Kernel discrepancy estimation minimax lower bound proven to be $n^{-1/2}$

Researchers have established that the minimax lower bound for estimating kernel discrepancies, including MMD, HSIC, and KSD, is $n^{-1/2}$ on general topological spaces. This rate is achieved under mild kernel assumptions and confirms the parametric rate's optimality beyond finite-dimensional Euclidean settings with unbounded kernels. The findings also extend to the estimation of the mean embedding and centered cross-covariance operator, settling questions about optimal estimation for these kernel discrepancies. AI

IMPACT Establishes theoretical optimality for key distribution comparison methods used in machine learning.

RANK_REASON Academic paper published on arXiv detailing theoretical findings in machine learning. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv stat.ML →

• arXiv
• Jose Cribeiro-Ramallo

• paper
• other

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