **Benjamin Walker**, Christopher Landon, Andrew Ambrosy, Marat Fudim, Nicholas Wysham, Botros Toro, Sumanth Swaminathan, **Terry Lyons**

**ScoEHR: Generating Synthetic Electronic Health Records using Continuous-time Diffusion Models **

Machine Learning for Healthcare, 2023

Coralia Cartis, Wenqi Zhu

**Second-order methods for quartically-regularised cubic polynomials, with applications to high-order tensor methods **

arXiv:2308.15336

Michael Giles, Oliver Sheridan-Methven

**Approximating inverse cumulative distribution functions to produce approximate random variables **

ACM TOMS, 2023

Michael Giles

**Monte Carlo and Quasi-Monte Carlo Methods **

MCQMC, 2022

Giuseppe Ughi, Jared Tanner

**Mutual information of neural network initializations: a random matrix theory study**

(In review)

Rasheed Ibraheem, Yue Wu, **Terry Lyons, **Goncalo dos Reis

**Early prediction of Lithium-ion cell degradation trajectories using signatures of voltage curves up to 4-minute sub-sampling rates **

APPLIED ENERGY, 2023

Youness Boutaib, **Terry Lyons**

**A new definition of rough paths on manifolds **

Annales de la Faculte des sciences de Toulouse, 2022

Yue Wu, Guy M. Goodwin, **Terry Lyons, **Kate E.A. Saunders

**Identifying psychiatric diagnosis from missing mood data through the use of log-signature features **

PLOS ONE, 2022

Talia Tseriotou, Adam Tsakalidis, Peter Foster, **Terry Lyons, **Maria Liakata

**Sequential Path Signature Networks for Personalised Longitudinal Language Modeling **

Findings of ACL, 2023

Cristopher Salvi, Joscha Diehl, **Terry Lyons, **Rosa Preiss, Jeremy Reizenstein

**A structure theorem for streamed information **

Journal of Algebra, 2023

Satoshi Hayakawa, **Harald Oberhauser** and **Terry Lyons**

**Sampling-based Nystrom Approximation and Kernel Quadrature **

Proceedings of the 40th International Conference on Machine Learning, 2023

Andy Wathen

**Some comments on preconditioning for Normal Equations and Least Squares**

2022, SIAM Review*, vol. 64, lss. 3*, pp. 640-649

Andy Wathen

**Some observations on preconditioning for non-self-adjoint and time-dependent problems**

2022, SIAM Journal on Matrix Analysis and Applications*, vol. *116, pp. 176-180

Adeline Fermanian, Jiawei Chang, **Terry Lyons** and Gérard Biau

**The insertion method to invert the signature of a path**

*arXiv:2304.01862*

Alexander Schell and **Harald Oberhauser**

**Nonlinear Independent Component Analysis for Discrete-Time and Continuous-Time Signals**

Accepted to appear in *The Annals of Statistics*

**Ben Walker**, Felix Krones, Ivan Kiskin, Guy Parsons, **Terry Lyons** and Adam Mahdi

**Dual Bayesian ResNet: A Deep Learning Approach to Heart Murmur Detection**

*2022 Computing in Cardiology (CinC)*, vol. 498, pp. 1-4

Carlos Améndola,

**Darrick Lee**and Chiara Meroni

**Convex Hulls of Curves: Volumes and Signatures**

*arXiv:2301.09405*

Congzheng Liu and **Wenqi Zhu **

**Newsvendor Conditional Value-at-Risk Minimisation with a Non-Parametric Approach**

Accepted for presentation at the 4^{th} IMA and OR Society Conference on Mathematics of Operational Research, 2023

Cris Salvi, Adeline Fermanian, **Terry Lyons** and James Morrill

**New directions in the applications of rough path theory**

Accepted for publication in *IEEE BITS the Information Theory Magazine*

**Karl Welzel** and **Raphael A Hauser**

**Generalizing Quasi-Newton Updates to Higher-Order Derivative Tensors**

*arXiv:2301.11678*

**Michael B Giles**

**MLMC techniques for discontinuous functions**

Accepted to appear in *Proceedings of MCQMC 2022*

Satoshi Hayakawa, **Harald Oberhauser** and **Terry Lyons**

**Hypercontractivity meets Random Convex Hulls: Analysis of Randomized Multivariate Cubatures **

Accepted for publication in *Proceedings of the Royal Society A*

Satoshi Hayakawa, **Terry Lyons** and **Harald Oberhauser**

**Estimating the probability that a given vector is in the convex hull of a random sample**

*Probability Theory and Related Fields (2023)*

**Terry Lyons** and Andrew D McLeod

**Generalised Recombination Interpolation Method (GRIM)**

*arXiv:2205.07495*

Thomas Cass, **Terry Lyons** and Xingcheng Xu

**Weighted signature kernels**

Accepted for publication in *Annals of Applied Probability*

Vincent PH Goverse, Jad Hamdan and **Jared Tanner**

**Optimal approximation complexity of high-dimensional functions with neural networks**

**Wenqi Zhu ** and Yuji Nakatsukasa

**Convergence and Near-optimal Sampling for Multivariate Function Approximations in Irregular Domains via Vandermonde with Arnoldi**

Accepted for presentation at the 29^{th} Biennial Numerical Analysis Conference, 2023

Xiaoqi Xu, **Darrick Lee**, Nicolas Drougard and Raphaëlle N Roy

**Signature methods for brain-computer interfaces**

Scientific Reports, 2023

Zehong Zhang, Fei Lu, Esther Xu Fei, **Terry Lyons**, Yannis Kevrekidis and Tom Woolf

**Benchmarking optimality of time series classification methods in distinguishing diffusions**

*arXiv:2301.13112*

### 2022

**Coralia Cartis** and Zhen Shao

**Random-subspace adaptive cubic regularisation method for nonconvex optimisationa>**

Accepted paper for NeurIPS 2022 workshop "Order up! The Benefits of Higher-Order Optimization in Machine Learning”

**Coralia Cartis**, Jaroslav Fowkes and Zhen Shao

**Randomised subspace methods for non-convex optimization, with applications to nonlinear least-squares** *arXiv:2211.09873*

Csaba Toth, **Darrick Lee**, Celia Hacker and **Harald Oberhauser**

**Capturing Graphs with Hypo-Elliptic Diffusions**

Accepted to appear in *Advances in Neural Information Processing Systems (NeurIPS 2022)*

**Elena Gal**, Shaun Singh, Aldo Pacchiano,

**Ben Walker**,

**Terry Lyons**and Jakob Foerster

**Unbiased decisions reduce regret: adversarial optimism for the bank loan problem**

KeCheng Chen, **Elena Gal**, Hong Yan and Haoliang Li

**Domain Generalization with small data**

Masaki Adachi, Satoshi Hayakawa, Martin Jørgensen, **Harald Oberhauser** and Michael A Osborne

**Fast Bayesian Inference with Batch Bayesian Quadrature via Kernel Recombination**

Accepted to appear in *Advances in Neural Information Processing Systems (NeurIPS 2022)*

Mohamed R Ibrahim and **Terry Lyons**

**ImageSig: A signature transform for ultra-lightweight image recognition**

*IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) 2022*

Oliver Sheridan-Methven and **Michael Giles**

**Approximating inverse cumulative distribution functions to produce approximate random variables**

Proceedings of International Congress on Mathematical Software 2024. To appear in the Springer series Lecture Notes in Computer Science (LNCS).

Patric Bonnier, Chong Liu and **Harald Oberhauser**

**Adapted topologies and higher rank signatures**

Accepted to appear in *Annals of Applied Probability*

Satoshi Hayakawa, **Harald Oberhauser** and **Terry Lyons**

**Positively weighted kernel quadrature via subsampling**

Accepted to appear in *Advances in Neural Information Processing Systems (NeurIPS 2022)*

**Wenqi Zhu **and **Coralia Cartis**

**Quartic Polynomial Sub-problem Solutions in Tensor Methods for Nonconvex Optimization**

Accepted paper for NeurIPS 2022 workshop "Order up! The Benefits of Higher-Order Optimization in Machine Learning”