Graph Dirichlet Energy for Fitting-Free Bivariate Causal Inference
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. The score is the Dirichlet energy of this signal, induced by the unnormalized graph Laplacian. The reverse score swaps the variables, and the lower-energy direction is inferred as causal. The method requires neither regression fitting nor independence testing. After the empirical probability integral transform, its decisions are invariant under strictly monotone transformations of either variable, and the graph operations reduce to convolution...
| Authors | Povilas Daniušis |
|---|---|
| Primary category | cs.LG |
| Published | 15 October 2026 |
| Last updated at source | 15 October 2026 |
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