Proves sharp rates E_q(μ_N, ω) ≍ N^{-(1/2)(1 + q/β)} for empirical energy distance approximation under Ahlfors regularity of exponent β.
Borgwardt, Malte J
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Causality-encoded diffusion models use a known DAG to train graph-consistent conditional diffusions for observational recovery, interventional sampling via fixed-variable propagation, and a resampling-based directed edge test with convergence rates depending on local dimension.
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Sharp Rates of MMD Empirical Estimation with Power Kernels
Proves sharp rates E_q(μ_N, ω) ≍ N^{-(1/2)(1 + q/β)} for empirical energy distance approximation under Ahlfors regularity of exponent β.
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Causality-Encoded Diffusion Models for Interventional Sampling and Edge Inference
Causality-encoded diffusion models use a known DAG to train graph-consistent conditional diffusions for observational recovery, interventional sampling via fixed-variable propagation, and a resampling-based directed edge test with convergence rates depending on local dimension.