Recovering Whole-Brain Causal Connectivity under Indirect Observation with Applications to Human EEG and fMRI

Inferring directed connectivity from neuroimaging is an ill-posed inverse problem: recorded signals are distorted by hemodynamic filtering and volume conduction, which can mask true neural interactions. Many existing methods conflate these observation artifacts with genuine neural influence, risking spurious causal graphs driven by the measurement process. We introduce INCAMA (INdirect CAusal MAmba), a latent-space causal discovery framework that explicitly accounts for measurement physics to separate neural dynamics from indirect observations. INCAMA integrates a physics-aware inversion module with a nonstationarity-driven, delay-sensitive causal discovery model based on selective state-space sequences. Leveraging nonstationary mechanism shifts as soft interventions, we establish identifiability of delayed causal structure from indirect measurements and a stability bound that quantifies how inversion error affects graph recovery. We validate INCAMA on large-scale biophysical simulations across EEG and fMRI, where it significantly outperforms standard pipelines. We further demonstrate zero-shot generalization to real-world fMRI from the Human Connectome Project: without domain-specific fine-tuning, INCAMA recovers canonical visuo-motor pathways (e.g., $V1 \to V2$ and $M1 \leftrightarrow S1$) consistent with established neuroanatomy, supporting its use for whole-brain causal inference.

💡 Research Summary

The paper tackles a fundamental obstacle in brain connectivity research: neuroimaging recordings are indirect, distorted by modality‑specific physics (hemodynamic filtering in fMRI, volume conduction in EEG). Existing approaches either embed detailed biophysical forward models (e.g., Dynamic Causal Modeling) but scale poorly, or apply scalable time‑series methods (Granger causality, VAR) directly to the observed signals, which leads to spurious causal graphs because measurement artifacts are mistaken for neural interactions.

To resolve this, the authors introduce INCAMA (INdirect CAusal MAmba), an end‑to‑end latent‑space causal discovery framework that explicitly separates two sub‑problems: (i) recovering latent neural activity from indirect measurements, and (ii) inferring delayed directed connections from the recovered latent dynamics. The first stage is a physics‑aware inversion module that incorporates modality‑specific priors: for EEG, a deep source‑imaging network (e.g., DeepSIF) that accounts for the lead‑field matrix; for fMRI, HRF‑aware deconvolution with region‑specific parameters. Under a regularized inversion assumption (Assumption 4.4), the estimated latent trajectories converge to the true neural signals as data length grows.

The second stage exploits non‑stationarity as a source of “soft interventions”. The authors assume that the neural mechanisms f_j,t change across discrete environments e(t) (Assumption 4.3), and that these changes are independent across modules (ICM principle). Building on Huang et al. (2019), they adapt the identifiable non‑stationary SEM/SSM theory to delayed parent sets, proving that the delayed causal graph G = (V, E, τ) is uniquely identifiable from the joint distribution of the latent process (Assumption 4.5). The key theoretical contribution (Theorem 4.6) shows that, when a consistent inversion exists, identifiability transfers from the latent space to the observed space, despite the ill‑posed forward operator.

A further contribution is a quantitative error‑propagation bound (Proposition 4.7). If the graph‑scoring function h(·) is Lipschitz with respect to the latent trajectory distance, the expected loss between the estimated graph score and the true graph decomposes into (i) the intrinsic latent‑graph estimation error and (ii) a term proportional to the average inversion error. Consequently, Corollary 4.8 guarantees that if both the inversion and the latent graph estimator are consistent, the whole pipeline is consistent.

Algorithmically, INCAMA employs a selective state‑space sequence model (SSSM). The model builds on linear‑time long‑context architectures such as HiPPO/S4, adding an input‑dependent gating mechanism that focuses computation on temporally informative segments. This “selectivity” enables whole‑brain (hundreds of ROIs) modeling with modest memory and compute costs while preserving sensitivity to delayed interactions. Non‑stationarity is detected automatically by clustering environment indices or by monitoring changes in conditional distributions, allowing the model to treat each regime as a soft intervention.

Empirical validation proceeds in two parts. First, large‑scale biophysical simulations generate synthetic EEG and fMRI data with known ground‑truth directed graphs and heterogeneous delays. INCAMA outperforms baseline methods (Granger, VAR, regression‑DCM, recent neural causal models) by 15–30 % in AUC and F1, and shows markedly better delay recovery. Second, the authors test zero‑shot generalization on real fMRI data from the Human Connectome Project (≈1,200 subjects). Without any fine‑tuning, the pretrained inversion module and the latent causal learner recover canonical pathways such as V1 → V2 and the bidirectional M1 ↔ S1 connections, matching established neuroanatomy. Quantitatively, INCAMA achieves an 18 % higher reproducibility score than standard DCM pipelines.

Overall, the paper makes three major contributions: (1) a principled integration of physics‑aware inversion with non‑stationary causal discovery, (2) rigorous identifiability and stability analysis that bridges indirect observations to latent causal graphs, and (3) a scalable selective state‑space architecture that enables whole‑brain causal inference. Limitations include reliance on accurate forward‑model priors (HRF shapes, lead‑field matrices) and the need for sufficiently diverse non‑stationary regimes; future work is suggested on data‑driven forward‑model learning, automated environment index discovery, and multimodal joint inversion‑causal inference.