The Evidential Regression Network (ERN) represents a novel approach that
integrates deep learning with Dempster-Shafer's theory to predict a target and
quantify the associated uncertainty. Guided by the underlying theory, specific
activation functions must be employed to enforce non-negative values, which is
a constraint that compromises model performance by limiting its ability to
learn from all samples. This paper provides a theoretical analysis of this
limitation and introduces an improvement to overcome it. Initially, we define
the region where the models can't effectively learn from the samples. Following
this, we thoroughly analyze the ERN and investigate this constraint. Leveraging
the insights from our analysis, we address the limitation by introducing a
novel regularization term that empowers the ERN to learn from the whole
training set. Our extensive experiments substantiate our theoretical findings
and demonstrate the effectiveness of the proposed solution.

本文介绍了一种结合深度学习和 Dempster-Shafer 理论的新方法，即证据回归网络 (ERN)，用于预测目标并量化相关不确定性。通过理论分析，我们发现一种限制模型性能的约束，并引入一种改进方法以克服此限制。我们探索了 ERN 并提出了一种新的正则化项，使 ERN 能够从整个训练集中学习。大量实验证实了我们的理论发现，并证明了所提出解决方案的有效性。

不确定性规范化的证据回归

Uncertainty Regularized Evidential Regression

The Evidential regression network (ENet) estimates a continuous target and
its predictive uncertainty without costly Bayesian model averaging. However, it
is possible that the target is inaccurately predicted due to the gradient
shrinkage problem of the original loss function of the ENet, the negative log
marginal likelihood (NLL) loss. In this paper, the objective is to improve the
prediction accuracy of the ENet while maintaining its efficient uncertainty
estimation by resolving the gradient shrinkage problem. A multi-task learning
(MTL) framework, referred to as MT-ENet, is proposed to accomplish this aim. In
the MTL, we define the Lipschitz modified mean squared error (MSE) loss
function as another loss and add it to the existing NLL loss. The Lipschitz
modified MSE loss is designed to mitigate the gradient conflict with the NLL
loss by dynamically adjusting its Lipschitz constant. By doing so, the
Lipschitz MSE loss does not disturb the uncertainty estimation of the NLL loss.
The MT-ENet enhances the predictive accuracy of the ENet without losing
uncertainty estimation capability on the synthetic dataset and real-world
benchmarks, including drug-target affinity (DTA) regression. Furthermore, the
MT-ENet shows remarkable calibration and out-of-distribution detection
capability on the DTA benchmarks.

提出了一种多任务学习框架 MT-ENet，通过将 Lipschitz 修正均方误差（MSE）损失函数添加到负对数边缘似然 (NLL) 损失中，动态调整 Lipschitz 常数，以解决 Evidential regression network (ENet) 的梯度收缩问题，并提高其预测精度，同时保持其良好的不确定性估计能力，该方法在药物 - 靶标亲和力 (DTA) 回归等实际基准测试中表现出了出色的校准和超出分布检测能力。