Explaining hidden mechanisms: a generative model for causal graphs with nonlinear latent factors.

Biomedical data analysis can now recover large families of condition-specific causal graphs, yet these results are often too complex for humans to interpret mechanistically. To address this challenge, we adopt a generative perspective, we address this challenge by formulating a structural-equation-based generative model in which each observed graph is generated from a small number of latent causal mechanisms under a bidirectional causal-consistency constraint linking latent and observed causal effects. Building on this formulation, we propose Truncated Reconstruction based Interpretable Prediction (TRIP), an inference method that estimates shared latent mechanisms from observed causal graphs and condition indicators in a way that preserves interpretability across abstraction levels by learning an orthonormal projection and jointly optimizing a prediction loss and a graph-reconstruction loss. TRIP can be viewed as a supervised low-dimensional projection of graph families that makes latent mechanisms directly interpretable in terms of observed causal effects, while preserving both structural and predictive information. We validate the method on synthetic benchmarks, including a spiral-in-noise stress test, and on EMT-related gene regulatory networks derived from cancer cell-line gene expression data. Across these experiments, TRIP recovers nonlinear latent mechanisms, improves predictive performance, and organizes large condition-specific networks into interpretable mechanistic axes that can be inspected, compared, and used for hypothesis generation.