LearnAD: Learning Interpretable Rules for Brain Networks in Alzheimer's Disease Classification

AI summary

Overview

Research area: Neuro-symbolic machine learning applied to clinical neuroscience, specifically Alzheimer's disease (AD) classification from structural brain connectomes derived from MRI.

Technical level: Advanced. The paper assumes familiarity with graph neural networks, inductive logic programming, Answer Set Programming (ASP), and the Learning from Answer Sets (LAS) framework.

Scope: The paper introduces LearnAD, a method that combines statistical or deep learning models for feature selection with the FastLAS symbolic learner to produce fully interpretable rules distinguishing cognitively normal (CN) from Alzheimer's disease patients using data from the Alzheimer's Disease Neuroimaging Study (ADNI).

What This Paper Is About

Machine learning models can predict Alzheimer's disease from brain imaging, but the strongest performers (Random Forests, graph neural networks, convolutional neural networks) are black boxes, so clinicians cannot verify whether they learn genuine disease markers or confounds. Symbolic machine learning produces transparent rules but has been difficult to apply to the unstructured, noisy nature of MRI data. LearnAD addresses this gap by first using a statistical or deep model to select the most relevant brain connections, then using the FastLAS symbolic learner to induce global interpretable rules over those connections.

Key Contributions

1. A neuro-symbolic pipeline (LearnAD) with four components — a Statistical ML Model, a Feature Selector, a Network-to-Knowledge Generator (NKG), and a Symbolic Model (FastLAS) — that learns global interpretable rules from structural brain connectomes.
2. Three instantiations of the approach using different statistical components to define the relevant feature space: LearnAD(DT), LearnAD(RF), and LearnAD(GCN), allowing comparison of which statistical model is most effective for feature selection when paired with a symbolic learner.
3. Automatic generation of symbolic learning tasks from unstructured MRI data: the NKG constructs the examples E and hypothesis space S_M for FastLAS, including a semi-parametric representation of connection strengths as structured context.
4. The first application of inductive logic programming to brain network analysis, as far as the authors are aware, generating a hypothesis for subgraphs extracted from a GNN and reporting which brain connections are reliably associated with AD status.

Main Findings

• Best instance versus baselines: LearnAD(DT) achieves 65.72 ± 2.38% accuracy, which outperforms a Decision Tree trained on the full network (58.58 ± 2.66%), is comparable to an SVM (66.35 ± 1.42%), and is below a Random Forest (69.90 ± 1.61%) and a GCN (68.94 ± 2.00%) trained on all features.
• Ablation against models on the selected feature set: LearnAD(DT) outperforms DT* (63.86 ± 3.49%), while LearnAD(RF) (65.65 ± 2.55%) slightly underperforms RF* (70.70 ± 1.73%) — a 5.05% gap the authors treat as a trade-off for improved interpretability. No GCN* baseline is reported because the selected graphs are too sparse to train on.
• Feature selection regularises the Decision Tree: Explicit feature selection improves DT accuracy from the full network to DT* by 5.28%; the gain for RF* is negligible because ensembles are less prone to overfitting.
• Interpretability measured in atoms: The best-performing symbolic model has 23.48 ± 1.6 atoms, compared with 250.91 ± 38.2 atoms for the DT and 797.00 ± 5.35 atoms for the RF. DT* rules have bodies of up to 8 conditions (set by the maximum tree depth), whereas FastLAS favours compressed optimal hypotheses that yield much shorter rules.
• GNN distillation gap: LearnAD(GCN) achieves 62.97 ± 2.62% accuracy, 5.97% lower than the GCN trained on the full network, suggesting most of the GCN's predictive signal can be captured by simple rules; the residual gap may come from noise introduced by GNNExplainer and the Feature Selector, or from the difficulty of distilling message passing into concise logical constraints.
• Stable, clinically plausible connections: Rules involving the left temporal pole–left hippocampus connection appear consistently across all random seeds, and rules involving the right precuneus–right superior parietal connection appear in approximately 80% of seeds. The paper links these to hippocampal atrophy in AD and to memory impairment in old-age AD patients.
• Heterogeneity of AD: The learned semi-parametric rules encode subject-level thresholds over connection strengths, and multiple threshold boundaries are observed across subjects, which the authors suggest may reflect distinct patterns of degradation or different disease subtypes.

Methodology in Plain English

The researchers took structural connectomes — weighted graphs where nodes are brain regions and edges are white matter connections — from 304 ADNI participants (152 CN and 152 AD, matched by age and sex). Each connectome covers 84 brain regions of interest from the Desikan–Killiany atlas, extracted with the Clinica software platform from T1W and DWI MRI. Because tractography can create spurious edges, connectomes were thresholded to keep 30% of edges, giving 70% sparsity.

The pipeline then works in two stages. First, a statistical model is trained on the full connectomes: a Decision Tree or Random Forest selects the top k_global connections by their total reduction in Gini Impurity, while a GCN uses GNNExplainer to extract k_instance salient edges per training graph, after which the top k_total edges are kept by frequency across all training graphs. Second, the Network-to-Knowledge Generator converts these selected connections into a FastLAS learning task: each patient becomes a weighted context-dependent partial interpretation whose context lists region pairs and their connectivity strengths, and the hypothesis space consists of rules that conclude AD from combinations of connection strengths and comparators (greater than, less than, and so on).

Connectivity strengths were rounded to four decimal places and scaled by 1000 because the solver cannot handle real numbers. A base noisy penalty of 1 was applied per example, with AD penalties rescaled by the CN-to-AD ratio, and AD examples were partitioned into disjoint subsets to keep the learning task tractable (3 disjoint sets for LearnAD(DT), 4 for LearnAD(RF), 3 for LearnAD(GCN)). The final hypothesis is the union of rules learned across those tasks. Learned rules were evaluated at inference time with Clingo. Evaluation used repeated stratified cross-validation with 10 repeats using distinct random seeds, each on a fresh 90% subsample, with folds stratified by diagnosis, sex, and MRI machine manufacturer.

Why This Matters

Impact on research. Most high-performing AD classifiers are opaque, which limits their clinical credibility and makes it impossible to check whether they learn disease biology or scanner artefacts. LearnAD shows that a symbolic learner can reach accuracy comparable to established models while producing rules small enough (23.48 ± 1.6 atoms) for a human to read, and it offers a way to inspect what a GNN is actually using — the authors frame the work as a way to deepen understanding of GNN behaviour in clinical neuroscience.

Real-world applications.

• Clinical decision support that presents a short, auditable list of affected connections rather than an opaque risk score.
• Biomarker discovery, where learned rules naming specific connections (for example left temporal pole–left hippocampus) can guide hypotheses and further imaging studies.
• Regulatory and validation contexts where a model's reasoning must be inspected before deployment in a healthcare setting.
• Cross-cohort generalisation studies, since concise logical rules are easier to transfer and re-test than large learned weight matrices.

Industry relevance. Neuro-symbolic pipelines that pair deep models with symbolic learners are relevant to medical AI vendors that need explainable outputs, to graph analytics platforms in healthcare, and to the broader effort to make graph neural networks auditable. The commercial involvement of ILASP LTD as an author affiliation points to interest in the symbolic learning tooling itself.

Future Directions

• Extending the approach to time series data of structural MRI, so rules can describe change over time rather than a single imaging time point.
• Incorporating additional imaging modalities, specifically functional MRI and PET data, beyond the structural MRI and DWI used here.
• Reducing the accuracy gap between LearnAD(GCN) and the full-feature GCN, including addressing the noise the authors attribute to GNNExplainer and the Feature Selector.
• Exploring non-uniform penalties — for example downweighting examples with low prediction confidence or brain regions less frequently observed during the explanation stage — which the paper raises but does not implement.

Target Audience

Researchers and practitioners in neuro-symbolic AI, inductive logic programming, and explainable machine learning; clinical neuroscientists and neuroimaging researchers studying Alzheimer's disease and brain connectomes; and medical AI developers who need interpretable models but cannot accept large accuracy losses relative to black-box baselines. Readers without background in Answer Set Programming will find the symbolic sections (Sections 2.2 and 4.4) demanding.

Authors’ abstract

We introduce LearnAD, a neuro-symbolic method for predicting Alzheimer's disease from brain magnetic resonance imaging data, learning fully interpretable rules. LearnAD applies statistical models, Decision Trees, Random Forests, or GNNs to identify relevant brain connections, and then employs FastLAS to learn global rules. Our best instance outperforms Decision Trees, matches Support Vector Machine accuracy, and performs only slightly below Random Forests and GNNs trained on all features, all while remaining fully interpretable. Ablation studies show that our neuro-symbolic approach improves interpretability with comparable performance to pure statistical models. LearnAD demonstrates how symbolic learning can deepen our understanding of GNN behaviour in clinical neuroscience.