Latent Confounded Causal Discovery via Lie Bracket Geometry

arXiv:2606.19610v2 Announce Type: replace-cross Abstract: We study causal discovery from observational and interventional regimes when latent variables may affect the measured system. Our first algorithm, BRIDGE (Bracket Residuals for Interventional Discovery and Geometric Estimation), combines a density-ratio or transport engine with a high-recall geometric screen and passes the retained arrows to a score-based or differentiable discovery method. The main formulation and experiments use known single-node intervention targets; in that regime the screen is designed to retain candidate directed effects, while a downstream learner determines the final graph or equivalence-class representation. Our second algorithm, Spectral Kernel Flow Matching (SKFM), amortizes the response fields, summarizes residual nonclosure by a spectral visible-footprint subspace, and applies an order-dependent graph extractor. Direct extraction succeeds on calibrated chains and selected motifs, but is unstable on harder random DAGs when the order must be learned. On ten-node nonlinear random DAGs, the more reliable hybrid role of the geometry is as a candidate generator: calibrated SKFM/Bridge fields followed by local BIC scoring achieve mean directed F_1simeq0.86. Sachs protein signaling provides a real-data stress test and supports a diagnostic, not fully identified, interpretation. The contribution is therefore a practical interventional screening pipeline, explicit guarantees for screen retention and residual-footprint rank under stated assumptions, and a falsifiable account of the boundary between geometric diagnostics and causal identification.

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Source: arXiv cs.AI | 2026-07-28