Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD

arXiv:2607.24235 · stat.ML, cs.LG, math.ST · Submitted 2026-07-27 · Read on arXiv

Jose Cribeiro-Ramallo, Florian Kalinke, Zoltán Szabó

stat.ML, cs.LG, math.ST

Submitted: 2026-07-27

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

Terminology

• Hilbert Space — 14× in this paper · explained in 2 episodes
• In International Conference on Machine Learning — 14× in this paper
• Embeddings — 7× in this paper · explained in 2 episodes
• Homogeneity — 7× in this paper · explained in 2 episodes
• Gradient Flow — 3× in this paper · explained in 2 episodes
• Alignment — 2× in this paper · explained in 1 episode
• Clustering — 2× in this paper · explained in 2 episodes
• Copula — 2× in this paper · explained in 2 episodes
• Core — 2× in this paper · explained in 2 episodes
• In Algorithmic Learning Theory — 2× in this paper
• In International Conference on Learning Representations — 2× in this paper
• Minimax optimality — 2× in this paper · explained in 2 episodes
• Quantization — 2× in this paper · explained in 12 episodes
• Self-Supervised Learning — 2× in this paper · explained in 8 episodes
• Uncertainty in Artificial Intelligence — 2× in this paper
• World Model — 2× in this paper · explained in 7 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Additivity — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• Causal Discovery — 1× in this paper · explained in 2 episodes
• Causal Inference — 1× in this paper · explained in 4 episodes
• Computational Tractability — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Explainability — 1× in this paper · explained in 3 episodes
• Feature Selection — 1× in this paper · explained in 4 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Modeling — 1× in this paper · explained in 3 episodes
• Generative Models — 1× in this paper · explained in 2 episodes
• Representation Learning — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Keep it Tighter -- A Story on Analytical Mean Embeddings
• Minimax Estimation of Kernel Stein Discrepancy: Trace versus Hilbert-Schmidt Scales
• Nystr\"om Kernel Stein Discrepancy Tests
• KerJEPA: Kernel Discrepancies for Euclidean Self-Supervised Learning

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