Predictive Uncertainty Estimation via Prior Networks

By Andrey Malinin, Mark John Francis Gales. 2018

1,146 citations recorded by the source corpus.

Estimating how uncertain an AI system is in its predictions is important to improve the safety of such systems. Uncertainty in predictive can result from uncertainty in model parameters, irreducible data uncertainty and uncertainty due to distributional mismatch between the test and training data distributions. Different actions might be taken depending on the source of the uncertainty so it is important to be able to distinguish between them. Recently, baseline tasks and metrics have been defined and several practical methods to estimate uncertainty developed. These methods, however, attempt to model uncertainty due to distributional mismatch either implicitly through model uncertainty or as data uncertainty. This work proposes a new framework for modeling predictive uncertainty called Prior Networks (PNs) which explicitly models distributional uncertainty. PNs do this by parameterizing a prior distribution over predictive distributions. This work focuses on uncertainty for classification and evaluates PNs on the tasks of identifying out-of-distribution (OOD) samples and detecting misclassification on the MNIST dataset, where they are found to outperform previous methods. Experiments on synthetic and MNIST and CIFAR-10 data show that unlike previous non-Bayesian methods PNs are able to distinguish between data and distributional uncertainty.

Subfields: Artificial Intelligence, Safety, Robustness & Interpretability, Probabilistic & Bayesian Methods

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Citations in the corpus

Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness (2020, methodology): “…an intuitive form, and has already been used widely as a training objective in many uncertainty works that leverage adversarial training and generative modeling to detect OOD examples (Hafner et al., 2018; Harang and Rudd, 2018; Lee et al., 2018; Malinin and Gales, 2018b; Meinke and Hein, 2020).”
Do not Forget to Attend to Uncertainty while Mitigating Catastrophic Forgetting (2021, background): “It has been shown that the deep learning models are overconfident for the wrong prediction [27]; thus, the prediction probabilities do not truly reflect the knowledge.”
Efficient and Scalable Bayesian Neural Nets with Rank-1 Factors (2020, background): “In principle, BNNs can permit graceful failure, signalling when a model does not know what to predict (Kendall & Gal, 2017; Dusenberry et al., 2019), and can also generalize better to out-of-distribution examples (Louizos & Welling, 2017; Malinin & Gales, 2018).”
Prior Networks for Detection of Adversarial Attacks (2018, methodology): “On the other hand, a Prior Network [22] p(π|x∗; θ̂) 2 directly parametrizes a prior distribution over categorical output distributions (in this work the Dirichlet distribution) and is explicitly trained to yield the desired behaviour of the distribution over distributions.”
Deep Anomaly Detection with Outlier Exposure (2018, background): “Many other works (de Vries et al., 2016; Subramanya et al., 2017; Malinin & Gales, 2018; Bevandic et al., 2018) also encourage the model to have lower confidence on anomalous examples.”
Energy-based Out-of-distribution Detection (2020, methodology): “Auxiliary data allows the model to be explicitly regularized through ﬁne-tuning, producing lower conﬁdence on anomalous examples [2, 9, 26, 27, 37].”
U-CAM: Visual Explanation Using Uncertainty Based Class Activation Maps (2019, methodology): “However, estimating epistemic uncertainty [33] is computationally expensive, and thus we measure the predictive uncertainty, having both aleatoric and epistemic uncertainties present in it.”
Deep Evidential Regression (2019, methodology): “To date, evidential deep learning has been targeted towards discrete classification problems [42, 32, 22] and has required either a well-defined distance measure to a maximally uncertain prior [42] or relied on training with OOD data to inflate model uncertainty [32, 31].”
Ensemble Distribution Distillation (2019, methodology): “An ensemble of models can be viewed as a set of samples from an implicit distribution of output distributions: Recently, a new class of models was proposed, called Prior Networks [24], which explicitly parameterize a conditional distribution over output distributions p ( π | x ∗ ; ˆ θ ) using a sing”
In Defense of Pseudo-Labeling: An Uncertainty-Aware Pseudo-label Selection Framework for Semi-Supervised Learning (2021, background): “Uncertainty and Calibration Estimating network prediction uncertainty has been a deeply studied topic (Graves, 2011; Blundell et al., 2015; Louizos & Welling, 2016; Lakshminarayanan et al., 2017; Malinin & Gales, 2018; Maddox et al., 2019; Welling & Teh, 2011).”
Noise Contrastive Priors for Functional Uncertainty (2018, background): “Malinin and Gales (2018) propose prior networks to avoid an explicit belief over parameters for classification tasks.”
Attending to Discriminative Certainty for Domain Adaptation (2019, methodology): “We apply label smoothing in classifier similar to [7, 6, 5].”
Pitfalls of In-Domain Uncertainty Estimation and Ensembling in Deep Learning (2020, methodology): “…(Quinonero-Candela et al., 2005), metrics of calibration (Guo et al., 2017; Nixon et al., 2019), performance of misclassiﬁcation detection (Malinin & Gales, 2018), and threshold–accuracy curves Here TACE is reported for VGG16BN model on CIFAR-100 dataset and is evaluated at the optimal…”
Revisiting the Calibration of Modern Neural Networks (2021, methodology): “…trend for highly accurate modern neural networks to be poorly calibrated, as suggested previously (Guo et al., 2017; Lakshminarayanan et al., 2017; Malinin & Gales, 2018; Thulasidasan et al., 2019; Hendrycks et al., 2020b; Ovadia et al., 2019; Wenzel et al., 2020; Havasi et al., 2021; Rahaman &…”
Universal Source-Free Domain Adaptation (2020, background): “The major challenge in this setting is to detect target samples from the unobserved categories (similar to detection of out-of-distribution samples [31]) in a fully-unsupervised scenario.”
Contrastive Training for Improved Out-of-Distribution Detection (2020, background): “[2], Malinin & Gales [21], Chen et al.”
MOS: Towards Scaling Out-of-distribution Detection for Large Semantic Space (2021, methodology): “OOD Detection with Model Fine-tuning An orthogonal line of work explores training with auxiliary outlier data for model regularization [3, 11, 33, 35, 43, 31].”