Statistics > Machine Learning
[Submitted on 7 Feb 2023 (v1), last revised 27 Dec 2023 (this version, v3)]
Title:How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control
View PDF HTML (experimental)Abstract:Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions, important questions remain on the reliability and trustworthiness of these sampling procedures for their responsible use in critical scenarios. Conformal prediction is a modern tool to construct finite-sample, distribution-free uncertainty guarantees for any black-box predictor. In this work, we focus on image-to-image regression tasks and we present a generalization of the Risk-Controlling Prediction Sets (RCPS) procedure, that we term $K$-RCPS, which allows to $(i)$ provide entrywise calibrated intervals for future samples of any diffusion model, and $(ii)$ control a certain notion of risk with respect to a ground truth image with minimal mean interval length. Differently from existing conformal risk control procedures, ours relies on a novel convex optimization approach that allows for multidimensional risk control while provably minimizing the mean interval length. We illustrate our approach on two real-world image denoising problems: on natural images of faces as well as on computed tomography (CT) scans of the abdomen, demonstrating state of the art performance.
Submission history
From: Jacopo Teneggi [view email][v1] Tue, 7 Feb 2023 23:01:16 UTC (16,259 KB)
[v2] Tue, 13 Jun 2023 14:40:26 UTC (9,969 KB)
[v3] Wed, 27 Dec 2023 14:48:05 UTC (9,970 KB)
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