Automatic Laplace Collapsed Sampling: Scalable Marginalisation of Latent Parameters via Automatic Differentiation
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 $d_θ+ d_z$ to just $d_θ$, making Bayesian evidence computation tractable for high-dimensional settings without hand-derived gradients or Hessians, and ...
| Authors | Toby Lovick, David Yallup, Will Handley |
|---|---|
| Primary category | cs.LG |
| Published | 27 March 2026 |
| Last updated at source | 27 March 2026 |
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