While both classical and neural network classifiers can achieve high accuracy, they fall short on offering uncertainty bounds on their predictions, making them unfit for safety-critical applications. Existing kernel-based classifiers that provide such bounds scale with $\mathcal O (n^{\sim3})$ in time, making them computationally intractable for large datasets. To address this, we propose a novel, computationally efficient classification algorithm based on the Nadaraya-Watson estimator, for whose estimates we derive frequentist uncertainty intervals. We evaluate our classifier on synthetically generated data and on electrocardiographic heartbeat signals from the MIT-BIH Arrhythmia database. We show that the method achieves competitive accuracy $>$\SI{96}{\percent} at $\mathcal O(n)$ and $\mathcal O(\log n)$ operations, while providing actionable uncertainty bounds. These bounds can, e.g., aid in flagging low-confidence predictions, making them suitable for real-time settings with resource constraints, such as diagnostic monitoring or implantable devices.

翻译：尽管经典分类器和神经网络分类器都能实现高精度，但它们无法提供预测的不确定性边界，这使得它们不适用于安全关键型应用。现有提供此类边界的基于核函数的分类器在时间复杂度上为$\mathcal O (n^{\sim3})$，导致其在大规模数据集上计算不可行。为解决这一问题，我们提出一种基于Nadaraya-Watson估计器的新型高效分类算法，并为其估计值推导了频率派不确定性区间。我们在合成数据以及MIT-BIH心律失常数据库的心电信号上评估了该分类器。结果表明，该方法在$\mathcal O(n)$和$\mathcal O(\log n)$运算量下实现超过96%的竞争性准确率，同时提供可操作的不确定性边界。例如，这些边界可帮助标记低置信度预测，从而适用于资源受限的实时场景，如诊断监测或植入式设备。