Given observed data and a probabilistic generative model, Bayesian inference
searches for the distribution of the model's parameters that could have yielded
the data. Inference is challenging for large population studies where millions
of measurements are performed over a cohort of hundreds of subjects, resulting
in a massive parameter space. This large cardinality renders off-the-shelf
Variational Inference (VI) computationally impractical.
In this work, we design structured VI families that efficiently tackle large
population studies. Our main idea is to share the parameterization and learning
across the different i.i.d. variables in a generative model, symbolized by the
model's \textit{plates}. We name this concept \textit{plate amortization}.
Contrary to off-the-shelf stochastic VI, which slows down inference, plate
amortization results in orders of magnitude faster to train variational
distributions.
Applied to large-scale hierarchical problems, PAVI yields expressive,
parsimoniously parameterized VI with an affordable training time. This faster
convergence effectively unlocks inference in those large regimes. We illustrate
the practical utility of PAVI through a challenging Neuroimaging example
featuring 400 million latent parameters, demonstrating a significant step
towards scalable and expressive Variational Inference.

在大规模人口研究中，通过设计结构化的变分推断方法，使用概率生成模型和参数分布，实现贝叶斯推断，加快了训练速度和收敛速度，为可扩展性和表达性变分推断迈出了重要一步。

PAVI: 板块摊销变分推断

PAVI: Plate-Amortized Variational Inference

Given some observed data and a probabilistic generative model, Bayesian
inference aims at obtaining the distribution of a model's latent parameters
that could have yielded the data. This task is challenging for large population
studies where thousands of measurements are performed over a cohort of hundreds
of subjects, resulting in a massive latent parameter space. This large
cardinality renders off-the-shelf Variational Inference (VI) computationally
impractical. In this work, we design structured VI families that can
efficiently tackle large population studies. To this end, our main idea is to
share the parameterization and learning across the different i.i.d. variables
in a generative model -symbolized by the model's plates. We name this concept
plate amortization, and illustrate the powerful synergies it entitles,
resulting in expressive, parsimoniously parameterized and orders of magnitude
faster to train large scale hierarchical variational distributions. We
illustrate the practical utility of PAVI through a challenging Neuroimaging
example featuring a million latent parameters, demonstrating a significant step
towards scalable and expressive Variational Inference.

本文提出使用结构化 VI 族来有效处理大量人口研究数据中的潜变量参数空间，并阐述 Plate Amortization 的思想可以加快训练，提高表达力，精简参数，在神经影像学实例中进行了应用，取得了可扩展性和可表达性 VI 的重要进展。