In this paper, we propose novel Gaussian process-gated hierarchical mixtures of experts (GPHMEs) that are used for building gates and experts. Unlike in other mixtures of experts where the gating models are linear to the input, the gating functions of our model are inner nodes built with Gaussian processes based on random features that are non-linear and non-parametric. Further, the experts are also built with Gaussian processes and provide predictions that depend on test data. The optimization of the GPHMEs is carried out by variational inference. There are several advantages of the proposed GPHMEs. One is that they outperform tree-based HME benchmarks that partition the data in the input space. Another advantage is that they achieve good performance with reduced complexity. A third advantage of the GPHMEs is that they provide interpretability of deep Gaussian processes and more generally of deep Bayesian neural networks. Our GPHMEs demonstrate excellent performance for large-scale data sets even with quite modest sizes.

We consider the problem of sequential estimation of the unknowns of state-space and deep state-space models that include estimation of functions and latent processes of the models. The proposed approach relies on Gaussian and deep Gaussian processes that are implemented via random feature-based Gaussian processes. With this model, we have two sets of unknowns, highly nonlinear unknowns (the values of the latent processes) and conditionally linear unknowns (the constant parameters of the random feature-based Gaussian processes). We present a method based on particle filtering where the constant parameters of the random feature-based Gaussian processes are integrated out in obtaining the predictive density of the states and do not need particles. We also propose an ensemble version of the method, with each member of the ensemble having its own set of features. With several experiments, we show that the method can track the latent processes up to a scale and rotation.

The coronavirus disease (COVID-19) has rapidly spread throughout the world and while pregnant women present the same adverse outcome rates, they are underrepresented in clinical research. We collected clinical data of 155 test-positive COVID-19 pregnant women at Stony Brook University Hospital. Many of these collected data are of multivariate categorical type, where the number of possible outcomes grows exponentially as the dimension of data increases. We modeled the data within the unsupervised Bayesian framework and mapped them into a lower-dimensional space using latent Gaussian processes. The latent features in the lower dimensional space were further used for predicting if a pregnant woman would be admitted to a hospital due to COVID-19 or would remain with mild symptoms. We compared the prediction accuracy with the dummy/one-hot encoding of categorical data and found that the latent Gaussian process had better accuracy.