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• Automatic Laplace Collapsed Sampling (ALCS) is a general framework for marginalizing latent parameters in Bayesian models using automatic differentiation.method 95%
• ALCS reduces the effective dimension for Bayesian evidence computation from d_θ + d_z to d_θ by collapsing high-dimensional latent variables z via MAP optimization and Laplace approximation.method 95%
• The MAP optimization and Hessian evaluation in ALCS are parallelized across live points on GPU hardware, enabling practical application at scale.technical 90%
• ALCS enables local approximations beyond Laplace, such as to the Student-t distribution, using automatic differentiation to improve evidence estimates for heavy-tailed latents.method 90%
• ALCS can be combined with nested sampling to explore the hyperparameter space robustly and efficiently.method 95%
• The computational scaling of ALCS is O(d_θ^3 * d_z), representing a substantial improvement over O((d_θ + d_z)^3) for joint nested sampling when d_θ << d_z.technical 90%
• ALCS is designed for near-Gaussian latent spaces and primarily targets quadratic surfaces, with potential breakdown in anisotropic spaces.limitation 85%
• ALCS can achieve exact-Gaussian accuracy and scale to d=25,600 latent dimensions in hierarchical models.result 90%

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