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Found 16 papers, 7 papers with code
Lecture notes on rough paths and applications to machine learning
These notes expound the recent use of the signature transform and rough path theory in data science and machine learning.
Theoretical Foundations of Deep Selective State-Space Models
Structured state-space models (SSMs) such as S4, stemming from the seminal work of Gu et al., are gaining popularity as effective approaches for modeling sequential data.
Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes
Inferring the causal structure underlying stochastic dynamical systems from observational data holds great promise in domains ranging from science and health to finance.
A Neural RDE approach for continuous-time non-Markovian stochastic control problems
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).
Non-adversarial training of Neural SDEs with signature kernel scores
Neural SDEs are continuous-time generative models for sequential data.
Neural signature kernels as infinite-width-depth-limits of controlled ResNets
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.
New directions in the applications of rough path theory
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
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.
Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processes
Stochastic processes are random variables with values in some space of paths.
SigGPDE: Scaling Sparse Gaussian Processes on Sequential Data
Making predictions and quantifying their uncertainty when the input data is sequential is a fundamental learning challenge, recently attracting increasing attention.
Neural CDEs for Long Time Series via the Log-ODE Method
Neural Controlled Differential Equations (Neural CDEs) are the continuous-time analogue of an RNN, just as Neural ODEs are analogous to ResNets.
Neural Rough Differential Equations for Long Time Series
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.
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on EigenWorms
The Signature Kernel is the solution of a Goursat PDE
Recently, there has been an increased interest in the development of kernel methods for learning with sequential data.
Distribution Regression for Sequential Data
In this paper, we develop a rigorous mathematical framework for distribution regression where inputs are complex data streams.
Sig-SDEs model for quantitative finance
Mathematical models, calibrated to data, have become ubiquitous to make key decision processes in modern quantitative finance.
Deep Signature Transforms
The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class.
