Neural Backward Filtering Forward Guiding

Gefan Yang; Frank van der Meulen; Stefan Sommer

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arXiv · 2601.23030

Neural Backward Filtering Forward Guiding

Gefan Yang·Frank van der Meulen·Stefan Sommer

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Abstract

Inference in nonlinear continuous stochastic processes on trees is challenging, particularly when observations are sparse and the topology is complex. Exact smoothing via Doob's $h$-transform is intractable for general nonlinear dynamics. We propose Neural Backward Filtering Forward Guiding (NBFFG), a unified framework for both discrete transitions and continuous diffusions. Our method constructs a variational posterior by leveraging a proxy linear-Gaussian process. This proxy process yields a closed-form backward filter that serves as a guide, steering the generative path toward high-likelihood regions. We then learn a neural residual to capture the non-linear discrepancies. This formulation allows for an unbiased pathwise subsampling scheme, reducing the training complexity from tree-size dependent to path-length dependent. Empirical results show that NBFFG outperforms baselines on synthetic benchmarks, and we demonstrate the method on a high-dimensional inference task in phylogenetic analysis with reconstruction of ancestral butterfly wing shapes.

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BibTeX RIS

Gefan Yang, Frank van der Meulen, Stefan Sommer. 2026-01-30. Neural Backward Filtering Forward Guiding. https://arxiv.org/abs/2601.23030

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