[Paper Review] On the Usefulness of Deep Ensemble Diversity for Out-of-Distribution Detection

Guoxuan Xia, Christos-Savvas Bouganis|arXiv (Cornell University)|Jul 15, 2022

Anomaly Detection Techniques and Applications4 citations

TL;DR

This paper challenges the common belief that deep ensemble diversity, measured by mutual information (MI), improves out-of-distribution (OOD) detection in ImageNet-scale models. Instead, it demonstrates that ensembling diverse binary OOD detectors—specifically by averaging task-specific scores like Energy—yields superior performance, with average Energy over an ensemble achieving state-of-the-art FPR@95 of 4.48% on the best OOD benchmark.

ABSTRACT

The ability to detect Out-of-Distribution (OOD) data is important in safety-critical applications of deep learning. The aim is to separate In-Distribution (ID) data drawn from the training distribution from OOD data using a measure of uncertainty extracted from a deep neural network. Deep Ensembles are a well-established method of improving the quality of uncertainty estimates produced by deep neural networks, and have been shown to have superior OOD detection performance compared to single models. An existing intuition in the literature is that the diversity of Deep Ensemble predictions indicates distributional shift, and so measures of diversity such as Mutual Information (MI) should be used for OOD detection. We show experimentally that this intuition is not valid on ImageNet-scale OOD detection -- using MI leads to 30-40% worse %FPR@95 compared to single-model entropy on some OOD datasets. We suggest an alternative explanation for Deep Ensembles' better OOD detection performance -- OOD detection is binary classification and we are ensembling diverse classifiers. As such we show that practically, even better OOD detection performance can be achieved for Deep Ensembles by averaging task-specific detection scores such as Energy over the ensemble.

Motivation & Objective

• To investigate whether deep ensemble diversity, as measured by mutual information (MI), reliably indicates out-of-distribution (OOD) inputs in ImageNet-scale models.
• To challenge the widely held intuition that high ensemble diversity correlates with distributional shift and thus aids OOD detection.
• To identify the true mechanism behind deep ensembles’ superior OOD detection performance compared to single models.
• To evaluate whether ensembling better OOD detection scores, such as Energy, further improves performance beyond standard uncertainty metrics.

Proposed method

• The authors evaluate multiple uncertainty scores—ensemble entropy (Ens. H), average entropy (Av. H), mutual information (MI), and Energy—on ImageNet-scale OOD detection benchmarks.
• They compute MI using the standard decomposition: MI ≈ Ens. H - Av. H, interpreting it as a measure of ensemble diversity.
• They compare OOD detection performance using AUROC and FPR@95 across single models and deep ensembles, with scores averaged over ensemble members.
• They apply Jensen’s inequality to theoretically justify why ensembling diverse binary OOD classifiers improves detection performance.
• They propose and evaluate averaging a task-specific score (Energy) over the ensemble, showing it consistently outperforms other uncertainty metrics.
• They conduct extensive experiments on multiple OOD datasets, including ImageNet-R, TinyImageNet, and ObjectNet, under standard evaluation protocols.

Experimental results

Research questions

• RQ1 Does mutual information (MI) between ensemble members reliably indicate out-of-distribution (OOD) inputs in ImageNet-scale models?
• RQ2 Why do deep ensembles outperform single models in OOD detection, and is it due to ensemble diversity or another mechanism?
• RQ3 Can ensembling a better OOD detection score, such as Energy, further improve performance beyond standard uncertainty metrics?
• RQ4 Is the performance gain from deep ensembles due to the averaging of diverse error patterns across ensemble members in a binary classification setting?

Key findings

• Mutual information (MI), used as a diversity metric, performs significantly worse than single-model entropy, with FPR@95 values 30-40% higher on some OOD datasets.
• Ensemble entropy (Ens. H) and average entropy (Av. H) consistently outperform their single-model counterparts, indicating that ensembling improves uncertainty estimation.
• Averaging the Energy score over the ensemble yields the best overall OOD detection performance, achieving a FPR@95 of 4.48% on the ObjectNet OOD benchmark.
• The best-performing method, average Energy, achieves a 99.08% AUROC on ObjectNet, outperforming both single-model Energy and all other ensemble-based uncertainty scores.
• The study finds no evidence that ensemble diversity (via MI) correlates with OOD inputs at scale, undermining a widely cited intuition in the literature.
• The superior performance of deep ensembles is better explained by ensembling diverse binary OOD detectors that compensate for each other’s errors, rather than by diversity as a direct OOD indicator.