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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2606.01954 |
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| _version_ | 1866917554838044672 |
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| author | Ortega, Luis A. Masegosa, Andrés R. Nielsen, Thomas D. |
| author_facet | Ortega, Luis A. Masegosa, Andrés R. Nielsen, Thomas D. |
| contents | Implicit-process priors define distributions over functions through flexible generative mechanisms, making them attractive for Bayesian function-space modelling. However, performing posterior inference with such priors is challenging because their induced function-space distributions are typically not available in closed form. One practical strategy is to approximate the prior using a finite collection of sampled functions, and then represent posterior functions as learned combinations of these samples. Existing approaches commonly place a Gaussian variational distribution over the combination weights. While tractable, this choice limits the shapes of posterior uncertainty that can be represented, especially when the true posterior is asymmetric, heavy-tailed, or multimodal. We propose Flow-Transformed Implicit Processes (FTIP), a variational inference method that makes this finite-dimensional function-space approximation more expressive. Instead of using a Gaussian distribution over the combination weights, FTIP uses a normalizing flow to define a richer variational distribution. This induces a flexible posterior distribution over functions while preserving tractable optimization. We train the model using a Black-Box α objective, allowing us to compare mass-covering and mode-seeking variational behaviour. Experiments show that FTIP captures asymmetric and multimodal posterior structure in function space that Gaussian coefficient approximations tend to smooth or collapse. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_01954 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Flow-Transformed Implicit Processes for Function-Space Variational Inference Ortega, Luis A. Masegosa, Andrés R. Nielsen, Thomas D. Machine Learning Implicit-process priors define distributions over functions through flexible generative mechanisms, making them attractive for Bayesian function-space modelling. However, performing posterior inference with such priors is challenging because their induced function-space distributions are typically not available in closed form. One practical strategy is to approximate the prior using a finite collection of sampled functions, and then represent posterior functions as learned combinations of these samples. Existing approaches commonly place a Gaussian variational distribution over the combination weights. While tractable, this choice limits the shapes of posterior uncertainty that can be represented, especially when the true posterior is asymmetric, heavy-tailed, or multimodal. We propose Flow-Transformed Implicit Processes (FTIP), a variational inference method that makes this finite-dimensional function-space approximation more expressive. Instead of using a Gaussian distribution over the combination weights, FTIP uses a normalizing flow to define a richer variational distribution. This induces a flexible posterior distribution over functions while preserving tractable optimization. We train the model using a Black-Box α objective, allowing us to compare mass-covering and mode-seeking variational behaviour. Experiments show that FTIP captures asymmetric and multimodal posterior structure in function space that Gaussian coefficient approximations tend to smooth or collapse. |
| title | Flow-Transformed Implicit Processes for Function-Space Variational Inference |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2606.01954 |