Covariance-Adaptive Bouncy Particle Samplers via Split Lagrangian Dynamics
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| Format: | Preprint |
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2025
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| _version_ | 1866918150644170752 |
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| author | Chevallier, Augustin Raab, Erik |
| author_facet | Chevallier, Augustin Raab, Erik |
| contents | Piecewise Deterministic Markov Processes (PDMPs) provide a powerful framework for continuous-time Monte Carlo, with the Bouncy Particle Sampler (BPS) as a prominent example. Recent advances through the Metropolised PDMP framework allow local adaptivity in step size and effective path length, the latter acting as a refreshment rate. However, current PDMP samplers cannot adapt to local changes in the covariance structure of the target distribution.
We extend BPS by introducing a position-dependent velocity distribution that varies with the local covariance structure of the target. Building on ideas from Riemannian Manifold Hamiltonian Monte Carlo and its velocity-based variant, Lagrangian Dynamical Monte Carlo, we construct a PDMP for which changes in the metric trigger additional velocity update events. Using a metric derived from the target Hessian, the resulting algorithm adapts to the local covariance structure.
Through a series of controlled experiments, we provide practical guidance on when the proposed covariance-adaptive BPS should be preferred over standard PDMP algorithms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24847 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Covariance-Adaptive Bouncy Particle Samplers via Split Lagrangian Dynamics Chevallier, Augustin Raab, Erik Computation Piecewise Deterministic Markov Processes (PDMPs) provide a powerful framework for continuous-time Monte Carlo, with the Bouncy Particle Sampler (BPS) as a prominent example. Recent advances through the Metropolised PDMP framework allow local adaptivity in step size and effective path length, the latter acting as a refreshment rate. However, current PDMP samplers cannot adapt to local changes in the covariance structure of the target distribution. We extend BPS by introducing a position-dependent velocity distribution that varies with the local covariance structure of the target. Building on ideas from Riemannian Manifold Hamiltonian Monte Carlo and its velocity-based variant, Lagrangian Dynamical Monte Carlo, we construct a PDMP for which changes in the metric trigger additional velocity update events. Using a metric derived from the target Hessian, the resulting algorithm adapts to the local covariance structure. Through a series of controlled experiments, we provide practical guidance on when the proposed covariance-adaptive BPS should be preferred over standard PDMP algorithms. |
| title | Covariance-Adaptive Bouncy Particle Samplers via Split Lagrangian Dynamics |
| topic | Computation |
| url | https://arxiv.org/abs/2509.24847 |