Gaussian Process Latent Variable Models (GPLVMs) have become increasingly popular for unsupervised tasks such as dimensionality reduction and missing data recovery due to their flexibility and non-linear nature. An importance-weighted version of the Bayesian GPLVMs has been proposed to obtain a tighter variational bound. However, this version of the approach is primarily limited to analyzing simple data structures, as the generation of an effective proposal distribution can become quite challenging in high-dimensional spaces or with complex data sets. In this work, we propose an Annealed Importance Sampling (AIS) approach to address these issues. By transforming the posterior into a sequence of intermediate distributions using annealing, we combine the strengths of Sequential Monte Carlo samplers and VI to explore a wider range of posterior distributions and gradually approach the target distribution. We further propose an efficient algorithm by reparameterizing all variables in the evidence lower bound (ELBO). Experimental results on both toy and image datasets demonstrate that our method outperforms state-of-the-art methods in terms of tighter variational bounds, higher log-likelihoods, and more robust convergence.

该研究针对高维空间或复杂数据集中生成有效提议分布的挑战，提出了一种退火重要性采样方法，以改进高斯过程潜变量模型的变分推断。通过将后验变换为一系列中间分布，该方法结合了序列蒙特卡洛采样器和变分推断的优势，从而提升了变分界限的紧致性和模型的收敛性。实验结果显示，所提方法在多个数据集上优于现有最先进技术。

通过随机梯度退火重要性采样的高斯过程潜变量模型变分学习