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

Automatic Laplace Collapsed Sampling: Scalable Marginalisation of Latent Parameters via Automatic Differentiation | Signal Canvas | ScienceToStartup

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Canonical route: /signal-canvas/automatic-laplace-collapsed-sampling-scalable-marginalisation-of-latent-parameters-via-automatic-differentiation

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Proof freshness: stale
Proof status: unverified
Display score: 4/10
Last proof check: 2026-03-30
Score updated: 2026-04-02
Score fresh until: 2026-05-02
References: 15
Source count: 3
Coverage: 50%

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Evidence Receipt

Route status: building

Claims: 8

References: 15

Proof: Verification pending

Freshness state: computing

Source paper: Automatic Laplace Collapsed Sampling: Scalable Marginalisation of Latent Parameters via Automatic Differentiation

PDF: https://arxiv.org/pdf/2603.26644v1

Source count: 3

Coverage: 50%

Last proof check: 2026-03-30T22:29:48.773Z

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Subject: Automatic Laplace Collapsed Sampling: Scalable Marginalisation of Latent Parameters via Automatic Differentiation

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Ignore

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Claim map

Strong 8Mixed 0Weak 0

Evidencepartial
We present Automatic Laplace Collapsed Sampling (ALCS), a general framework for marginalising latent parameters in Bayesian models using automatic differentiation
Implicationpartial
This is the core definition of ALCS provided in the abstract and introduction.
Verificationpartial
partial
Evidencepartial
This reduces the effective dimension from d_θ+ d_z to just d_θ, making Bayesian evidence computation tractable for high-dimensional settings
Implicationpartial
The abstract explicitly states this dimensionality reduction and the mechanism by which it is achieved.
Verificationpartial
partial
Evidencepartial
The MAP optimisation and Hessian evaluation are parallelised across live points on GPU-hardware, making the method practical at scale.
Implicationpartial
The abstract mentions parallelization on GPUs as a key enabler for scalability.
Verificationpartial
partial
Evidencepartial
We also show that automatic differentiation enables local approximations beyond Laplace to parametric families such as the Student-t, which improves evidence estimates for heavy-tailed latents.
Implicationpartial
The abstract explicitly states that autodiff enables approximations beyond Laplace and mentions the Student-t distribution as an example for heavy-tailed latents.
Verificationpartial
partial
Evidencepartial
which we combine with nested sampling to explore the hyperparameter space in a robust and efficient manner.
Implicationpartial
This combination is stated as a core aspect of the ALCS framework in the abstract.
Verificationpartial
partial
Evidencepartial
This scales asO(d^3_θ ×d z), which ford θ ≪d z represents a substantial improvement over theO((d θ +d z)3)cost of joint nested sampling.
Implicationpartial
The paper explicitly states the computational scaling for ALCS and compares it to full nested sampling.
Verificationpartial
partial
Evidencepartial
ALCS is designed for near-Gaussian latent spaces, and as such we are primarily targeting quadratic surfaces. Although optimisation in such spaces scales well [Liu and Nocedal, 1989, Zhang et al., 2022], it breaks down in anisotropic spaces
Implicationpartial
The analysis section discusses the design intent and limitations regarding latent space geometry.
Verificationpartial
partial
Evidencepartial
a hierarchical supernova model (demonstrating exact-Gaussian accuracy andD= 25,600scaling)
Implicationpartial
The experiments section mentions a hierarchical supernova model demonstrating exact-Gaussian accuracy and scaling to 25,600 dimensions.
Verificationpartial
partial

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

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