[Paper Review] Uncertainty Quantification and Deep Ensembles

Rahul Rahaman, Alexandre H. Thiéry|arXiv (Cornell University)|Jul 17, 2020

Anomaly Detection Techniques and ApplicationsComputer Science45 references31 citations

TL;DR

The paper analyzes how deep ensembles interact with mixup and calibration in low-data settings, showing ensembling can hurt calibration and proposing a Pool-Then-Calibrate approach with temperature scaling to substantially improve calibration.

ABSTRACT

Deep Learning methods are known to suffer from calibration issues: they typically produce over-confident estimates. These problems are exacerbated in the low data regime. Although the calibration of probabilistic models is well studied, calibrating extremely over-parametrized models in the low-data regime presents unique challenges. We show that deep-ensembles do not necessarily lead to improved calibration properties. In fact, we show that standard ensembling methods, when used in conjunction with modern techniques such as mixup regularization, can lead to less calibrated models. This text examines the interplay between three of the most simple and commonly used approaches to leverage deep learning when data is scarce: data-augmentation, ensembling, and post-processing calibration methods. Although standard ensembling techniques certainly help boost accuracy, we demonstrate that the calibration of deep ensembles relies on subtle trade-offs. We also find that calibration methods such as temperature scaling need to be slightly tweaked when used with deep-ensembles and, crucially, need to be executed after the averaging process. Our simulations indicate that this simple strategy can halve the Expected Calibration Error (ECE) on a range of benchmark classification problems compared to standard deep-ensembles in the low data regime.

Motivation & Objective

• Motivate and quantify uncertainty calibration issues in over-parameterized deep models trained with limited data.
• Examine how data augmentation (mixup) and ensemble averaging interact to affect calibration.
• Assess post-processing calibration methods and the effect of aggregation order on calibration performance.

Proposed method

• Analyze calibration properties of deep ensembles under data scarcity and mixup augmentation.
• Compare linear pooling, median/trimmed pooling, and temperature scaling as post-processing steps.
• Propose Pool-Then-Calibrate: train models, then fit a single temperature parameter on validation data after aggregation.
• Evaluate different pooling and calibration orders (A-D) across multiple datasets and architectures.
• Use proper scoring rules (e.g., cross-entropy) to optimize calibration parameters.

Experimental results

Research questions

• RQ1 How do deep ensembles affect calibration in low-data regimes, especially with mixup augmentation?
• RQ2 Does post-processing calibration (temperature scaling) interact with ensemble averaging in a way that improves or worsens calibration?
• RQ3 What pooling/calibration order (pool-then-calibrate vs calibrate-then-pool) yields best calibration performance across datasets?
• RQ4 Can a simple Pool-Then-Calibrate strategy substantially reduce ECE while preserving accuracy and NLL/Brier gains?

Key findings

• Ensembling predictions often reduces confidence, which can help calibration when individual models are over-confident but does not inherently improve calibration.
• Mixup augmentation tends to make networks under-confident, and ensembling such networks can worsen calibration unless calibrated appropriately.
• Temperature scaling should be applied after pooling (averaging) of predictions to mitigate under-confidence from ensemble averaging.
• Pool-Then-Calibrate (aggregate first, then calibrate with a single temperature) can halve the ECE on several benchmark tasks in low-data settings.
• Calibrating individual models before pooling is less effective than pooling first and then calibrating, due to order of operations and interaction effects.
• Across multiple datasets, pooling strategies like average/median/trimmed pooling show varying gains, with pool-then-calibrate often outperforming naive averaging.