Neural Backward Filtering Forward Guiding

• URL: http://arxiv.org/abs/2601.23030v1
• Date: Fri, 30 Jan 2026 14:39:50 GMT
• Title: Neural Backward Filtering Forward Guiding
• Authors: Gefan Yang, Frank van der Meulen, Stefan Sommer,
• Abstract summary: Inference in non-linear continuous processes on trees is challenging when observations are sparse (leaf-only) and the topology is complex.<n>We propose Neural Backward Filtering Forward Guiding (NBFFG), a unified framework for both discrete transitions and continuous diffusions.
• Score: 2.676349883103404
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Inference in non-linear continuous stochastic processes on trees is challenging, particularly when observations are sparse (leaf-only) and the topology is complex. Exact smoothing via Doob's $h$-transform is intractable for general non-linear dynamics, while particle-based methods degrade in high dimensions. 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 an auxiliary linear-Gaussian process. This auxiliary 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--parameterized as a normalizing flow or a controlled SDE--to capture the non-linear discrepancies. This formulation allows for an unbiased path-wise 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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