Gradient Estimation via Differentiable Metropolis-Hastings
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910495739478016 |
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| author | Arya, Gaurav Schauer, Moritz Seyer, Ruben |
| author_facet | Arya, Gaurav Schauer, Moritz Seyer, Ruben |
| contents | Metropolis-Hastings estimates intractable expectations - can differentiating the algorithm estimate their gradients? The challenge is that Metropolis-Hastings trajectories are not conventionally differentiable due to the discrete accept/reject steps. Using a technique based on recoupling chains, our method differentiates through the Metropolis-Hastings sampler itself, allowing us to estimate gradients with respect to a parameter of otherwise intractable expectations. Our main contribution is a proof of strong consistency and a central limit theorem for our estimator under assumptions that hold in common Bayesian inference problems. The proofs augment the sampler chain with latent information, and formulate the estimator as a stopping tail functional of this augmented chain. We demonstrate our method on examples of Bayesian sensitivity analysis and optimizing a random walk Metropolis proposal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14451 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gradient Estimation via Differentiable Metropolis-Hastings Arya, Gaurav Schauer, Moritz Seyer, Ruben Statistics Theory Probability Computation Metropolis-Hastings estimates intractable expectations - can differentiating the algorithm estimate their gradients? The challenge is that Metropolis-Hastings trajectories are not conventionally differentiable due to the discrete accept/reject steps. Using a technique based on recoupling chains, our method differentiates through the Metropolis-Hastings sampler itself, allowing us to estimate gradients with respect to a parameter of otherwise intractable expectations. Our main contribution is a proof of strong consistency and a central limit theorem for our estimator under assumptions that hold in common Bayesian inference problems. The proofs augment the sampler chain with latent information, and formulate the estimator as a stopping tail functional of this augmented chain. We demonstrate our method on examples of Bayesian sensitivity analysis and optimizing a random walk Metropolis proposal. |
| title | Gradient Estimation via Differentiable Metropolis-Hastings |
| topic | Statistics Theory Probability Computation |
| url | https://arxiv.org/abs/2406.14451 |