[2603.26644] Automatic Laplace Collapsed Sampling: Scalable Marginalisation of Latent Parameters via Automatic Differentiation

Computer Science > Machine Learning arXiv:2603.26644 (cs) [Submitted on 27 Mar 2026] Title:Automatic Laplace Collapsed Sampling: Scalable Marginalisation of Latent Parameters via Automatic Differentiation Authors:Toby Lovick, David Yallup, Will Handley View a PDF of the paper titled Automatic Laplace Collapsed Sampling: Scalable Marginalisation of Latent Parameters via Automatic Differentiation, by Toby Lovick and 2 other authors View PDF HTML (experimental) Abstract:We present Automatic Laplace Collapsed Sampling (ALCS), a general framework for marginalising latent parameters in Bayesian models using automatic differentiation, which we combine with nested sampling to explore the hyperparameter space in a robust and efficient manner. At each nested sampling likelihood evaluation, ALCS collapses the high-dimensional latent variables $z$ to a scalar contribution via maximum a posteriori (MAP) optimisation and a Laplace approximation, both computed using autodiff. This reduces the effective dimension from $d_\theta + d_z$ to just $d_\theta$, making Bayesian evidence computation tractable for high-dimensional settings without hand-derived gradients or Hessians, and with minimal model-specific engineering. The MAP optimisation and Hessian evaluation are parallelised across live points on GPU-hardware, making the method practical at scale. We also show that automatic differentiation enables local approximations beyond Laplace to parametric families such as the Student-$t$, which...