Efficiently Vectorized MCMC on Modern Accelerators
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918079791890432 |
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| author | Dance, Hugh Glaser, Pierre Orbanz, Peter Adams, Ryan |
| author_facet | Dance, Hugh Glaser, Pierre Orbanz, Peter Adams, Ryan |
| contents | With the advent of automatic vectorization tools (e.g., JAX's $\texttt{vmap}$), writing multi-chain MCMC algorithms is often now as simple as invoking those tools on single-chain code. Whilst convenient, for various MCMC algorithms this results in a synchronization problem -- loosely speaking, at each iteration all chains running in parallel must wait until the last chain has finished drawing its sample. In this work, we show how to design single-chain MCMC algorithms in a way that avoids synchronization overheads when vectorizing with tools like $\texttt{vmap}$ by using the framework of finite state machines (FSMs). Using a simplified model, we derive an exact theoretical form of the obtainable speed-ups using our approach, and use it to make principled recommendations for optimal algorithm design. We implement several popular MCMC algorithms as FSMs, including Elliptical Slice Sampling, HMC-NUTS, and Delayed Rejection, demonstrating speed-ups of up to an order of magnitude in experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficiently Vectorized MCMC on Modern Accelerators Dance, Hugh Glaser, Pierre Orbanz, Peter Adams, Ryan Mathematical Software Machine Learning Computation With the advent of automatic vectorization tools (e.g., JAX's $\texttt{vmap}$), writing multi-chain MCMC algorithms is often now as simple as invoking those tools on single-chain code. Whilst convenient, for various MCMC algorithms this results in a synchronization problem -- loosely speaking, at each iteration all chains running in parallel must wait until the last chain has finished drawing its sample. In this work, we show how to design single-chain MCMC algorithms in a way that avoids synchronization overheads when vectorizing with tools like $\texttt{vmap}$ by using the framework of finite state machines (FSMs). Using a simplified model, we derive an exact theoretical form of the obtainable speed-ups using our approach, and use it to make principled recommendations for optimal algorithm design. We implement several popular MCMC algorithms as FSMs, including Elliptical Slice Sampling, HMC-NUTS, and Delayed Rejection, demonstrating speed-ups of up to an order of magnitude in experiments. |
| title | Efficiently Vectorized MCMC on Modern Accelerators |
| topic | Mathematical Software Machine Learning Computation |
| url | https://arxiv.org/abs/2503.17405 |