Structured Bayesian Gaussian process latent variable model
This work addresses computational challenges in modeling spatially correlated data for applications like image and video processing, though it appears incremental as it builds on existing Bayesian GP-LVM frameworks.
The authors tackled the problem of modeling high-dimensional data with spatial correlations by introducing a structured Bayesian Gaussian process latent variable model that uses parameterized spatial kernels and structure-exploiting algebra for computational tractability, achieving efficient inference through collapsed variational bounds and demonstrating applications in image and video data imputation.
We introduce a Bayesian Gaussian process latent variable model that explicitly captures spatial correlations in data using a parameterized spatial kernel and leveraging structure-exploiting algebra on the model covariance matrices for computational tractability. Inference is made tractable through a collapsed variational bound with similar computational complexity to that of the traditional Bayesian GP-LVM. Inference over partially-observed test cases is achieved by optimizing a "partially-collapsed" bound. Modeling high-dimensional time series systems is enabled through use of a dynamical GP latent variable prior. Examples imputing missing data on images and super-resolution imputation of missing video frames demonstrate the model.