To improve the uncertainty quantification of variance networks, we propose a novel tree-structured local neural network model that partitions the feature space into multiple regions based on uncertainty heterogeneity. A tree is built upon giving the training data, whose leaf nodes represent different regions where region-specific neural networks are trained to predict both the mean and the variance for quantifying uncertainty. The proposed Uncertainty-Splitting Neural Regression Tree (USNRT) employs novel splitting criteria. At each node, a neural network is trained on the full data first, and a statistical test for the residuals is conducted to find the best split, corresponding to the two sub-regions with the most significant uncertainty heterogeneity between them. USNRT is computationally friendly because very few leaf nodes are sufficient and pruning is unnecessary. Furthermore, an ensemble version can be easily constructed to estimate the total uncertainty including the aleatory and epistemic. On extensive UCI datasets, USNRT or its ensemble shows superior performance compared to some recent popular methods for quantifying uncertainty with variances. Through comprehensive visualization and analysis, we uncover how USNRT works and show its merits, revealing that uncertainty heterogeneity does exist in many datasets and can be learned by USNRT.

翻译：为了提升方差网络的不确定性量化能力，我们提出一种新颖的基于树结构的局部神经网络模型，该模型根据不确定性异质性将特征空间划分为多个区域。基于训练数据构建一棵决策树，其叶节点代表不同区域，在这些区域中训练特定区域的神经网络以同时预测均值和方差，从而实现不确定性量化。所提出的不确定分裂神经回归树（USNRT）采用了新颖的分裂准则。在每个节点处，首先在整个数据上训练一个神经网络，然后对残差进行统计检验以找到最佳分裂点，该分裂点对应两个子区域，它们之间的不确定性异质性最为显著。USNRT计算效率高，因为仅需极少叶节点且无需剪枝。此外，可轻松构建集成版本来估计总不确定性（包括偶然不确定性和认知不确定性）。在广泛的UCI数据集上，USNRT及其集成方法在基于方差的不确定性量化方面展现出优于近期多种流行方法的性能。通过全面的可视化与分析，我们揭示了USNRT的工作原理及其优势，表明不确定性异质性确实存在于许多数据集中，且可被USNRT有效学习。