Spectral Regularized Kernel Goodness-of-Fit Tests

Understand

Maximum mean discrepancy (MMD) has enjoyed a lot of success in many machine learning and statistical applications, including non-parametric hypothesis testing, because of its ability to handle non-Euclidean data.

• Recently, it has been demonstrated in Balasubramanian et al.(2021) that the goodness-of-fit test based on MMD is not minimax optimal while a Tikhonov regularized version of it is, for an appropriate choice of the regularization parameter.
• However, the results in Balasubramanian et al.
• (2021) are obtained under the restrictive assumptions of the mean element being zero, and the uniform boundedness condition on the eigenfunctions of the integral operator.