Latent-Space Causal Discovery from Indirect Neuroimaging Observations

This paper introduces INCAMA, a physics-aware framework that combines latent-space inversion with a delay-aware Mamba encoder to recover directed neural causal structures from distorted neuroimaging signals, demonstrating superior performance over baselines in both simulations and real-world fMRI data.

The Gist

The Big Problem: The "Muddy Window"

Imagine you are trying to figure out who is talking to whom in a crowded room, but you can't see the people. You can only hear the sound coming through a thick, foggy, and distorted window.

• The People: These are the neurons in your brain.
• The Talking: This is the "causal influence" (one brain area telling another to do something).
• The Window: This is the brain scanner (fMRI or EEG).

The problem is that the window distorts the sound.

• fMRI (The Slow, Blurry Window): The scanner doesn't hear the neurons directly. It hears the blood flow response, which is like a slow echo that blurs the timing. If Person A speaks, the scanner might think Person B spoke first because the echo is delayed.
• EEG (The Mixed-Up Window): The scanner is on the scalp, so the sound from different people mixes together before it reaches the microphone. It's like hearing a choir where you can't tell which singer is which.

Because of this distortion, if you just look at the raw data, you might think two brain areas are connected when they aren't, or you might miss a connection that actually exists.

The Solution: INCAMA (The "Smart Translator")

The authors propose a new method called INCAMA. Think of it as a two-step translator that cleans up the signal before trying to figure out the conversation.

Step 1: The "Physics-Aware" Cleaner (Inversion)

Before trying to find connections, INCAMA first tries to "undo" the distortion of the window.

• For fMRI: It acts like a specialized de-blurring tool. It knows exactly how blood flow slows down brain signals (the HRF) and mathematically reverses that blur to guess what the original neural "spark" looked like.
• For EEG: It acts like a sound mixer that knows how the skull mixes signals. It tries to separate the mixed-up choir back into individual singers.

Crucial Point: The paper claims this step is "physics-aware." It doesn't just guess; it uses the known laws of physics (how blood flows, how electricity travels through the skull) to guide the cleaning process.

Step 2: The "Detective" (Latent Causal Discovery)

Once the signals are cleaned up (restored to their "latent" or hidden state), the second part of INCAMA acts as a detective.

• The Clue: The detective looks for changes. The paper argues that if the rules of the conversation change slightly over time (non-stationarity)—like if the volume goes up or down in a specific pattern—you can figure out who is leading the conversation.
• The Tool: It uses a modern AI architecture called Mamba (a type of "Selective State Space Model"). Imagine Mamba as a super-efficient librarian who can read a very long book (hours of brain data) and remember the most important details without getting overwhelmed. It looks for patterns where one brain area's activity predicts another's, specifically looking for delays (e.g., Area A changes, and 2 seconds later, Area B changes).

The Theory: Why It Works (The "Safety Net")

The authors didn't just build a tool; they wrote a math proof to explain when it works.

• The Guarantee: They proved that if you can clean the signal well enough (Step 1), and if the brain's activity changes in a way that provides clues (Step 2), you can mathematically guarantee that you can find the true connections.
• The Error Bound: They also proved that if your cleaning step isn't perfect (which it never is), the final answer won't be a total disaster. The error in the final answer is directly tied to how bad the cleaning was. It's a "graceful degradation"—if the window is a little muddy, the answer is a little fuzzy, but it doesn't collapse.

The Experiments: Did It Work?

The authors tested this in two ways:

1. The "Virtual Brain" (Simulations):

   • They created a fake brain on a computer where they knew the exact truth (who talked to whom).
   • They ran the simulation through the "muddy window" (adding realistic fMRI and EEG distortions).
   • Result: INCAMA found the connections 2 to 3 times better than existing methods. It was much more accurate at figuring out the true map of the brain.

2. The "Real World" Check (HCP Data):

   • They took real data from the Human Connectome Project (people doing a motor task, like moving their hands).
   • They did not retrain the model on this real data (Zero-shot). They just used the model trained on the fake brain.
   • Result: The model found connections that made sense biologically. For example, it correctly identified that the visual cortex (seeing) connects to the motor cortex (moving) during a hand-movement task. It didn't find random noise; it found the "highways" of the brain that scientists already know exist.

Summary of Claims

• What they built: A system that first cleans up distorted brain scan data using physics, then uses AI to find the direction of influence between brain regions.
• What they proved: Mathematically, this works if the cleaning is good and the brain activity changes over time.
• What they showed: It works better than current methods on simulated data and finds biologically sensible patterns in real human data without needing to be retrained.

What they do NOT claim:

• They do not claim this is ready for diagnosing individual patients.
• They do not claim they found the "absolute truth" of the human brain (since real human ground truth is impossible to know).
• They do not claim it works for subcortical (deep brain) structures, only the outer cortex (the "skin" of the brain).

In short, INCAMA is a new way to look through the "muddy window" of brain scans, clean the image using physics, and then use smart AI to map out who is talking to whom in the brain.

Technical Summary

Technical Summary: Latent-Space Causal Discovery from Indirect Neuroimaging Observations

Problem Statement

Neuroimaging modalities such as EEG and fMRI do not observe neural causal variables directly. Instead, they capture indirect signals distorted by modality-specific forward operators: EEG signals are spatially mixed via volume conduction (leadfield), while fMRI signals are temporally blurred by the hemodynamic response function (HRF). Consequently, statistical dependencies observed in sensor or voxel space do not necessarily reflect the underlying latent neural causal influence. Existing methods face a trade-off: Dynamic Causal Modeling (DCM) incorporates biophysical realism but lacks scalability, while observation-space methods (e.g., Granger Causality, VAR) scale well but remain sensitive to mixing and hemodynamic filtering, often failing to recover true directed structure.

The core challenge addressed is: Under what assumptions can a delayed directed graph of latent neural activity be identified from indirect, physics-distorted observations, and how can this be achieved at scale?

Methodology: INCAMA

The authors propose INCAMA (INdirect CAusal MAmba), an end-to-end framework that couples physics-aware inversion with latent-space causal discovery. The architecture follows a two-stage pipeline:

1. Stage 1: Physics-Aware Inversion
   The model learns a regularized inverse mapping $g_\theta$ to recover latent neural trajectories $\hat{z}_{1:T}$ from observations $x_{1:T}$. Crucially, this stage is constrained by the known forward physics $H_\psi$:

   • For EEG: The model learns to invert the leadfield mixing ($x_t \approx L_\psi z_t$), effectively performing source localization (inspired by DeepSIF) to unmixed spatial sources.
   • For fMRI: The model jointly estimates latent neural activity and region-specific HRF parameters to deconvolve the BOLD signal ($x_t \approx H_\psi * z_t$), mitigating hemodynamic confounds.
     The inversion is trained to ensure the reconstructed trajectories are physically meaningful neural signals, not generic embeddings.

2. Stage 2: Latent-Space Causal Discovery
   Once latent trajectories are recovered, the model employs a Mamba (Selective State Space Model) backbone to perform delay-aware causal discovery.

   • Mechanism: It leverages nonstationarity (time-varying coupling strengths) as informative variation to identify causal directions, a concept grounded in the theory of independent causal mechanisms (ICM).
   • Architecture: A shared Mamba encoder processes ROI time series. Directed interactions are modeled via multi-lag linearized kernels (short, mid, long delays) to capture transmission delays.
   • Sparsification: A top-$k$ selection mechanism enforces biological sparsity, retaining the strongest edges to form the final directed graph $\hat{G}$.

The entire pipeline is trained end-to-end on biophysical simulations (The Virtual Brain, TVB), allowing the causal objective to shape the inversion stage to produce representations optimal for graph identifiability.

Theoretical Contributions

The paper formalizes the conditions under which causal discovery is possible from indirect observations:

• Conditional Identifiability: The authors prove that if the latent trajectories are consistently recoverable from indirect observations (Assumption 4.4) and the latent dynamics exhibit nonstationary mechanism shifts (Assumption 4.3), the delayed graph $G$ is identifiable from the observation distribution $P(x_{1:T})$. This is a reduction of latent-space identifiability (Huang et al., 2019) to the indirect observation setting.
• Error Propagation Bound: A key theoretical result (Proposition 4.7) establishes that the error in graph recovery is bounded by the inversion error. Specifically, if the inversion procedure is consistent, the end-to-end estimator is consistent. This provides a theoretical guarantee that bounded errors in reconstructing latent states lead to bounded errors in the estimated causal graph.

Experimental Results

The evaluation utilizes controlled simulations with known ground truth and a zero-shot transfer to real human data.

• Simulated Data (TVB):

  • EEG: INCAMA significantly outperforms baselines (MNE/sLORETA + Granger/VAR, DeepSIF + TCN/GNN) in recovering directed structure. It achieves an F1 score of 0.643 compared to ~0.16–0.21 for baselines, demonstrating that joint physics-aware inversion is critical for overcoming volume conduction.
  • fMRI: INCAMA achieves an F1 score of 0.610, substantially higher than rDCM (0.258) and deconvolution-based linear methods. It also demonstrates superior computational efficiency, operating at ~5 GFLOPs compared to rDCM's ~100 GFLOPs.
  • Robustness: The model shows graceful degradation under physics misspecification (e.g., ±20% HRF scaling or leadfield noise), with F1 dropping by less than 0.002 or 5.1% respectively, confirming it learns transferable causal structure rather than memorizing simulator physics.

• Real Data (HCP Motor Task):

  • Applied zero-shot to 1,079 subjects from the Human Connectome Project (HCP), INCAMA produces sparse directed estimates concentrated in canonical visuo-motor pathways (e.g., V1→V2, PM→M1).
  • While absolute precision is low (0.022) due to the vast search space and unmodeled subcortical drivers, the model achieves high recall (0.610) for canonical edges, significantly outperforming observation-space baselines (FIR + Granger: F1 ~0.005). This suggests the learned scores capture task-relevant anatomical consistency.

Significance and Claims

The paper positions INCAMA as a scalable route to whole-brain directed connectivity inference by explicitly modeling measurement distortion rather than treating it as noise.

• Key Claim: The work demonstrates that nonstationarity can serve as an identifying signal for causal direction even in the presence of severe indirect observation distortions, provided the inversion is physics-aware.
• Limitations: The authors explicitly state that the recovered graph represents effective cortical connectivity conditioned on subcortical influences (as subcortical structures are excluded from the 68-ROI atlas). The validation on real data is indirect (based on anatomical/task-network consistency) because ground-truth causal connectivity in humans is unavailable.
• Impact: The framework bridges the gap between biophysical realism and scalability, offering a method that is theoretically grounded in identifiability conditions and empirically robust to the specific distortions of EEG and fMRI.