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Basic implementation with GPy of an Automatic Bayesian Covariance Discovery (ABCD) system

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Basic implementation with GPy of an Automatic Bayesian Covariance Discovery (ABCD) system

(as in Lloyd, James Robert; Duvenaud, David Kristjanson; Grosse, Roger Baker; Tenenbaum, Joshua B.; Ghahramani, Zoubin (2014): Automatic construction and natural-language description of nonparametric regression models. In: National Conference on Artificial Intelligence, 7/27/2014, pp. 1242-1250. Available online at


import numpy as np
import GPy_ABCD

if __name__ == '__main__':
    X = np.linspace(-10, 10, 101)[:, None]
    Y = np.cos( (X - 5) / 2 )**2 * X * 2 + np.random.randn(101, 1)

    best_mods, all_mods, all_exprs = GPy_ABCD.find_best_model(X, Y,
        start_kernels = standard_start_kernels, p_rules = production_rules_all,
        restarts = 5, utility_function = 'BIC', rounds = 2, buffer = 3,
        dynamic_buffer = True, verbose = False, parallel = True)

    # Typical full output printout

    for mod_depth in all_mods: print(', '.join([str(mod.kernel_expression) for mod in mod_depth]) + f'\n{len(mod_depth)}')

    from matplotlib import pyplot as plt
    for bm in best_mods[:3]:

    predict_X = np.linspace(10, 15, 50)[:, None]
    preds = best_mods[0].predict(predict_X)

Note: if the parallel argument is True then the function should be called from within a if __name__ == '__main__':


pip install GPy_ABCD


Python 3.7

See requirements.txt

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