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Quantifying Classification Uncertainty using Regularized Evidential Neural Networks

Xujiang Zhao, Yuzhe Ou, Lance Kaplan, Feng Chen, Jin-Hee Cho

arXiv:1910.06864v1cs.LGcs.AIcs.CV

TL;DR

Neural networks do not explicitly model uncertainty in class probabilities, while evidential neural networks leave different causes of uncertainty unmodeled. The paper regularizes ENNs for distinct uncertainty dimensions and reports more desirable uncertainty estimates and stronger out-of-distribution performance for selected variants.

  • Problem

    Neural networks do not explicitly handle uncertainty in class probabilities, and evidential neural networks do not explicitly account for distinct uncertainty types such as vacuity or dissonance.

    Source: Introduction · p. 1

  • Method

    The paper trains evidential neural networks with regularizations associated with vacuity and dissonance.

    Source: Background · p. 4

  • Results

    ENN-Vac-Diss outperformed the other methods on out-of-distribution detection, while ENN-Vac also outperformed the baselines; the variants showed more desirable vacuity and dissonance measurements.

    Source: Conclusion & Future Work · p. 6

  • Takeaways & Limitations

    ENN-Vac shows higher vacuity for more out-of-distribution samples, while ENN-Diss shows higher dissonance particularly near class boundaries.

    Source: Conclusion & Future Work · p. 6

    The authors identify unstable performance when multiple uncertainty dimensions are considered and plan validation on more real-world datasets.

    Source: Conclusion & Future Work · p. 6

Abstract

from arXiv · show

Traditional deep neural nets (NNs) have shown the state-of-the-art performance in the task of classification in various applications. However, NNs have not considered any types of uncertainty associated with the class probabilities to minimize risk due to misclassification under uncertainty in real life. Unlike Bayesian neural nets indirectly infering uncertainty through weight uncertainties, evidential neural networks (ENNs) have been recently proposed to support explicit modeling of the uncertainty of class probabilities. It treats predictions of an NN as subjective opinions and learns the function by collecting the evidence leading to these opinions by a deterministic NN from data. However, an ENN is trained as a black box without explicitly considering different types of inherent data uncertainty, such as vacuity (uncertainty due to a lack of evidence) or dissonance (uncertainty due to conflicting evidence). This paper presents a new approach, called a {\em regularized ENN}, that learns an ENN based on regularizations related to different characteristics of inherent data uncertainty. Via the experiments with both synthetic and real-world datasets, we demonstrate that the proposed regularized ENN can better learn of an ENN modeling different types of uncertainty in the class probabilities for classification tasks.

Introduction

Deep neural networks do not explicitly account for uncertainty in class probabilities, while evidential neural networks model that uncertainty without distinguishing its causes. The paper proposes regularized ENNs and evaluates them on synthetic and real-world datasets.

Introduction

  • Uncertainty from different root causes can be misinterpreted, and misclassification in safety-critical settings such as autonomous driving can be highly risky.Source: Introduction · p. 1
  • Evidential neural networks model class-probability uncertainty by treating predictions as subjective opinions and learning the evidence behind them, but do not explicitly model dimensions such as vacuity or dissonance.Source: Introduction · p. 1
  • The proposed regularized ENNs explicitly incorporate different inherent uncertainty dimensions, and the paper compares them with unregularized ENNs and NNs on synthetic and real-world datasets.Source: Introduction · p. 1

Motivational Scenarios

The paper frames uncertainty quantification as relevant to classification-based decisions in public and government settings. It uses image classification for autonomous cars as a concrete example.

Motivational Scenarios

  • The motivating scenarios include unfamiliar objects in self-driving cars, unknown disease outbreaks, and cyberattacks on power networks, where uncertainty can complicate decisions.Source: Motivational Scenarios · p. 2
  • For an unfamiliar truck in an autonomous-car setting, vacuity represents lack of evidence for a previously unknown class, while conflicting evidence can also raise uncertainty.Source: Motivational Scenarios · p. 2
  • The paper narrows its subsequent discussion to image classification, quantifying uncertainty when a classifier recognizes objects from known or unknown classes.Source: Motivational Scenarios · p. 2

Related Work

Prior work approaches uncertainty through Bayesian deep learning and belief or evidence theory. These traditions consider different uncertainty dimensions and modeling strategies.

Related Work

  • Bayesian deep learning distinguishes aleatoric and epistemic uncertainty, with aleatoric uncertainty further divided into homoscedastic and heteroscedastic forms.Source: Related Work · p. 2
  • Bayesian methods include simultaneous aleatoric and epistemic uncertainty estimation, distributional uncertainty, and dropout variational inference; other node-classification methods do not focus on uncertainty decomposition.Source: Related Work · p. 2
  • Belief and evidence theories study uncertainty in unreliable or conflicting information; Subjective Logic considers vacuity and vagueness, with later work also studying dissonance and consonance.Source: Related Work · p. 2

Background

Subjective Logic represents class predictions with belief, uncertainty, and base-rate components, distinguishing lack of evidence from conflict among class evidence. ENNs produce class evidence and Dirichlet-based probabilities, while the proposed regularized ENN adds vacuity- and dissonance-related learning signals.

Background

  • A multinomial subjective opinion comprises belief masses, an uncertainty mass for vacuity, and a base-rate distribution; its projected probabilities combine belief and uncertainty-weighted base rates.Evidence contributes to class strength alongside a non-informative prior weight.Source: Background · pp. 2–3
  • Vacuity reflects insufficient evidence, whereas dissonance reflects conflicting belief masses; dissonance is zero when all belief masses are zero, even though vacuity is one.Similar evidence across classes raises dissonance, and high vacuity can coexist with high dissonance.Source: Background · p. 3
  • An ENN replaces softmax with a non-negative evidence output, forms Dirichlet parameters as evidence plus one, and uses the Dirichlet mean to estimate class probabilities.The described ENN uses a sum-of-squared-loss objective to estimate the Dirichlet parameters.Source: Background · p. 3
  • The standard ENN is trained as a black box with a squared-error loss and an epistemic-uncertainty regularizer, but need not return high epistemic uncertainty far from both training data and decision boundaries.The regularizer is intended to favor high epistemic uncertainty where errors are likely, such as decision boundaries.Source: Background · pp. 3–4
  • The proposed regularized ENN assigns high vacuity to out-of-distribution samples and high dissonance to samples with conflicting neighboring labels, then minimizes a loss with uncertainty trade-offs and a nearest-neighbor KL term.DIN excludes OOD and conflicting-neighbor samples; λ1 and λ2 control the importance of expected vacuity and dissonance.Source: Background · p. 4

Experiments & Results

The experiments compare regularized ENNs with ENNs and standard neural networks on synthetic and CIFAR10 data. The combined vacuity-and-dissonance model performs best on CIFAR10 OOD detection, while synthetic results show uncertainty patterns that depend on the regularization and selected OOD samples.

Experiments & Results

Experimental Setup

  • For CIFAR10 OOD testing, five classes were in-distribution, two were used as OOD, and three were reserved for OOD testing.The comparison included standard softmax L2, ENN, and ENNs regularized for vacuity, dissonance, or both.Source: Experimental Setup · p. 5
  • The LeNet comparison models used 20 and 50 filters in the first and second convolutional layers, respectively, and 500 fully connected hidden units.Vacuity and dissonance regularization parameters were both set to 0.01.Source: Experimental Setup · p. 5

Experimental Results

  • ENN-Vac showed higher vacuity far from training data, and ENN-Diss showed stronger dissonance near class boundaries.Vacuity estimates depended on OOD sample selection; the selected samples did not produce the desired high vacuity across the upper and side regions.Source: Experimental Results · p. 5, Figure 3 · p. 6
  • ENN-Vac-Diss outperformed the other methods on CIFAR10 OOD detection, while ENN-Diss was comparable with ENN.ENN-Vac also outperformed the baseline methods; the empirical CDF curves closer to the bottom right are considered desirable.Source: Experimental Results · p. 6

Conclusion & Future Work

The paper concludes that regularizing ENNs for vacuity and dissonance improves uncertainty estimation in classification. The combined model performed best on OOD detection, and the authors identify broader validation and improved OOD sample generation as future work.

Conclusion

  • ENN-Vac-Diss outperformed the other methods on OOD detection, and ENN-Vac outperformed the baselines when vacuity was regularized.The authors report more reasonable vacuity and dissonance estimates in classification prediction and OOD detection.Source: Conclusion & Future Work · p. 6
  • ENN-Vac showed higher vacuity for more OOD samples, while ENN-Diss showed higher dissonance near class boundaries.The authors describe these results as promising for classification prediction and OOD detection tasks.Source: Conclusion & Future Work · p. 6

Future Work

  • Future work includes investigating unstable performance, generating more effective OOD samples, validating on more real-world datasets, and addressing vagueness in hyper opinions.Source: Conclusion & Future Work · p. 6
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