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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.23030 |
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| _version_ | 1866917496655708160 |
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| author | Yang, Gefan van der Meulen, Frank Sommer, Stefan |
| author_facet | Yang, Gefan van der Meulen, Frank Sommer, Stefan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_23030 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Neural Backward Filtering Forward Guiding Yang, Gefan van der Meulen, Frank Sommer, Stefan Machine Learning Methodology 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. |
| title | Neural Backward Filtering Forward Guiding |
| topic | Machine Learning Methodology |
| url | https://arxiv.org/abs/2601.23030 |