Hierarchical Uncertainty Exploration via Feedforward Posterior Trees
This addresses the problem of uncertainty exploration for researchers and practitioners in fields like image restoration, though it is incremental as it builds on existing summarization techniques.
The paper tackles the challenge of visualizing high-dimensional posterior distributions in ill-posed inverse problems by introducing a method that predicts hierarchical tree-valued summaries in a single neural network forward pass, achieving comparable performance to a baseline diffusion-based sampler with orders of magnitude greater speed.
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.