Unified Unbiased Variance Estimation for Maximum Mean Discrepancy: Robust Finite-Sample Performance with Imbalanced Data and Exact Acceleration under Null and Alternative Hypotheses
The maximum mean discrepancy (MMD) is a kernel-based nonparametric statistic for two-sample testing, whose inferential accuracy depends critically on variance characterization. Existing work provides various finite-sample estimators of the MMD variance, often differing under the null and alternative hypotheses and across balanced or imbalanced sampling schemes. In this paper, we study the variance of the MMD statistic through its U-statistic representation and Hoeffding decomposition, and establish a unified finite-sample characterization covering different hypotheses and sample configurations. Building on this analysis, we propose an exact acceleration method for the univariate case under the Laplacian kernel, which reduces the overall computational complexity from $\mathcal O(n^2)$ to $\mathcal O(n \log n)$.
Code (0)
등록된 구현이 없습니다.
Tasks
Two-sample testingSimilar Papers 제목 키워드 기반
A new adjusted maximum likelihood method for the Fay–Herriot small area model
In the context of the Fay–Herriot model, a mixed regression model routinely used to combine information from various sources in small area estimation, certain adjustments to a standard likelihood (e.g., profile, residu…
regressionOrder Matters: Improving Domain Adaptation by Reordering Data
Domain shift remains a key challenge in deploying machine learning models to the real world. Unsupervised domain adaptation (UDA) aims to address this by minimising domain discrepancy during training, but the discrepancy…
Unsupervised Domain AdaptationImage ClassificationEntropy Regularization for Population Estimation
Entropy regularization is known to improve exploration in sequential decision-making problems. We show that this same mechanism can also lead to nearly unbiased and lower-variance estimates of the mean reward in the opti…
Decision MakingSequential Decision MakingBarankin-Type Bound for Constrained Parameter Estimation
In constrained parameter estimation, the classical constrained Cramer-Rao bound (CCRB) and the recent Lehmann-unbiased CCRB (LU-CCRB) are lower bounds on the performance of mean-unbiased and Lehmann-unbiased estimators, …
Direction of Arrival Estimationparameter estimationVocal Bursts Type PredictionA Biased Estimator for MinMax Sampling and Distributed Aggregation
MinMax sampling is a technique for downsampling a real-valued vector which minimizes the maximum variance over all vector components. This approach is useful for reducing the amount of data that must be sent over a const…