We present the Streaming Gaussian Dirichlet Random Field (S-GDRF) model, a novel approach for modeling a stream of spatiotemporally distributed, sparse, high-dimensional categorical observations. The proposed approach efficiently learns global and local patterns in spatiotemporal data, allowing for fast inference and querying with a bounded time complexity. Using a high-resolution data series of plankton images classified with a neural network, we demonstrate the ability of the approach to make more accurate predictions compared to a Variational Gaussian Process (VGP), and to learn a predictive distribution of observations from streaming categorical data. S-GDRFs open the door to enabling efficient informative path planning over high-dimensional categorical observations, which until now has not been feasible.

We propose a generative model for the spatio-temporal distribution of high dimensional categorical observations. These are commonly produced by robots equipped with an imaging sensor such as a camera, paired with an image classifier, potentially producing observations over thousands of categories. The proposed approach combines the use of Dirichlet distributions to model sparse co-occurrence relations between the observed categories using a latent variable, and Gaussian processes to model the latent variable's spatio-temporal distribution. Experiments in this paper show that the resulting model is able to efficiently and accurately approximate the temporal distribution of high dimensional categorical measurements such as taxonomic observations of microscopic organisms in the ocean, even in unobserved (held out) locations, far from other samples. This work's primary motivation is to enable deployment of informative path planning techniques over high dimensional categorical fields, which until now have been limited to scalar or low dimensional vector observations.