Artificial neural networks (ANNs) are highly flexible predictive models. However, reliably quantifying uncertainty for their predictions is a continuing challenge. There has been much recent work on "recalibration" of predictive distributions for ANNs, so that forecast probabilities for events of interest are consistent with certain frequency evaluations of them. Uncalibrated probabilistic forecasts are of limited use for many important decision-making tasks. To address this issue, we propose a localized recalibration of ANN predictive distributions using the dimension-reduced representation of the input provided by the ANN hidden layers. Our novel method draws inspiration from recalibration techniques used in the literature on approximate Bayesian computation and likelihood-free inference methods. Most existing calibration methods for ANNs can be thought of as calibrating either on the input layer, which is difficult when the input is high-dimensional, or the output layer, which may not be sufficiently flexible. Through a simulation study, we demonstrate that our method has good performance compared to alternative approaches, and explore the benefits that can be achieved by localizing the calibration based on different layers of the network. Finally, we apply our proposed method to a diamond price prediction problem, demonstrating the potential of our approach to improve prediction and uncertainty quantification in real-world applications.

翻译：人工神经网络（ANN）是具有高度灵活性的预测模型。然而，可靠地量化其预测的不确定性仍是一个持续挑战。近期大量研究关注ANN预测分布的"再校准"问题，使关注事件预测概率与其频率评估结果保持一致。未校准的概率型预测在许多重要决策任务中实用价值有限。为解决该问题，我们提出利用ANN隐藏层提供的降维输入表示，对ANN预测分布进行局部化再校准。这一新方法借鉴了近似贝叶斯计算和无似然推断方法文献中的再校准技术。现有ANN校准方法可归为两类：在输入层进行校准（当输入为高维时较为困难）或在输出层进行校准（灵活性可能不足）。通过仿真研究，我们证明了该方法相较替代方案具有更优性能，并探索了基于网络不同层进行局部校准可获得的增益。最后，我们将该方法应用于钻石价格预测问题，展示了其在实际应用中改进预测与不确定性量化的潜力。