Estimating the uncertainty of a model’s prediction on a test point is a crucial part of ensuring reliability and calibration under distribution shifts.A minimum description length approach to this problem uses the predictive normalized maximum likelihood (pNML) distribution, which considers every possible label for a data point, and decreases confidence in a prediction if other labels are also consistent with the model and training data. In this work we propose IF-COMP, a scalable and efficient approximation of the pNML distribution that linearizes the model with a temperature-scaled Boltzmann influence function. IF-COMP can be used to produce well-calibrated predictions on test points as well as measure complexity in both labelled and unlabelled settings. We experimentally validate IF-COMP on uncertainty calibration, mislabel detection, and OOD detection tasks, where it consistently matches or beats strong baseline methods.

Influence functions efficiently estimate the effect of removing a single training data point on a model's learned parameters. While influence estimates align well with leave-one-out retraining for linear models, recent works have shown this alignment is often poor in neural networks. In this work, we investigate the specific factors that cause this discrepancy by decomposing it into five separate terms. We study the contributions of each term on a variety of architectures and datasets and how they vary with factors such as network width and training time. While practical influence function estimates may be a poor match to leave-one-out retraining for nonlinear networks, we show that they are often a good approximation to a different object we term the proximal Bregman response function (PBRF). Since the PBRF can still be used to answer many of the questions motivating influence functions, such as identifying influential or mislabeled examples, our results suggest that current algorithms for influence function estimation give more informative results than previous error analyses would suggest.

Models that perform well on a training domain often fail to generalize to out-of-domain (OOD) examples.Data augmentation is a common method used to prevent overfitting and improve OOD generalization.However, in natural language, it is difficult to generate new examples that stay on the underlying data manifold.We introduce SSMBA, a data augmentation method for generating synthetic training examples by using a pair of corruption and reconstruction functions to move randomly on a data manifold.We investigate the use of SSMBA in the natural language domain, leveraging the manifold assumption to reconstruct corrupted text with masked language models.In experiments on robustness benchmarks across 3 tasks and 9 datasets, SSMBA consistently outperforms existing data augmentation methods and baseline models on both in-domain and OOD data, achieving gains of 0.8% accuracy on OOD Amazon reviews, 1.8% accuracy on OOD MNLI, and 1.4 BLEU on in-domain IWSLT14 German-English. 1