mlsanityData to 7 Oct 2026

Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs

arXiv 2206.14284 ↗First posted 28 Jun 2022stat.ML cs.LG cs.NAcited by 7

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Abstract (arXiv)

This paper studies the problem of forecasting general stochastic processes using a path-dependent extension of the Neural Jump ODE (NJ-ODE) framework citepherrera2021neural. While NJ-ODE was the first framework to establish convergence guarantees for the prediction of irregularly observed time series, these results were limited to data stemming from Ito-diffusions with complete observations, in particular Markov processes, where all coordinates are observed simultaneously. In this work, we generalise these results to generic, possibly non-Markovian or discontinuous, stochastic processes with incomplete observations, by utilising the reconstruction properties of the signature transform. These theoretical results are supported by empirical studies, where it is shown that the path-dependent NJ-ODE outperforms the original NJ-ODE framework in the case of non-Markovian data. Moreover, we show that PD-NJ-ODE can be applied successfully to classical stochastic filtering problems and to limit order book (LOB) data.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 18 of its 53 references that are in the map. First posted on arXiv 28 Jun 2022.

Builds on

18 of 53 references.

References · 18

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2016Recurrent Neural Networks for Multivariate Time Series with Missing Valuescited by 548
  3. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 501
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  7. 2020Neural Rough Differential Equations for Long Time Seriescited by 140
  8. 2016A Primer on the Signature Method in Machine Learningcited by 100
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  10. 2019Deep Signature Transformscited by 75
  11. 2020Generative Adversarial Networks (GANs Survey): Challenges, Solutions, and Future Directionscited by 65
  12. 2017Benchmark Dataset for Mid-Price Forecasting of Limit Order Book Data with Machine Learning Methodscited by 49
6 more
  1. 2018The iisignature library: efficient calculation of iterated-integral signatures and log signaturescited by 38
  2. 2020Neural Jump Ordinary Differential Equations: Consistent Continuous-Time Prediction and Filteringcited by 33
  3. 2019Embedding and learning with signaturescited by 29
  4. 2018Using Deep Learning for price prediction by exploiting stationary limit order book featurescited by 27
  5. 2016Classification-based Financial Markets Prediction using Deep Neural Networkscited by 25
  6. 2017Tensor Representation in High-Frequency Financial Data for Price Change Predictioncited by 9

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 2; 2025: 1; 2026: 3.

7 papers.

  1. 2023Extending Path-Dependent NJ-ODEs to Noisy Observations and a Dependent Observation Frameworkcited by 6
  2. 2025CLEAR: Calibrated Learning for Epistemic and Aleatoric Riskcited by 6
  3. 2024Learning Chaotic Systems and Long-Term Predictions with Neural Jump ODEscited by 3
  4. 2024Nonparametric Filtering, Estimation and Classification using Neural Jump ODEscited by 1
  5. 2026Anticipatory Reinforcement Learning: From Generative Path-Laws to Distributional Value Functionscited by 0
  6. 2026Generative Path-Law Jump-Diffusion: Sequential MMD-Gradient Flows and Generalisation Bounds in Marcus-Signature RKHScited by 0
  7. 2026Operator Neural Jump ODEs: L2-optimal prediction in function spacescited by 0