Infinite-Horizon Gaussian Processes
Infinite-Horizon Gaussian Processes
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发表时间：
2018-11
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通讯作者：
A. Solin;J. Hensman;Richard E. Turner
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作者：
A. Solin;J. Hensman;Richard E. Turner
高斯过程提供了一个灵活的框架，用于预测，消除噪声和解释长时间数据集。状态空间建模（卡尔曼滤波）使这些非参数模型能够通过将复杂性降低到数据点数量的线性来部署在长数据集上。在状态维m中，复杂度仍然是立方的，这是实际应用的障碍。在某些特殊情况下（高斯似然，规则间距），当数据很长时，GP后验将达到稳定的后验状态。我们利用这一点，并制定了一个推断方案，一般的可能性，推断是基于单扫描EP（假设密度过滤）的GP。无限时域模型处理状态维度中的立方成本，并将状态维度m中的成本降低到每个数据点O（m^2）。该模型被扩展到超参数的在线学习。我们展示了大型有限长度建模问题的示例，并介绍了该方法如何在智能手机上实时运行以100 Hz更新的连续数据流。
Gaussian processes provide a flexible framework for forecasting, removing noise, and interpreting long temporal datasets. State space modelling (Kalman filtering) enables these non-parametric models to be deployed on long datasets by reducing the complexity to linear in the number of data points. The complexity is still cubic in the state dimension m which is an impediment to practical application. In certain special cases (Gaussian likelihood, regular spacing) the GP posterior will reach a steady posterior state when the data are very long. We leverage this and formulate an inference scheme for GPs with general likelihoods, where inference is based on single-sweep EP (assumed density filtering). The infinite-horizon model tackles the cubic cost in the state dimensionality and reduces the cost in the state dimension m to O(m^2) per data point. The model is extended to online-learning of hyperparameters. We show examples for large finite-length modelling problems, and present how the method runs in real-time on a smartphone on a continuous data stream updated at 100 Hz.