Finite-Sample Unbiased Variance of MMD under Unbalanced Sampling: Exact Estimation and Quasi-Linear Computation

arXiv:2601.13874 · stat.ML, cs.LG · Submitted 2026-01-20 · Read on arXiv

stat.ML, cs.LG

Submitted: 2026-01-20

Updated: 2026-09-16

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Maximum Mean Discrepancy — 12× in this paper
• Accuracy — 5× in this paper · explained in 1 episode
• Distribution Shift — 5× in this paper · explained in 5 episodes
• Consistency — 3× in this paper · explained in 3 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Adam — 2× in this paper · explained in 2 episodes
• Adaptation — 2× in this paper · explained in 1 episode
• Benchmark — 2× in this paper · explained in 2 episodes
• Calibration — 2× in this paper · explained in 7 episodes
• Domain Adaptation — 2× in this paper · explained in 5 episodes
• Robustness — 2× in this paper · explained in 5 episodes
• Alignment — 1× in this paper · explained in 1 episode
• Bayesian Inference — 1× in this paper · explained in 5 episodes
• Core — 1× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Models — 1× in this paper · explained in 2 episodes
• Influence Functions — 1× in this paper · explained in 2 episodes
• Minimax optimality — 1× in this paper · explained in 2 episodes
• Reproducing Kernel Hilbert Space (RKHS) — 1× in this paper · explained in 3 episodes
• Systematic Bias — 1× in this paper · explained in 3 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy
• Unbiased estimators for the variance of MMD estimators
• Maximum Mean Discrepancy with Unequal Sample Sizes via Generalized U-Statistics
• TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems

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