Abstract When continuously monitoring processes over time, data is collected along a whole period, from which only certain time instants and certain time intervals may play a crucial role in the data analysis. We develop a method that addresses the problem of selecting a finite and small set of short intervals (or instants) able to capture the information needed to predict a response variable from multivariate functional data using Support Vector Regression (SVR). In addition to improving interpretability, storage requirements, and monitoring cost, feature selection can potentially reduce overfitting by mitigating data autocorrelation. We propose a continuous optimization algorithm to fit the SVR parameters and select intervals and instants. Our approach takes advantage of the functional nature of the data by formulating a new bilevel optimization problem that integrates selection of intervals and instants, tuning of some key SVR parameters and fitting the SVR. We illustrate the usefulness of our proposal in some benchmark data sets.

中文翻译：

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使用支持向量回归为多元函数数据选择时刻和区间

摘要 随着时间的推移对过程进行连续监测，数据是在整个时期内收集的，从中只有某些时刻和某些时间间隔可能在数据分析中起关键作用。我们开发了一种方法，该方法解决了选择有限且小的短间隔（或瞬间）集的问题，这些短间隔（或时刻）能够使用支持向量回归 (SVR) 从多元函数数据中捕获预测响应变量所需的信息。除了提高可解释性、存储要求和监控成本外，特征选择还可以通过减轻数据自相关来潜在地减少过度拟合。我们提出了一种连续优化算法来拟合 SVR 参数并选择间隔和时刻。我们的方法通过制定一个新的双层优化问题来利用数据的功能特性，该问题集成了间隔和时刻的选择、一些关键 SVR 参数的调整和 SVR 拟合。我们在一些基准数据集中说明了我们的提议的有用性。