Learning GPLVM with arbitrary kernels using the unscented transformation
This work addresses a computational limitation for researchers and practitioners using GPLVM in machine learning, offering a more efficient deterministic method for variational inference with arbitrary kernels.
The authors tackled the computational bottleneck in Gaussian Process Latent Variable Models (GPLVM) caused by exponential complexity in quadrature methods for arbitrary kernels, proposing the unscented transformation as a solution that achieves comparable or better performance with linear scaling in dimension.
Gaussian Process Latent Variable Model (GPLVM) is a flexible framework to handle uncertain inputs in Gaussian Processes (GPs) and incorporate GPs as components of larger graphical models. Nonetheless, the standard GPLVM variational inference approach is tractable only for a narrow family of kernel functions. The most popular implementations of GPLVM circumvent this limitation using quadrature methods, which may become a computational bottleneck even for relatively low dimensions. For instance, the widely employed Gauss-Hermite quadrature has exponential complexity on the number of dimensions. In this work, we propose using the unscented transformation instead. Overall, this method presents comparable, if not better, performance than offthe-shelf solutions to GPLVM and its computational complexity scales only linearly on dimension. In contrast to Monte Carlo methods, our approach is deterministic and works well with quasi-Newton methods, such as the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. We illustrate the applicability of our method with experiments on dimensionality reduction and multistep-ahead prediction with uncertainty propagation.