A conformal predictive system(CPS) is based on the learning framework of conformal prediction, which outputs cumulative distribution functions(CDFs) for labels in regression problems. The CDFs output by a CPS provide useful information for users, as they not only provide probability for the events related to the test labels, but also can be transformed to prediction intervals with the corresponding quantiles. Moreover, CPSs have the property of validity since the distributions and intervals they output have statistical compatibility with the realizations. This property is very useful for many risk-sensitive applications such as financial time series forecast and weather forecast. However, as based on conformal predictors, CPSs inherit the computational issue. To build a fast CPS, in this paper, we propose a CPS with regularized extreme learning machine as the underlying algorithm. To be specific, we combine the leave-one-out cross-conformal predictive system(Leave-One-Out CCPS), a variant of the original CPS, with regularized extreme learning machine(RELM), which is named as LOO-CCPS-RELM. We analyse the computational complexity of it and prove its asymptotic validity based on some regularity assumptions. We also prove that the error rate of the prediction interval output by LOO-CCPS-RELM is under control in the asymptotic setting. Experiments with 20 public data sets were conducted to test LOO-CCPS-RELM and the results showed that LOO-CCPS-RELM is empirically valid and compared favourably with the other CPSs.

中文翻译：

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具有正则化极限学习机的快速共形预测系统。

保形预测系统（CPS）基于保形预测的学习框架，该系统为回归问题中的标签输出累积分布函数（CDF）。CPS输出的CDF为用户提供有用的信息，因为它们不仅提供与测试标签有关的事件的概率，而且可以转换为具有相应分位数的预测间隔。此外，由于CPS输出的分布和间隔与实现具有统计兼容性，因此具有有效性。此属性对于许多风险敏感的应用程序非常有用，例如财务时间序列预测和天气预报。但是，基于保形预测变量，CPS会继承计算问题。为了建立快速的CPS，在本文中，我们提出了一种使用正则化极限学习机作为基础算法的CPS。具体来说，我们将原始CPS的变体之一留一法跨保形预测系统（Leave-One-Out CCPS）与正则化的极限学习机（RELM）相结合，后者被称为LOO-CCPS- RELM。我们分析了它的计算复杂性，并基于一些规律性假设证明了它的渐近有效性。我们还证明，在渐近设置下，LOO-CCPS-RELM输出的预测间隔的错误率处于受控状态。进行了20个公共数据集的实验以测试LOO-CCPS-RELM，结果表明LOO-CCPS-RELM在经验上是有效的，并且与其他CPS相比具有优势。我们将原始CPS的变体留一法跨保形预测系统（Leave-One-Out CCPS）与正则化极限学习机（RELM）相结合，后者被称为LOO-CCPS-RELM。我们分析了它的计算复杂性，并基于一些规律性假设证明了它的渐近有效性。我们还证明，在渐近设置下，LOO-CCPS-RELM输出的预测间隔的错误率处于受控状态。进行了20个公共数据集的实验以测试LOO-CCPS-RELM，结果表明LOO-CCPS-RELM在经验上是有效的，并且与其他CPS相比具有优势。我们将原始CPS的变体留一法跨保形预测系统（Leave-One-Out CCPS）与正则化极限学习机（RELM）相结合，后者被称为LOO-CCPS-RELM。我们分析了它的计算复杂性，并基于一些规律性假设证明了它的渐近有效性。我们还证明，在渐近设置下，LOO-CCPS-RELM输出的预测间隔的错误率处于受控状态。进行了20个公共数据集的实验以测试LOO-CCPS-RELM，结果表明LOO-CCPS-RELM在经验上是有效的，并且与其他CPS相比具有优势。我们还证明，在渐近设置下，LOO-CCPS-RELM输出的预测间隔的错误率处于受控状态。进行了20个公共数据集的实验以测试LOO-CCPS-RELM，结果表明LOO-CCPS-RELM在经验上是有效的，并且与其他CPS相比具有优势。我们还证明，在渐近设置下，LOO-CCPS-RELM输出的预测间隔的错误率处于受控状态。进行了20个公共数据集的实验以测试LOO-CCPS-RELM，结果表明LOO-CCPS-RELM在经验上是有效的，并且与其他CPS相比具有优势。