New Causal Inference Method Using Interventional Score Geometry

A recent study published on arXiv (2607.21914) presents a novel interventional method for causal inference utilizing score geometry. The author contends that observational score fields, which are based on joint densities, fail to indicate causal direction since structural models with the same observational distributions exhibit identical geometries. To tackle this issue, the paper introduces an interventional counterpart: a hard intervention do(X_k = ξ) confines the distribution to the submanifold where x_k = ξ, with its score determined by the remaining d-1 free coordinates. Causal influence X_k → X_j is characterized by the variation in the interventional marginal distribution of X_j concerning ξ, and the derivative of this marginal interventional score offers a local sufficient condition for influence. Additionally, the paper highlights that projecting the observational score onto permissible intervention directions does not typically yield the causal response, as two models may have identical projected scores.