Title: A unified uncertainty-informed approach for risk management of deep learning models in the open world

Authors: Long Xue, Sai-Ho Chung, Lechang Yang, Xiao-Lin Wang, and Xiaoge Zhang

Abstract: Equipping deep learning models with a principled uncertainty quantification (UQ) has become essential for ensuring their reliable performance in the open world. To handle uncertainty arising from two prevalent sources – distribution shift and out-of-distribution (OOD) – in the open-world settings, this paper presents a unified uncertainty-informed approach for quantifying and managing the risks these factors pose to the dependable function of deep learning models. Toward this goal, we propose leveraging a principled UQ approach — Spectral-normalized Neural Gaussian Process (SNGP) — to quantify the epistemic uncertainty associated with model predictions. Unlike other UQ methods in the literature, SNGP is characterized by two unique properties: (1) applying spectral normalization to the weights of the neural network’s hidden layers to preserve the relative distances among data points during data transformations; (2) replacing the traditional output layer of neural networks with a Gaussian process to enable distance-aware uncertainty estimation. Based on SNGP’s uncertainty estimate, we apply Youden’s index to determine an optimal threshold for categorizing the uncertainty into distinct levels, thereby enabling decision-makers to make uncertainty-informed decisions. Two datasets of varying scale are used to demonstrate how the proposed method facilitates risk assessment and management of deep learning models in the open environment. Computational results reveal that the proposed method achieves prediction performance comparable to Monte Carlo dropout and deep ensemble methods. Importantly, the proposed approach outperforms the other two methods by providing a computationally efficient, consistent, and principled uncertainty estimation under no distribution shift, distribution shift, and OOD conditions.

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