An Active Learning Methodology for Efficient Estimation of Expensive Noisy Black-Box Functions Using Gaussian Process Regression

Estimation of black-box functions often requires evaluating an extensive number of expensive noisy points. Learning algorithms can actively compare the similarity between the evaluated and unevaluated points to determine the most informative subsequent points for efficient estimation of expensive functions in a sequential procedure. In this paper, we propose an active learning methodology based on the integration of Laplacian regularization and active learning - Cohn (ALC) measure for identification of the most informative points for efficient estimation of noisy black-box functions using Gaussian processes. We propose two simple greedy search algorithms for sequential optimization of the tuning parameters and determination of subsequent points based on the information from the previously evaluated points. We also enhance the graph Laplacian with the information of both the predictor and response variables to capture the similarity between the points more effectively. The proposed methodology is particularly suited for problems involving estimation of expensive black-box functions with a high level of noise and plenty of unevaluated points. Using a case study for analysis of the kinematics of pitching in baseball as well as simulation experiments, we demonstrate the performance of the proposed methodology against existing methods in the literature in terms of estimation error.