# Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions

arXiv: https://arxiv.org/abs/2206.03369 · HTML: https://mlsanity.com/paper/2206.03369/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 55 references that are in the map.
- First posted on arXiv 7 Jun 2022.

## Builds on (most cited first, 11 of 11)

- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations](https://mlsanity.com/paper/1706.04702/) (2017)
- [Solving high-dimensional Hamilton-Jacobi-Bellman PDEs using neural networks: perspectives from the theory of controlled diffusions and measures on path space](https://mlsanity.com/paper/2005.05409/) (2020)
- [Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations](https://mlsanity.com/paper/1709.05963/) (2017)
- [Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations](https://mlsanity.com/paper/1804.07010/) (2018)
- [Machine Learning for semi linear PDEs](https://mlsanity.com/paper/1809.07609/) (2018)
- [Neural networks-based backward scheme for fully nonlinear PDEs](https://mlsanity.com/paper/1908.00412/) (2019)
- [Learning Deep Stochastic Optimal Control Policies using Forward-Backward SDEs](https://mlsanity.com/paper/1902.03986/) (2019)
- [Path Integral Control and State Dependent Feedback](https://mlsanity.com/paper/1406.4026/) (2014)
- [Variational approach to rare event simulation using least-squares regression](https://mlsanity.com/paper/1901.09195/) (2019)
- [Inference on high-dimensional implicit dynamic models using a guided intermediate resampling filter](https://mlsanity.com/paper/1708.08543/) (2017)

## Built on by (most cited first, 4 of 4)

- [Amortized Control of Continuous State Space Feynman-Kac Model for Irregular Time Series](https://mlsanity.com/paper/2410.05602/) (2024)
- [Functional Adjoint Sampler: Scalable Sampling on Infinite Dimensional Spaces](https://mlsanity.com/paper/2511.06239/) (2025)
- [Stochastic Optimal Control for Continuous-Time fMRI Representation Learning](https://mlsanity.com/paper/2502.04892/) (2025)
- [Efficient Inference for Coupled Hidden Markov Models in Continuous Time and Discrete Space](https://mlsanity.com/paper/2510.12916/) (2025)

## Abstract (arXiv)

This paper is concerned with online filtering of discretely observed nonlinear diffusion processes. Our approach is based on the fully adapted auxiliary particle filter, which involves Doob's h-transforms that are typically intractable. We propose a computational framework to approximate these h-transforms by solving the underlying backward Kolmogorov equations using nonlinear Feynman-Kac formulas and neural networks. The methodology allows one to train a locally optimal particle filter prior to the data-assimilation procedure. Numerical experiments illustrate that the proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters in the regime of highly informative observations, when the observations are extreme under the model, or if the state dimension is large.