PAVI: Plate-Amortized Variational Inference

TL;DR

PAVI introduces a plate-amortized variational inference method that significantly accelerates Bayesian inference in large-scale hierarchical models, enabling practical and scalable analysis of massive datasets like neuroimaging with hundreds of millions of parameters.

Contribution

The paper proposes a novel plate amortization technique for variational inference, improving training speed and scalability for large population studies.

Findings

Achieved orders of magnitude faster training times.

Enabled inference on neuroimaging data with 400 million parameters.

Demonstrated practical utility in large-scale hierarchical models.

Abstract

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.