Spectral Regularized Kernel Goodness-of-Fit Tests. (arXiv:2308.04561v1 [math.ST])

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 …

applications arxiv data hypothesis kernel machine machine learning math mean minimax non-euclidean non-parametric parametric statistical success test testing tests