Many machine learning problems can be framed in the context of estimating
functions, and often these are time-dependent functions that are estimated in
real-time as observations arrive. Gaussian processes (GPs) are an attractive
choice for modeling real-valued nonlinear functions due to their flexibility
and uncertainty quantification. However, the typical GP regression model
suffers from several drawbacks: i) Conventional GP inference scales O(N3)
with respect to the number of observations; ii) updating a GP model
sequentially is not trivial; and iii) covariance kernels often enforce
stationarity constraints on the function, while GPs with non-stationary
covariance kernels are often intractable to use in practice. To overcome these
issues, we propose an online sequential Monte Carlo algorithm to fit mixtures
of GPs that capture non-stationary behavior while allowing for fast,
distributed inference. By formulating hyperparameter optimization as a
multi-armed bandit problem, we accelerate mixing for real time inference. Our
approach empirically improves performance over state-of-the-art methods for
online GP estimation in the context of prediction for simulated non-stationary
data and hospital time series data