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Improving Uncertainty Quantification of Variance Networks by Tree-Structured Learning

Wenxuan MaXing Yan
Dec 2022
摘要
To improve uncertainty quantification of variance networks, we propose anovel tree-structured local neural network model that partitions the featurespace into multiple regions based on uncertainty heterogeneity. A tree is builtupon giving the training data, whose leaf nodes represent different regionswhere region-specific neural networks are trained to predict both the mean andthe variance for quantifying uncertainty. The proposed Uncertainty-SplittingNeural Regression Tree (USNRT) employs novel splitting criteria. At each node,a neural network is trained on the full data first, and a statistical test forthe residuals is conducted to find the best split, corresponding to the twosub-regions with the most significant uncertainty heterogeneity. USNRT iscomputationally friendly because very few leaf nodes are sufficient and pruningis unnecessary. On extensive UCI datasets, in terms of both calibration andsharpness, USNRT shows superior performance compared to some recent popularmethods for variance prediction, including vanilla variance network, deepensemble, dropout-based methods, tree-based models, etc. Through comprehensivevisualization and analysis, we uncover how USNRT works and show its merits.
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