We study post-calibration uncertainty for trained ensembles of classifiers. Specifically, we consider both aleatoric (label noise) and epistemic (model) uncertainty. Among the most popular and widely used calibration methods in classification are temperature scaling (i.e., pool-then-calibrate) and conformal methods. However, the main shortcoming of these calibration methods is that they do not balance the proportion of aleatoric and epistemic uncertainty. Not balancing these uncertainties can severely misrepresent predictive uncertainty, leading to overconfident predictions in some input regions while being underconfident in others. To address this shortcoming, we present a simple but powerful calibration algorithm Joint Uncertainty Calibration (JUCAL) that jointly calibrates aleatoric and epistemic uncertainty. JUCAL jointly calibrates two constants to weight and scale epistemic and aleatoric uncertainties by optimizing the negative log-likelihood (NLL) on the validation/calibration dataset. JUCAL can be applied to any trained ensemble of classifiers (e.g., transformers, CNNs, or tree-based methods), with minimal computational overhead, without requiring access to the models' internal parameters. We experimentally evaluate JUCAL on various text classification tasks, for ensembles of varying sizes and with different ensembling strategies. Our experiments show that JUCAL significantly outperforms SOTA calibration methods across all considered classification tasks, reducing NLL and predictive set size by up to 15% and 20%, respectively. Interestingly, even applying JUCAL to an ensemble of size 5 can outperform temperature-scaled ensembles of size up to 50 in terms of NLL and predictive set size, resulting in up to 10 times smaller inference costs. Thus, we propose JUCAL as a new go-to method for calibrating ensembles in classification.

We introduce Statistical Flow Matching (SFM), a novel and mathematically rigorous flow-matching framework on the manifold of parameterized probability measures inspired by the results from information geometry. We demonstrate the effectiveness of our method on the discrete generation problem by instantiat-ing SFM on the manifold of categorical distributions whose geometric properties remain unexplored in previous discrete generative models. Utilizing the Fisher information metric, we equip the manifold with a Riemannian structure whose intrinsic geometries are effectively leveraged by following the shortest paths of geodesics. We develop an efficient training and sampling algorithm that overcomes numerical stability issues with a diffeomorphism between manifolds. Our distinctive geometric perspective of statistical manifolds allows us to apply optimal transport during training and interpret SFM as following the steepest direction of the natural gradient. Unlike previous models that rely on variational bounds for likelihood estimation, SFM enjoys the exact likelihood calculation for arbitrary probability measures. We manifest that SFM can learn more complex patterns on the statistical manifold where existing models often fail due to strong prior assumptions. Comprehensive experiments on real-world generative tasks ranging from image, text to biological domains further demonstrate that SFM achieves higher sampling quality and likelihood than other discrete diffusion or flow-based models. Our code is available at https://github.com/ccr-cheng/

Neural networks are known toproduce poor uncertainty estimations, and avariety of approaches have been proposed to remedy this issue.

FromTheorem 2,thevariational gap is strictly positive as long as the rotation part of the score network remainstobenonzero.

This paper introduces a data-adaptive nonlinear diffusion process for score-based diffusion models.

Ideally, we want networks to be accurate, calibrated and confident. We show that, as opposed to the standard cross-entropy loss, focal loss [19] allows us to learn models that are already very well calibrated. When combined with temperature scaling, whilst preserving accuracy, it yields state-of-the-art calibrated models. We provide a thorough analysis of the factors causing miscalibration, and use the insights we glean from this to justify the empirically excellent performance of focal loss.

Ineachstep, A's output distribution is within ζ of the true distribution N(t,1;S). Consider a hypothetical sampling algorithm A0 in which A is run, and then the output is altered by rejection to match the true distribution.

Ourresult follows from a statistical and computational analysis of the Stochastic Gradient Descent (SGD) algorithm for solving a natural adaptation of the LASSO optimization problem that accommodates truncation.