- The paper introduces MvHo-IB, a multi-view info bottleneck framework that integrates nonlinear pairwise and higher-order interactions from fMRI data for brain disorder diagnosis.
- It employs matrix-based Rényi entropy estimation and a custom 3D CNN to encode topological brain network features efficiently.
- Empirical results on UCLA, ADNI, and EOEC datasets show significant accuracy improvements and enhanced interpretability via Grad-CAM visualizations.
The paper introduces MvHo-IB, a multi-view learning framework that integrates nonlinear pairwise and higher-order interactions (HOIs) for brain disorder diagnosis using fMRI data. The approach leverages information-theoretic measures, specifically O-information, and a matrix-based R\'enyi's α-order entropy estimator to quantify and extract HOIs, and employs a specialized 3D CNN architecture (Brain3DCNN) to exploit the topological structure of brain networks. The framework is regularized via a multi-view information bottleneck (IB) objective, promoting compact and predictive representations.
Theoretical Contributions
MvHo-IB addresses two major limitations in current fMRI-based diagnostic models:
- Pairwise Limitation: Most existing models focus on pairwise functional connectivity (FC), neglecting the complex, nonlinear, and multivariate dependencies that characterize neural computation.
- Noise and Redundancy: Many approaches do not explicitly address the impact of noisy or redundant interactions, which can degrade generalization and interpretability.
The framework advances the field by:
- Employing O-information: This measure, rooted in information theory, quantifies the nature (synergy vs. redundancy) of multivariate dependencies among triplets of brain regions, providing a signed scalar that distinguishes between genuinely new joint information and repeated signals.
- Matrix-based R\'enyi's Entropy Estimation: The use of a nonparametric, kernel-based estimator enables efficient and robust computation of multivariate entropies and mutual information directly from high-dimensional fMRI time series, bypassing the need for explicit density estimation.
- Multi-View Information Bottleneck: By formulating the learning objective as a multi-view IB problem, the model jointly maximizes the predictive information about the diagnosis while minimizing the retained information from each view, thus compressing task-irrelevant features.
Methodological Details
The MvHo-IB pipeline consists of the following key components:
- Feature Construction: For each subject, two representations are derived:
- A C×C mutual information matrix (pairwise nonlinear FC).
- A C×C×C O-information tensor (triple-wise HOIs).
- Encoders:
- GIN Encoder: Processes the pairwise FC matrix using a Graph Isomorphism Network.
- Brain3DCNN: Processes the O-information tensor using a 3D CNN with custom edge-to-edge (E2E), edge-to-node (E2N), and node-to-graph (N2G) layers, designed to respect the spatial and topological locality of brain networks.
- Fusion and Classification: The outputs of both encoders are fused via a multi-layer perceptron, followed by a nonlinear classifier.
- Objective Function: The loss combines cross-entropy for prediction and entropy-based regularization terms for each view, weighted by tunable coefficients.
Pseudocode Sketch
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for batch in dataloader:
X, Y = batch # fMRI time series and labels
# Compute pairwise MI matrix and O-information tensor
MI_matrix = compute_mutual_information(X)
O_tensor = compute_O_information(X)
# Encode each view
z1 = GIN_encoder(MI_matrix)
z2 = Brain3DCNN(O_tensor)
# Fuse representations
z = fusion_MLP(concat(z1, z2))
# Predict diagnosis
Y_pred = classifier(z)
# Compute loss
ce_loss = cross_entropy(Y_pred, Y)
entropy_z1 = matrix_based_entropy(z1)
entropy_z2 = matrix_based_entropy(z2)
loss = ce_loss + beta1 * entropy_z1 + beta2 * entropy_z2
# Backpropagation
optimizer.zero_grad()
loss.backward()
optimizer.step() |
Empirical Results
MvHo-IB was evaluated on three benchmark fMRI datasets (UCLA, ADNI, EOEC), outperforming eight competitive baselines, including GNNs, information-theoretic, and hypergraph-based models. Notably, it achieved:
- UCLA: 83.12% ± 5.74%
- ADNI: 73.23% ± 4.37%
- EOEC: 82.13% ± 6.96%
These results represent a significant improvement over both pairwise-only and hypergraph-based HOI models. Ablation studies confirm that both the nonlinear pairwise and HOI views contribute complementary discriminative information, and that the IB regularization further enhances generalization.
Interpretability and Clinical Relevance
The model's interpretability is demonstrated via Grad-CAM visualizations, which highlight both pairwise and triple-wise interactions that are neurobiologically plausible and consistent with clinical findings. For example, in schizophrenia, the model identifies interactions within and between higher cognition and subcortical networks, as well as novel triple-network interactions involving temporal and sensorimotor regions.
Practical Implications
- Automated HOI Extraction: By leveraging O-information, the framework avoids manual hypergraph construction and the associated biases of similarity metrics and pruning rules.
- Scalability: The matrix-based entropy estimator enables efficient computation of high-order dependencies, though the extension to orders beyond three remains computationally intensive.
- Generalization and Robustness: The IB objective effectively suppresses noise and redundancy, improving reliability in clinical settings.
- Interpretability: The model provides actionable insights into the distributed neural mechanisms underlying psychiatric disorders, supporting biomarker discovery.
Limitations and Future Directions
- Computational Complexity: While third-order HOIs are tractable, higher-order extensions (e.g., K-way tensors) are computationally demanding. Potential solutions include Gaussian approximations and low-rank matrix-based entropy approximations.
- Extension to Other Modalities: The framework is general and could be adapted to multimodal neuroimaging or other domains where HOIs are relevant.
- Clinical Translation: Further validation on larger, more diverse cohorts and integration with clinical workflows are necessary for translational impact.
Conclusion
MvHo-IB represents a principled, information-theoretic approach to integrating nonlinear pairwise and higher-order dependencies in brain network analysis. Its empirical superiority, interpretability, and extensibility position it as a strong candidate for future research in neuroimaging-based diagnosis and beyond. The methodology also provides a template for multi-view, information-bottleneck-based learning in other domains where complex, high-order interactions are critical.
