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

arXiv: https://arxiv.org/abs/2206.14284 · HTML: https://mlsanity.com/paper/2206.14284/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 53 references that are in the map.
- First posted on arXiv 28 Jun 2022.

## Builds on (most cited first, 18 of 18)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [GRU-ODE-Bayes: Continuous modeling of sporadically-observed time series](https://mlsanity.com/paper/1905.12374/) (2019)
- [Neural SDEs as Infinite-Dimensional GANs](https://mlsanity.com/paper/2102.03657/) (2021)
- [Neural Rough Differential Equations for Long Time Series](https://mlsanity.com/paper/2009.08295/) (2020)
- [A Primer on the Signature Method in Machine Learning](https://mlsanity.com/paper/1603.03788/) (2016)
- [Kernels for sequentially ordered data](https://mlsanity.com/paper/1601.08169/) (2016)
- [Deep Signature Transforms](https://mlsanity.com/paper/1905.08494/) (2019)
- [Generative Adversarial Networks (GANs Survey): Challenges, Solutions, and Future Directions](https://mlsanity.com/paper/2005.00065/) (2020)
- [Benchmark Dataset for Mid-Price Forecasting of Limit Order Book Data with Machine Learning Methods](https://mlsanity.com/paper/1705.03233/) (2017)
- [The iisignature library: efficient calculation of iterated-integral signatures and log signatures](https://mlsanity.com/paper/1802.08252/) (2018)
- [Neural Jump Ordinary Differential Equations: Consistent Continuous-Time Prediction and Filtering](https://mlsanity.com/paper/2006.04727/) (2020)
- [Embedding and learning with signatures](https://mlsanity.com/paper/1911.13211/) (2019)
- [Using Deep Learning for price prediction by exploiting stationary limit order book features](https://mlsanity.com/paper/1810.09965/) (2018)
- [Classification-based Financial Markets Prediction using Deep Neural Networks](https://mlsanity.com/paper/1603.08604/) (2016)
- [Tensor Representation in High-Frequency Financial Data for Price Change Prediction](https://mlsanity.com/paper/1709.01268/) (2017)

## Built on by (most cited first, 7 of 7)

- [Extending Path-Dependent NJ-ODEs to Noisy Observations and a Dependent Observation Framework](https://mlsanity.com/paper/2307.13147/) (2023)
- [CLEAR: Calibrated Learning for Epistemic and Aleatoric Risk](https://mlsanity.com/paper/2507.08150/) (2025)
- [Learning Chaotic Systems and Long-Term Predictions with Neural Jump ODEs](https://mlsanity.com/paper/2407.18808/) (2024)
- [Nonparametric Filtering, Estimation and Classification using Neural Jump ODEs](https://mlsanity.com/paper/2412.03271/) (2024)
- [Anticipatory Reinforcement Learning: From Generative Path-Laws to Distributional Value Functions](https://mlsanity.com/paper/2604.04662/) (2026)
- [Generative Path-Law Jump-Diffusion: Sequential MMD-Gradient Flows and Generalisation Bounds in Marcus-Signature RKHS](https://mlsanity.com/paper/2604.05008/) (2026)
- [Operator Neural Jump ODEs: L2-optimal prediction in function spaces](https://mlsanity.com/paper/2607.23110/) (2026)

## 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.