Uncertainty estimation methods using deep learning approaches strive against separating how uncertain the state of the world manifests to us via measurement (objective end) from the way this gets scrambled with the model specification and training procedure used to predict such state (subjective means) — e.g., number of neurons, depth, connections, priors (if the model is bayesian), weight initialization, etc. This poses the question of the extent to which one can eliminate the degrees of freedom associated with these specifications and still being able to capture the objective end. Here, a novel non-parametric quantile estimation method for continuous random variables is introduced, based on the simplest neural network architecture with one degree of freedom: a single neuron. Its advantage is first shown in synthetic experiments comparing with the quantile estimation achieved from ranking the order statistics (specifically for small sample size) and with quantile regression. In real-world applications, the method can be used to quantify predictive uncertainty under the split conformal prediction setting, whereby prediction intervals are estimated from the residuals of a pre-trained model on a held-out validation set and then used to quantify the uncertainty in future predictions — the single neuron used here as a structureless “thermometer” that measures how uncertain the pre-trained model is. Benchmarking regression and classification experiments demonstrate that the method is competitive in quality and coverage with state-of-the-art solutions, with the added benefit of being more computationally efficient.

使用深度学习方法的不确定性估计方法力图将通过测量（客观结果）向我们展现的世界状态的不确定性与用于预测这种状态的模型规范和训练程序（主观手段）进行混杂的方式分开——例如、神经元数量、深度、连接、先验（如果模型是贝叶斯模型）、权重初始化等。这就提出了一个问题：在多大程度上可以消除与这些规范相关的自由度，并且仍然能够捕获客观结束。这里，介绍了一种新颖的连续随机变量非参数分位数估计方法，该方法基于最简单的具有一个自由度的神经网络架构：单个神经元。它的优势首先在综合实验中显示出来，与通过排序统计量（特别是小样本量）和分位数回归获得的分位数估计进行比较。在实际应用中，该方法可用于量化分割共形预测设置下的预测不确定性，从而根据保留验证集上预训练模型的残差来估计预测区间，然后用于量化不确定性在未来的预测中——这里使用的单个神经元作为无结构的“温度计”，用于测量预训练模型的不确定性。基准回归和分类实验表明，该方法在质量和覆盖范围上与最先进的解决方案具有竞争力，并且具有计算效率更高的额外优势。