Autoregressive Kernels For Time Series
Autoregressive Kernels For Time Series
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发表时间：
2011-01
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通讯作者：
Marco Cuturi;A. Doucet
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作者：
Marco Cuturi;A. Doucet
我们在这项工作中提出了一个用于可变长度时间序列的新内核系列。我们的工作建立在多元随机过程的向量自回归（VAR）模型的基础上：给定一个多元时间序列x，我们将VAR模型中不同参数θ的似然函数p_{\theta}(x)视为描述x的特征。为了比较两个时间序列 x 和 x'，我们形成它们的特征 p_{\theta}(x) p_{\theta}(x') 的乘积，它是使用矩阵正态逆 Wishart 先验对 w.r.t \theta 进行积分的。除其他属性外，当时间序列的维度 d 远大于所考虑的时间序列 x 和 x' 的长度时，可以轻松计算该内核。它也可以推广到在任意状态空间中取值的时间序列，只要状态空间本身具有核 kappa 即可。在这种情况下，x 和 x' 之间的核是由 kappa 对 x 和 x' 中枚举的观测值和观测值子序列生成的 Gram 矩阵的函数。我们描述了这种概括的计算有效的实现，它使用低秩矩阵分解技术。使用支持向量机执行的一组基准分类任务将这些内核与其他已知内核进行比较。
We propose in this work a new family of kernels for variable-length time series. Our work builds upon the vector autoregressive (VAR) model for multivariate stochastic processes: given a multivariate time series x, we consider the likelihood function p_{\theta}(x) of different parameters \theta in the VAR model as features to describe x. To compare two time series x and x', we form the product of their features p_{\theta}(x) p_{\theta}(x') which is integrated out w.r.t \theta using a matrix normal-inverse Wishart prior. Among other properties, this kernel can be easily computed when the dimension d of the time series is much larger than the lengths of the considered time series x and x'. It can also be generalized to time series taking values in arbitrary state spaces, as long as the state space itself is endowed with a kernel \kappa. In that case, the kernel between x and x' is a a function of the Gram matrices produced by \kappa on observations and subsequences of observations enumerated in x and x'. We describe a computationally efficient implementation of this generalization that uses low-rank matrix factorization techniques. These kernels are compared to other known kernels using a set of benchmark classification tasks carried out with support vector machines.