Graph Dirichlet Energy for Fitting-Free Bivariate Causal Inference

Key points

• For a candidate direction $X\to Y$, we construct a kernel similarity graph from $X$ and treat $Y$ as a graph signal.1
• The score is the Dirichlet energy of this signal, induced by the unnormalized graph Laplacian.1
• After the empirical probability integral transform, its decisions are invariant under strictly monotone transformations of either variable, and the graph operations reduce to convolutions, allowing exact evaluation in $O(n\log n)$ time and $O(n)$ memory.1
• Empirically, we compare GDECI with QCCD, GRCI, CAM, IGCI (two variants), RESIT, LOCI, QPE-k, and RECI (two variants), in accuracy on 1899 cause--effect pairs and in inference speed.1

Sources (1)

• [1]Graph Dirichlet Energy for Fitting-Free Bivariate Causal Inference
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 15, 01:51 PM

  We propose the Graph Dirichlet Energy Causal Inference (GDECI) criterion for distinguishing cause from effect in bivariate settings.

  For a candidate direction $X\to Y$, we construct a kernel similarity graph from $X$ and treat $Y$ as a graph signal.

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