Sequential Gaussian Processes for Online Learning of Nonstationary Functions
This work addresses the challenge of online learning for nonstationary functions, which is incremental as it builds on existing GP methods to handle real-time data with improved efficiency.
The paper tackled the problem of estimating nonstationary functions in real-time using Gaussian processes, which suffer from scalability, sequential updating, and stationarity constraints, by proposing a sequential Monte Carlo algorithm for infinite mixtures of GPs that improves performance over state-of-the-art methods in online GP estimation for non-stationary time-series data.
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: 1) Conventional GP inference scales $O(N^{3})$ with respect to the number of observations; 2) Updating a GP model sequentially is not trivial; and 3) Covariance kernels typically 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 a sequential Monte Carlo algorithm to fit infinite mixtures of GPs that capture non-stationary behavior while allowing for online, distributed inference. Our approach empirically improves performance over state-of-the-art methods for online GP estimation in the presence of non-stationarity in time-series data. To demonstrate the utility of our proposed online Gaussian process mixture-of-experts approach in applied settings, we show that we can sucessfully implement an optimization algorithm using online Gaussian process bandits.