A robust probabilistic classifier for functional data is developed to predict class membership based on functional input measurements and to provide a reliable probability estimates for class membership. The method combines a Bayes classifier and semi-parametric mixed effects model with robust tuning parameter to make the method robust to outlying curves, and to improve the accuracy of the risk or uncertainty estimates, which is crucial in medical diagnostic applications. The approach applies to functional data with varying ranges and irregular sampling without making parametric assumptions on the within-curve covariance. Simulation studies evaluate the proposed method and competitors in terms of sensitivity to heavy tailed functional distributions and outlying curves. Classification performance is evaluated by both error rate and logloss, the latter of which imposes heavier penalties on highly confident errors than on less confident errors. Runtime experiments on the R implementation indicate that the proposed method scales well computationally. Illustrative applications include data from quantitative ultrasound analysis and phoneme recognition.

中文翻译：

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适用于不规则采样功能数据的鲁棒概率分类

开发了功能数据的稳健概率分类器，以根据功能输入测量来预测类别成员资格，并为类别成员资格提供可靠的概率估计。该方法将贝叶斯分类器和半参数混合效应模型与鲁棒调整参数相结合，使该方法对外围曲线具有鲁棒性，并提高风险或不确定性估计的准确性，这在医疗诊断应用中至关重要。该方法适用于具有变化范围和不规则采样的函数数据，而不对曲线内协方差做出参数假设。仿真研究评估了所提出的方法和竞争对手对重尾函数分布和外围曲线的敏感性。分类性能通过错误率和对数损失来评估，后者对高置信度错误的惩罚比对低置信度错误的惩罚更重。R 实现的运行时实验表明，所提出的方法在计算上具有良好的扩展性。说明性应用包括来自定量超声分析和音素识别的数据。