Being Bayesian, Even Just a Bit, Fixes Overconfidence in ReLU Networks

Abstract

The point estimates of ReLU classification networks---arguably the most widely used neural network architecture---have been shown to yield arbitrarily high confidence far away from the training data. This architecture, in conjunction with a maximum a posteriori estimation scheme, is thus not calibrated nor robust. Approximate Bayesian inference has been empirically demonstrated to improve predictive uncertainty in neural networks, although the theoretical analysis of such Bayesian approximations is limited. We theoretically analyze approximate Gaussian distributions on the weights of ReLU networks and show that they fix the overconfidence problem. Furthermore, we show that even a simplistic, thus cheap, Bayesian approximation, also fixes these issues. This indicates that a sufficient condition for a calibrated uncertainty on a ReLU network is "to be a bit Bayesian". These theoretical results validate the usage of last-layer Bayesian approximation and motivate a range of a fidelity-cost trade-off. We further validate these findings empirically via various standard experiments using common deep ReLU networks and Laplace approximations.

arXiv commentICML 2020

References in corpus (17)

• On Calibration of Modern Neural Networks
• A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks
• Weight Uncertainty in Neural Networks
• Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift
• Evidential Deep Learning to Quantify Classification Uncertainty
• GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration
• Optimizing Neural Networks with Kronecker-factored Approximate Curvature
• Scalable Bayesian Optimization Using Deep Neural Networks
• Deep Anomaly Detection with Outlier Exposure
• Multiplicative Normalizing Flows for Variational Bayesian Neural Networks
• Stochastic Variational Deep Kernel Learning
• Adv-BNN: Improved Adversarial Defense through Robust Bayesian Neural Network
• Structured and Efficient Variational Deep Learning with Matrix Gaussian Posteriors
• On Last-Layer Algorithms for Classification: Decoupling Representation from Uncertainty Estimation
• Benchmarking the Neural Linear Model for Regression
• TRADI: Tracking deep neural network weight distributions for uncertainty estimation
• Non-Parametric Calibration for Classification

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