Search Results for author: Cristopher Salvi

Found 13 papers, 7 papers with code

A Neural RDE approach for continuous-time non-Markovian stochastic control problems

no code implementations25 Jun 2023 Melker Hoglund, Emilio Ferrucci, Camilo Hernandez, Aitor Muguruza Gonzalez, Cristopher Salvi, Leandro Sanchez-Betancourt, Yufei Zhang

We propose a novel framework for solving continuous-time non-Markovian stochastic control problems by means of neural rough differential equations (Neural RDEs) introduced in Morrill et al. (2021).

Neural signature kernels as infinite-width-depth-limits of controlled ResNets

1 code implementation30 Mar 2023 Nicola Muca Cirone, Maud Lemercier, Cristopher Salvi

Motivated by the paradigm of reservoir computing, we consider randomly initialized controlled ResNets defined as Euler-discretizations of neural controlled differential equations (Neural CDEs), a unified architecture which enconpasses both RNNs and ResNets.

Gaussian Processes

New directions in the applications of rough path theory

no code implementations9 Feb 2023 Adeline Fermanian, Terry Lyons, James Morrill, Cristopher Salvi

This article provides a concise overview of some of the recent advances in the application of rough path theory to machine learning.

Neural Stochastic PDEs: Resolution-Invariant Learning of Continuous Spatiotemporal Dynamics

1 code implementation19 Oct 2021 Cristopher Salvi, Maud Lemercier, Andris Gerasimovics

On the other hand, it extends Neural Operators -- generalizations of neural networks to model mappings between spaces of functions -- in that it can parameterize solution operators of SPDEs depending simultaneously on the initial condition and a realization of the driving noise.

SigGPDE: Scaling Sparse Gaussian Processes on Sequential Data

no code implementations10 May 2021 Maud Lemercier, Cristopher Salvi, Thomas Cass, Edwin V. Bonilla, Theodoros Damoulas, Terry Lyons

Making predictions and quantifying their uncertainty when the input data is sequential is a fundamental learning challenge, recently attracting increasing attention.

Gaussian Processes Time Series +2

Neural CDEs for Long Time Series via the Log-ODE Method

no code implementations28 Sep 2020 James Morrill, Patrick Kidger, Cristopher Salvi, James Foster, Terry Lyons

Neural Controlled Differential Equations (Neural CDEs) are the continuous-time analogue of an RNN, just as Neural ODEs are analogous to ResNets.

Time Series Time Series Analysis

Neural Rough Differential Equations for Long Time Series

3 code implementations17 Sep 2020 James Morrill, Cristopher Salvi, Patrick Kidger, James Foster, Terry Lyons

Neural controlled differential equations (CDEs) are the continuous-time analogue of recurrent neural networks, as Neural ODEs are to residual networks, and offer a memory-efficient continuous-time way to model functions of potentially irregular time series.

Irregular Time Series Time Series +2

The Signature Kernel is the solution of a Goursat PDE

3 code implementations26 Jun 2020 Cristopher Salvi, Thomas Cass, James Foster, Terry Lyons, Weixin Yang

Recently, there has been an increased interest in the development of kernel methods for learning with sequential data.

Dimensionality Reduction Time Series Analysis +1

Distribution Regression for Sequential Data

no code implementations10 Jun 2020 Maud Lemercier, Cristopher Salvi, Theodoros Damoulas, Edwin V. Bonilla, Terry Lyons

In this paper, we develop a rigorous mathematical framework for distribution regression where inputs are complex data streams.

regression Time Series +1

Sig-SDEs model for quantitative finance

no code implementations30 May 2020 Imanol Perez Arribas, Cristopher Salvi, Lukasz Szpruch

Mathematical models, calibrated to data, have become ubiquitous to make key decision processes in modern quantitative finance.

Model Selection Time Series +1

Deep Signature Transforms

2 code implementations NeurIPS 2019 Patric Bonnier, Patrick Kidger, Imanol Perez Arribas, Cristopher Salvi, Terry Lyons

The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class.

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