Hierarchical Uncertainty Exploration via Feedforward Posterior Trees

TL;DR

This paper introduces a neural network-based method for hierarchical visualization of posterior distributions in inverse problems, enabling fast and effective uncertainty quantification across multiple levels of detail.

Contribution

It presents a novel feedforward neural network approach that predicts tree-structured summaries of posteriors in a single pass, significantly improving speed over existing clustering methods.

Findings

Performs comparably to diffusion-based clustering in uncertainty visualization

Achieves orders of magnitude faster computation

Effective across diverse datasets and image restoration tasks

Abstract

When solving ill-posed inverse problems, one often desires to explore the space of potential solutions rather than be presented with a single plausible reconstruction. Valuable insights into these feasible solutions and their associated probabilities are embedded in the posterior distribution. However, when confronted with data of high dimensionality (such as images), visualizing this distribution becomes a formidable challenge, necessitating the application of effective summarization techniques before user examination. In this work, we introduce a new approach for visualizing posteriors across multiple levels of granularity using tree-valued predictions. Our method predicts a tree-valued hierarchical summarization of the posterior distribution for any input measurement, in a single forward pass of a neural network. We showcase the efficacy of our approach across diverse datasets and image restoration challenges, highlighting its prowess in uncertainty quantification and visualization. Our findings reveal that our method performs comparably to a baseline that hierarchically clusters samples from a diffusion-based posterior sampler, yet achieves this with orders of magnitude greater speed.