maximum_mean_discrepancy#

bayesflow.metrics.functional.maximum_mean_discrepancy(x: Tensor, y: Tensor, kernel: str = 'inverse_multiquadratic', unbiased: bool = False, **kwargs) → Tensor[source]#

Computes a mixture of Gaussian radial basis functions (RBFs) between the samples of x and y.

See the original paper below for details and different estimators:

Gretton, A., Borgwardt, K. M., Rasch, M. J., Schölkopf, B., & Smola, A. (2012). A kernel two-sample test. The Journal of Machine Learning Research, 13(1), 723-773. https://jmlr.csail.mit.edu/papers/v13/gretton12a.html

Parameters:

xTensor of shape (num_draws_x, num_features): Comprises num_draws_x Random draws from the “source” distribution P.
yTensor of shape (num_draws_y, num_features): Comprises num_draws_y Random draws from the “source” distribution Q.
kernelstr, optional (default - “inverse_multiquadratic”): The (mixture of) kernels to be used for the MMD computation.
unbiasedbool, optional (default - False): Whether to use the unbiased MMD estimator. Default is False.

Returns:

mmdTensor of shape (1, ): The biased or unbiased empirical maximum mean discrepancy (MMD) estimator.