Fast Computation of Gaussian Processes Augmented by Synthetic Simulator Data
Keywords: Gaussian processes, simulator, marginal likelihood, model selection
TL;DR: When augmenting the training data of a Gaussian process using a simulator, this method rapidly calculates which data to add to the training set.
Abstract: When the amount of training data is limited, augmenting it with generated data from a simulator can be a beneficial approach to improving prediction accuracy. However, there are no clear metrics on which generated data should be added to the training set and in what proportion, especially when the predictive model is a Gaussian Processes (GPs) model. To address this, we propose using the log marginal likelihood as a guiding metric. The log marginal likelihood is a theoretically grounded criterion for model selection. However, computing this metric for GPs is computationally expensive. To overcome this challenge, we introduce a faster method for calculating the log marginal likelihood by considering the Cholesky factor and matrix element dependencies. Experimental results demonstrate that metrics utilizing the log likelihood outperform basic methods in mean squared error on test set.
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Submission Number: 9476
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