Deterministic Uncertainty Estimation for Multi-Modal Regression With Deep Neural Networks

Abstract

Prediction interval (PI) is a common method to represent predictive uncertainty in regression by deep neural networks. This paper proposes an extension of the prediction interval by using a union of disjoint intervals. Since previous PI methods assumed a single-interval PI (one lower and upper bound), it suffers from performance degradation in uncertainty estimation when the conditional density function is multi-modal. This paper demonstrates the need to include multi-modality in uncertainty estimation for regression. To address the issue, we propose a novel method that generates a union of disjoint PI’s. With UCI benchmark experiments, the proposed method is shown to improve over current state-of-the-art uncertainty quantification methods, reducing an average PI width by over $27~\%$ . With qualitative experiments, it is shown that multi-modality often exists in real-world datasets, and our method produces high-quality PI’s compared to existing PI methods.

Keywords

• Deep learning
• uncertainty estimation
• multi-modal distribution
• regression