Variational Learning of Gaussian Process Latent Variable Models through Stochastic Gradient Annealed Importance Sampling
This work addresses a bottleneck in unsupervised learning tasks like dimensionality reduction for researchers and practitioners using GPLVMs, representing an incremental improvement over existing methods.
The paper tackles the challenge of generating effective proposal distributions for importance-weighted Bayesian Gaussian Process Latent Variable Models in high-dimensional or complex data by proposing an Annealed Importance Sampling approach combined with variational inference, which experimentally outperforms state-of-the-art methods with tighter variational bounds and higher log-likelihoods.
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.