Abstract
The current work introduces a novel combination of two Bayesian tools, Gaussian Processes (GPs) and the use of the Approximate Bayesian Computation (ABC) algorithm for kernel selection and parameter estimation for machine learning applications. The combined methodology that this research paper proposes and investigates offers the possibility to use different metrics and summary statistics of the kernels used for Bayesian regression. The presented work moves a step towards online, robust, consistent and automated mechanism to formulate optimal kernels (or even mean functions) and their hyperparameters simultaneously offering confidence evaluation when these tools are used for mathematical or engineering problems such as structural health monitoring (SHM) or system identification (SI).
Highlights
AND MOTIVATIONRegression analysis or classification using Bayesian formulation and Gaussian Processes (GPs) or relevance vector machines (RVMs) is becoming very popular and attractive due to incorporation of uncertainty and the bypassing of unattractive features from methods like neural networks
Due to its simplicity and desirable computational performance, GP has been applied in numerous domains in structural health monitoring (Cross, 2012; Dervilis et al, 2016; Worden and Cross, 2018) and civil and structural engineering to construct surrogate models, which can mimic the real behavior of large-scale complex systems/structures and make predictions
The article starts out with an introduction to the GPs and approximate Bayesian computation based on Sequential Monte Carlo (ABC-SMC) algorithm and the selection of the different hyperparameters required for its implementation
Summary
Regression analysis or classification using Bayesian formulation and Gaussian Processes (GPs) or relevance vector machines (RVMs) is becoming very popular and attractive due to incorporation of uncertainty and the bypassing of unattractive features from methods like neural networks. Gaussian processes (GPs) are a stochastic non-parametric Bayesian approach to regression and classification problems. These Gaussian processes are computationally very efficient, and non-linear learning is relatively easy. The initial and basic step in order to apply Gaussian process regression is to obtain a mean and covariance function. These functions are specified separately, and consist of a specification of a functional form and a set of parameters called hyperparameters. The article starts out with an introduction to the GPs and approximate Bayesian computation based on Sequential Monte Carlo (ABC-SMC) algorithm and the selection of the different hyperparameters required for its implementation. The core of the algorithm is coming from Rasmussen and Williams (2006)
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