Better Uncertainty Calibration via Proper Scores for Classification and Beyond

With model trustworthiness being crucial for sensitive real-world applications, practitioners are putting more and more focus on improving the uncertainty calibration of deep neural networks. Calibration errors are designed to quantify the reliability of probabilistic predictions but their estimators are usually biased and inconsistent. In this work, we introduce the framework of proper calibration errors, which relates every calibration error to a proper score and provides a respective upper bound with optimal estimation properties. This relationship can be used to reliably quantify the model calibration improvement. We theoretically and empirically demonstrate the shortcomings of commonly used estimators compared to our approach. Due to the wide applicability of proper scores, this gives a natural extension of recalibration beyond classification.Comment: Accepted at NeurIPS 202

Uncertainty Estimates of Predictions via a General Bias-Variance Decomposition

Reliably estimating the uncertainty of a prediction throughout the model lifecycle is crucial in many safety-critical applications. The most common way to measure this uncertainty is via the predicted confidence. While this tends to work well for in-domain samples, these estimates are unreliable under domain drift and restricted to classification. Alternatively, proper scores can be used for most predictive tasks but a bias-variance decomposition for model uncertainty does not exist in the current literature. In this work we introduce a general bias-variance decomposition for proper scores, giving rise to the Bregman Information as the variance term. We discover how exponential families and the classification log-likelihood are special cases and provide novel formulations. Surprisingly, we can express the classification case purely in the logit space. We showcase the practical relevance of this decomposition on several downstream tasks, including model ensembles and confidence regions. Further, we demonstrate how different approximations of the instance-level Bregman Information allow reliable out-of-distribution detection for all degrees of domain drift.Comment: Accepted at AISTATS 202

A Bias-Variance-Covariance Decomposition of Kernel Scores for Generative Models

Generative models, like large language models, are becoming increasingly relevant in our daily lives, yet a theoretical framework to assess their generalization behavior and uncertainty does not exist. Particularly, the problem of uncertainty estimation is commonly solved in an ad-hoc manner and task dependent. For example, natural language approaches cannot be transferred to image generation. In this paper we introduce the first bias-variance-covariance decomposition for kernel scores and their associated entropy. We propose unbiased and consistent estimators for each quantity which only require generated samples but not the underlying model itself. As an application, we offer a generalization evaluation of diffusion models and discover how mode collapse of minority groups is a contrary phenomenon to overfitting. Further, we demonstrate that variance and predictive kernel entropy are viable measures of uncertainty for image, audio, and language generation. Specifically, our approach for uncertainty estimation is more predictive of performance on CoQA and TriviaQA question answering datasets than existing baselines and can also be applied to closed-source models.Comment: Preprin

Parameterized Temperature Scaling for Boosting the Expressive Power in Post-Hoc Uncertainty Calibration

We address the problem of uncertainty calibration and introduce a novel calibration method, Parametrized Temperature Scaling (PTS). Standard deep neural networks typically yield uncalibrated predictions, which can be transformed into calibrated confidence scores using post-hoc calibration methods. In this contribution, we demonstrate that the performance of accuracy-preserving state-of-the-art post-hoc calibrators is limited by their intrinsic expressive power. We generalize temperature scaling by computing prediction-specific temperatures, parameterized by a neural network. We show with extensive experiments that our novel accuracy-preserving approach consistently outperforms existing algorithms across a large number of model architectures, datasets and metrics.Comment: Technical repor