How to Trust Your Diffusion Model: A Convex Optimization Approach to Conformal Risk Control

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.

Weakly Supervised Learning Significantly Reduces the Number of Labels Required for Intracranial Hemorrhage Detection on Head CT

Modern machine learning pipelines, in particular those based on deep learning (DL) models, require large amounts of labeled data. For classification problems, the most common learning paradigm consists of presenting labeled examples during training, thus providing strong supervision on what constitutes positive and negative samples. This constitutes a major obstacle for the development of DL models in radiology--in particular for cross-sectional imaging (e.g., computed tomography [CT] scans)--where labels must come from manual annotations by expert radiologists at the image or slice-level. These differ from examination-level annotations, which are coarser but cheaper, and could be extracted from radiology reports using natural language processing techniques. This work studies the question of what kind of labels should be collected for the problem of intracranial hemorrhage detection in brain CT. We investigate whether image-level annotations should be preferred to examination-level ones. By framing this task as a multiple instance learning problem, and employing modern attention-based DL architectures, we analyze the degree to which different levels of supervision improve detection performance. We find that strong supervision (i.e., learning with local image-level annotations) and weak supervision (i.e., learning with only global examination-level labels) achieve comparable performance in examination-level hemorrhage detection (the task of selecting the images in an examination that show signs of hemorrhage) as well as in image-level hemorrhage detection (highlighting those signs within the selected images). Furthermore, we study this behavior as a function of the number of labels available during training. Our results suggest that local labels may not be necessary at all for these tasks, drastically reducing the time and cost involved in collecting and curating datasets.

From Shapley back to Pearson: Hypothesis Testing via the Shapley Value

Machine learning models, in particular artificial neural networks, are increasingly used to inform decision making in high-stakes scenarios across a variety of fields--from financial services, to public safety, and healthcare. While neural networks have achieved remarkable performance in many settings, their complex nature raises concerns on their reliability, trustworthiness, and fairness in real-world scenarios. As a result, several a-posteriori explanation methods have been proposed to highlight the features that influence a model's prediction. Notably, the Shapley value--a game theoretic quantity that satisfies several desirable properties--has gained popularity in the machine learning explainability literature. More traditionally, however, feature importance in statistical learning has been formalized by conditional independence, and a standard way to test for it is via Conditional Randomization Tests (CRTs). So far, these two perspectives on interpretability and feature importance have been considered distinct and separate. In this work, we show that Shapley-based explanation methods and conditional independence testing for feature importance are closely related. More precisely, we prove that evaluating a Shapley coefficient amounts to performing a specific set of conditional independence tests, as implemented by a procedure similar to the CRT but for a different null hypothesis. Furthermore, the obtained game-theoretic values upper bound the $p$-values of such tests. As a result, we grant large Shapley coefficients with a precise statistical sense of importance with controlled type I error.

Fast Hierarchical Games for Image Explanations

As modern complex neural networks keep breaking records and solving harder problems, their predictions also become less and less intelligible. The current lack of interpretability often undermines the deployment of accurate machine learning tools in sensitive settings. In this work, we present a model-agnostic explanation method for image classification based on a hierarchical extension of Shapley coefficients --Hierarchical Shap (h-Shap)-- that resolves some of the limitations of current approaches. Unlike other Shapley-based explanation methods, h-Shap is scalable and can be computed without the need of approximation. Under certain distributional assumptions, such as those common in multiple instance learning, h-Shap retrieves the exact Shapley coefficients with an exponential improvement in computational complexity. We compare our hierarchical approach with popular Shapley-based and non-Shapley-based methods on a synthetic dataset, a medical imaging scenario, and a general computer vision problem, showing that h-Shap outperforms the state of the art in both accuracy and runtime. Code and experiments are made publicly available.