论文标题
时间序列的内核，具有不规则间隔的多元观测
Kernels for time series with irregularly-spaced multivariate observations
论文作者
论文摘要
时间序列是基于内核方法的有趣边界，其简单原因是没有旨在代表它们的内核及其独特特征的整体性。现有的顺序内核忽略了时间索引，许多人认为该系列必须定期间隔；一些这样的内核甚至不是PSD。在本手稿中，我们表明，一个“系列内核”足以代表不规律的多元时间序列，可以用众所周知的“向量内核”构建。我们还表明，使用我们的方法构建的所有系列内核都是PSD，因此广泛适用。我们通过制定基于高斯过程的策略（我们的系列内核）来证明这一点，以便在给予训练集时对测试系列进行预测。我们通过在多个数据集上估算其泛化误差并将其与相关基线进行比较来实验验证该策略。我们还证明，我们的系列内核可用于更传统的时间序列分类环境，在这种情况下，其性能与替代方法广泛一致。
Time series are an interesting frontier for kernel-based methods, for the simple reason that there is no kernel designed to represent them and their unique characteristics in full generality. Existing sequential kernels ignore the time indices, with many assuming that the series must be regularly-spaced; some such kernels are not even psd. In this manuscript, we show that a "series kernel" that is general enough to represent irregularly-spaced multivariate time series may be built out of well-known "vector kernels". We also show that all series kernels constructed using our methodology are psd, and are thus widely applicable. We demonstrate this point by formulating a Gaussian process-based strategy - with our series kernel at its heart - to make predictions about test series when given a training set. We validate the strategy experimentally by estimating its generalisation error on multiple datasets and comparing it to relevant baselines. We also demonstrate that our series kernel may be used for the more traditional setting of time series classification, where its performance is broadly in line with alternative methods.
