Reliable Uncertainty Estimates in Deep Neural Networks using Noise Contrastive Priors

By Danijar Hafner, Dustin Tran, Alex Irpan, Timothy P. Lillicrap, James Davidson. 2018

77 citations recorded by the source corpus.

Obtaining reliable uncertainty estimates of neural network predictions is a long standing challenge. Bayesian neural networks have been proposed as a solution, but it remains open how to specify their prior. In particular, the common practice of a standard normal prior in weight space imposes only weak regularities, causing the function posterior to possibly generalize in unforeseen ways on inputs outside of the training distribution. We propose noise contrastive priors (NCPs) to obtain reliable uncertainty estimates. The key idea is to train the model to output high uncertainty for data points outside of the training distribution. NCPs do so using an input prior, which adds noise to the inputs of the current mini batch, and an output prior, which is a wide distribution given these inputs. NCPs are compatible with any model that can output uncertainty estimates, are easy to scale, and yield reliable uncertainty estimates throughout training. Empirically, we show that NCPs prevent overfitting outside of the training distribution and result in uncertainty estimates that are useful for active learning. We demonstrate the scalability of our method on the flight delays data set, where we significantly improve upon previously published results.

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, background): “optimal solution we derived in (11) takes 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”
A Comprehensive guide to Bayesian Convolutional Neural Network with Variational Inference (2019, methodology): “…with standard normal prior represents uncertainty and noise separately but is overconﬁdent outside of the training distribution as deﬁned by [22] It is of paramount importance that uncertainty is split into aleatoric and epistemic quantities since it allows the modeller to evaluate the room…”
Deep Anomaly Detection with Outlier Exposure (2018, methodology): “Note that we made an attempt to distort images with noise and use these as outliers for OE, but the classifier quickly memorized this statistical pattern and did not detect new OOD examples any better than before (Hafner et al., 2018).”
Analyzing the role of model uncertainty for electronic health records (2019, background): “Model uncertainty has made many methodological advances in recent years—including reparameterization-based variational Bayesian neural networks [3, 7, 19, 21], Monte Carlo dropout [8], deep ensembles and efficient alternatives [20, 33], and function priors [9, 13, 22].”
Bayesian Deep Learning and a Probabilistic Perspective of Generalization (2020, methodology): “, Jacot et al., 2018). The marginal likelihood is often used for Bayesian hypothesis testing, model comparison, and hyperparameter tuning, with Bayes factors used to select between models (Kass & Raftery, 1995). MacKay (2003, Ch. 28) uses a diagram similar to Fig 2(a) to show the marginal likelihood”
Bayesian Layers: A Module for Neural Network Uncertainty (2018, methodology): “We are particularly inspired by research on uncertainty-aware functions: priors and algorithms for Bayesian neural networks (e.g., Wen et al., 2018; Hafner et al., 2018b), scaling up Gaussian”
Improving Confidence Estimates for Unfamiliar Examples (2018, background): “Hafner et al. [13] propose a loss that encourages high uncertainty on training samples whose features are permuted or perturbed by noise.”
Model Selection in Bayesian Neural Networks via Horseshoe Priors (2017, background): “, 2017), as well as data space priors (Hafner et al., 2019) have been proposed.”
Single-Model Uncertainties for Deep Learning (2018, background): “Examples of these strategy include noisecontrastive estimation [32], noise-contrastive priors [33], and GANs [30].”
Functional Variational Bayesian Neural Networks (2019, unknown): “Noise Contrastive Priors (Hafner et al., 2018) are somewhat similar in spirit to our work in that they use a random noise prior in the function space.”
Simple, Distributed, and Accelerated Probabilistic Programming (2018, background): “As current work, we are pushing on this design as a stage for fundamental research in generative models and Bayesian neural networks (e.g., [47, 51, 16]).”
Action and Perception as Divergence Minimization (2020, methodology): “Both forms have enabled learning world models for planning (Ebert et al., 2018; Ha and Schmidhuber, 2018; Zhang et al., 2019; Hafner et al., 2018; 2019a) and accelerated RL (Lange and Riedmiller, 2010; Jaderberg et al., 2016; Lee et al., 2019a; Yarats et al., 2019; Gregor et al., 2019).”
Sequential Neural Methods for Likelihood-free Inference (2018, background): “Recent work [2, 4, 7] has highlighted the concepts of aleatoric (referring to stochasticity inherent to our data) and epistemic uncertainty (traditional model uncertainty), discussing methods to disentangle these two confounding factors in deep learning.”