Sequential Gaussian Processes for Online Learning of Nonstationary Functions

• URL: http://arxiv.org/abs/1905.10003v5
• Date: Sat, 6 May 2023 11:30:13 GMT
• Title: Sequential Gaussian Processes for Online Learning of Nonstationary Functions
• Authors: Michael Minyi Zhang, Bianca Dumitrascu, Sinead A. Williamson, Barbara E. Engelhardt
• Abstract summary: 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.
• Score: 9.997259201098602
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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