A Bayesian inference framework for supervised Gaussian process latent variable models is introduced. The framework overcomes the high correlations between latent variables and hyperparameters by collapsing the statistical model through approximate integration of the latent variables. Using an unbiased pseudo estimate for the marginal likelihood, the exact hyperparameter posterior can then be explored using collapsed Gibbs sampling and, conditional on these samples, the exact latent posterior can be explored through elliptical slice sampling. The framework is tested on both simulated and real examples. When compared with the standard approach based on variational inference, this approach leads to significant improvements in the predictive accuracy and quantification of uncertainty, as well as a deeper insight into the challenges of performing inference in this class of models.

介绍了一种用于监督高斯过程潜在变量模型的贝叶斯推理框架。该框架通过对潜在变量进行近似积分来折叠统计模型，从而克服了潜在变量与超参数之间的高度相关性。使用边际可能性的无偏伪估计，然后可以使用折叠的Gibbs采样来探索确切的超参数后验，并且在这些样本的条件下，可以通过椭圆切片采样来探索确切的潜在后验。该框架已在模拟和真实示例上进行了测试。与基于变分推论的标准方法相比，该方法可显着提高预测准确性和不确定性的量化，