Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects

arXiv:2607.28981 · stat.ME, econ.EM, math.ST, stat.AP, stat.ML · Submitted 2026-07-31 · Read on arXiv

Wenxi Tan, Bing Li, Lingzhou Xue

stat.ME, econ.EM, math.ST, stat.AP, stat.ML

Submitted: 2026-07-31

Comments: 32 pages, 4 figures

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

Terminology

• Conditional Independence — 62× in this paper · explained in 2 episodes
• Hilbert Space — 24× in this paper · explained in 2 episodes
• Consistency — 15× in this paper · explained in 3 episodes
• Distance Profile Embedding — 13× in this paper
• Composition — 8× in this paper · explained in 2 episodes
• Embeddings — 8× in this paper · explained in 2 episodes
• Central Limit Theorem — 5× in this paper
• Causal Discovery — 3× in this paper · explained in 3 episodes
• Profile Association — 3× in this paper
• Regularization — 3× in this paper · explained in 3 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Unified Framework — 3× in this paper · explained in 6 episodes
• Asymptotic Normality — 2× in this paper · explained in 2 episodes
• Benchmark — 2× in this paper · explained in 2 episodes
• WHO Sexual and Reproductive Health and Research — 2× in this paper
• Abundance — 1× in this paper · explained in 1 episode
• Copula — 1× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Dimensionality Reduction — 1× in this paper · explained in 2 episodes
• Generalizability — 1× in this paper · explained in 6 episodes
• Hilbert-Schmidt Independence Criterion — 1× in this paper
• Inflation — 1× in this paper · explained in 2 episodes
• Kernel Conditional Independence — 1× in this paper
• Latent Variables — 1× in this paper · explained in 2 episodes
• Structural Constraints — 1× in this paper · explained in 2 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes
• Universality — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes
• Wasserstein Distance — 1× in this paper · explained in 6 episodes
• World Health Organization — 1× in this paper

Sources

• Doubly robust estimation of causal effects for random object outcomes with continuous treatments
• A Reproducing-Kernel-Based Nonparametric Test for Conditional Independence of Functional Data

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