Chained Gaussian Processes
Chained Gaussian Processes
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发表时间：
2016-04
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通讯作者：
Alan D. Saul;J. Hensman;Aki Vehtari;Neil D. Lawrence
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作者：
Alan D. Saul;J. Hensman;Aki Vehtari;Neil D. Lawrence
高斯过程模型是灵活的贝叶斯非参数回归方法。多变量高斯的性质意味着它们可以以加法模型的方式线性组合，并通过链接函数(如在广义线性模型中)来处理非高斯数据。然而，链接函数的形式是受限的，链接函数始终是可逆的，并且必须将感兴趣的参数转换为底层过程的线性组合。在许多可能性和模型中，非线性组合更合适。我们称这些更一般的模型为链式高斯过程：GP到似然参数的变换通常不是可逆的，这意味着只有在有多个(局部)链接，即链的情况下，线性化才是可能的。我们给出了一个链式GP的近似推理过程，该过程可伸缩，适用于任何因式分解的似然。我们证明了在一系列似然函数上的逼近。
Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to a linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models Chained Gaussian Processes: the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e. a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.