Dr Cristopher Salvi

Summary

I am a Lecturer (Assistant Professor) in Mathematics and Machine Learning jointly appointed by the Department of Mathematics at Imperial College and the AI initiative Imperial-X. Prior to this, I was a Chapman Fellow in Mathematics at Imperial College and I obtained my PhD from the University of Oxford under the supervision of Prof. Terry Lyons.

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The Mathematics of Sequence Modelling

My research interests are in the areas of rough analysis, signal processing, kernel methods for sequential data, and neural differential equations. In particular, I'm interested in developing mathematical techniques and numerical algorithms for sequence modelling. Next is a list of selected publications.

Rough Analysis & Signal Processing

1. A structure theorem for streamed information (J. Algebra 23) 
2. Higher order kernel mean embeddings (NeurIPS 21)
3. Deep signature transforms (NeurIPS 19)

Kernel Methods for Sequential Data

1. Signature kernels as infinite limits of cResNets (ICML 23)
2. Bayesian Gaussian Processes on sequential data (ICML 21) 
3. Distribution regression on sequential data (AISTATS 21)
4. Signature kernels are solutions to Goursat PDEs (SIAM 21)

Neural Differential Equations

1. Training neural SDEs with sig. kernel scores (NeurIPS 23) 
2. Neural SPDEs for spatio-temporal signals (NeurIPS 22)
3. Neural RDEs for long time series (ICML 21)