mlsanityData to 7 Oct 2026

Extending Path-Dependent NJ-ODEs to Noisy Observations and a Dependent Observation Framework

arXiv 2307.13147 ↗First posted 24 Jul 2023stat.ML cs.LG cs.NAcited by 6

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Abstract (arXiv)

The Path-Dependent Neural Jump Ordinary Differential Equation (PD-NJ-ODE) is a model for predicting continuous-time stochastic processes with irregular and incomplete observations. In particular, the method learns optimal forecasts given irregularly sampled time series of incomplete past observations. So far the process itself and the coordinate-wise observation times were assumed to be independent and observations were assumed to be noiseless. In this work we discuss two extensions to lift these restrictions and provide theoretical guarantees as well as empirical examples for them. In particular, we can lift the assumption of independence by extending the theory to much more realistic settings of conditional independence without any need to change the algorithm. Moreover, we introduce a new loss function, which allows us to deal with noisy observations and explain why the previously used loss function did not lead to a consistent estimator.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 17 of its 58 references that are in the map. First posted on arXiv 24 Jul 2023.

Builds on

17 of 58 references.

References · 17

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 501
  3. 2019GRU-ODE-Bayes: Continuous modeling of sporadically-observed time seriescited by 230
  4. 2020Neural Rough Differential Equations for Long Time Seriescited by 140
  5. 2019A Function Space View of Bounded Norm Infinite Width ReLU Nets: The Multivariate Casecited by 113
  6. 2019How do infinite width bounded norm networks look in function space?cited by 105
  7. 2017Filtering Variational Objectivescited by 91
  8. 2017Auto-Encoding Sequential Monte Carlocited by 64
  9. 2021What Kinds of Functions do Deep Neural Networks Learn? Insights from Variational Spline Theorycited by 60
  10. 2021Differentiable Particle Filtering via Entropy-Regularized Optimal Transportcited by 59
  11. 2018The iisignature library: efficient calculation of iterated-integral signatures and log signaturescited by 38
  12. 2020Neural Jump Ordinary Differential Equations: Consistent Continuous-Time Prediction and Filteringcited by 33
5 more
  1. 2022Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEscited by 7
  2. 2021Variational Marginal Particle Filterscited by 6
  3. 2019How Implicit Regularization of ReLU Neural Networks Characterizes the Learned Function -- Part I: the 1-D Case of Two Layers with Random First Layercited by 5
  4. 2021How Infinitely Wide Neural Networks Can Benefit from Multi-task Learning -- an Exact Macroscopic Characterizationcited by 4
  5. 2023How (Implicit) Regularization of ReLU Neural Networks Characterizes the Learned Function -- Part II: the Multi-D Case of Two Layers with Random First Layercited by 2

Built on by

Cited by year (2026 to 7 Oct)

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

6 papers.

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