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达到较高准确度，但它们在预测中无法提供不确定性边界，因此不适用于安全关键型应用。现有能提供此类边界的核方法分类器的时间复杂度为$\mathcal O (n^{\sim3})$，使其难以处理大规模数据集。为解决这一问题，我们提出了一种基于Nadaraya-Watson估计器的新型高效分类算法，并推导出该估计的频率学派不确定性区间。我们在合成生成数据及MIT-BIH心律失常数据库的心电信号上评估了该分类器。实验表明，该方法在$\mathcal O(n)$和$\mathcal O(\log n)$运算复杂度下达到了具有竞争力的准确率（$>$\SI{96}{\percent}），同时提供了可操作的不确定性边界。这些边界有助于标记低置信度预测，适用于诊断监测或植入式设备等资源受限的实时场景。