EN | Beyond Spurious Edges: Hybrid GNN × Causal Reasoning for Transparent and Reliable Ai Models

10 min readJul 1, 2025

One of the most critical challenges in contemporary AI models is hallucination, reliance on memorized patterns, inherent bias, lack of transparency, and limited traceability. To overcome these limitations, we will examine in detail a hybrid modeling approach that combines traditional causal inference techniques with modern deep learning architectures — namely, Graph Neural Networks (GNNs) integrated with Causal Reasoning.

Turkish version of this article (Bu makalemin Türkçe versiyonu) :

TR | Yanıltıcı Kenarların Ötesinde: Hibrit GNN ve Nedensel Akıl Yürütmeyle Şeffaf ve Güvenilir…

Günümüz Ai modellerdeki en büyük sorunların başında halüsilasyon, ezberden çıkarımlar yapma, önyargılı olma, şeffaflık…

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The GNN–Causal Reasoning hybrid model enables the integration of the mathematically rigorous foundations of Structural Causal Models (SCMs) with the generalization capabilities of GNNs. This fusion allows for both observational and interventional inference within complex systems.

Focusing on GNNs, these are specialized neural network architectures built upon a message-passing mechanism. This mechanism, forming the core component of our hybrid model, facilitates the transmission of information between nodes in a graph. Its key components include:

AGGREGATE: Merging messages received from neighboring nodes
UPDATE: Passing the aggregated messages through a neural network
Permutation Invariance: Ensuring independence from the order of nodes in the graph structure
Multi-layer Processing: Enabling k-hop neighborhood information propagation after k iterations

Now, let us return to our main focus. GNNs typically learn by leveraging statistical correlations within the data through the aforementioned components. While this enables them to achieve high training performance, the learned relationships are often not causal. In particular, GNNs tend to rely on spurious correlations between the target variable and graph components that are irrelevant or non-causal.

To illustrate this complex notion with an example: Consider a citation graph where authors’ institutional affiliations influence both certain insignificant citation patterns (denoted as variable V) and the overall impact score of the paper (denoted as Y). In such a scenario, the GNN may erroneously associate institutional information with paper impact, thereby learning a correlation-based rule that misrepresents the underlying causal structure.

When a GNN mistakenly interprets such patterns as causal, it tends to produce unstable and erroneous results when exposed to data outside the training distribution. Indeed, while standard GNNs often achieve high accuracy within the training distribution, their performance can degrade sharply on out-of-distribution (OOD) data. This degradation arises because the models overfit to non-causal cues present during training. Such behavior indicates that the model fails to capture the true underlying cause-effect relationships.

Now, let us examine the fundamental issues caused by correlation-based learning. From a causal perspective, the most prominent concern is the phenomenon known as confounding. Confounding occurs when hidden or uncontrolled variables influence both the input and the output, creating a spurious association between them.

Source: https://www.nature.com/articles/s41467-020-19784-9

In such cases, GNNs attribute effects to observable correlations rather than to the actual confounding variables. A clear example can illustrate this point: There is a positive correlation between jaundiced (yellow) eyes and liver failure among heavy alcohol consumers. However, artificially altering the eye color (e.g., reducing yellowing through external intervention) does not increase or decrease the risk of liver failure. Similarly, one might observe a spurious correlation such as “drowning incidents increase when ice cream sales rise.” The actual cause behind both is the increase in temperature during the summer season.

This distinction is critical for models like GNNs that primarily learn correlations. While they can capture statistical associations, they fail to grasp the true causal mechanisms. Therefore, when exposed to interventions or distributional shifts, GNNs that rely solely on correlations tend to underperform or behave unpredictably.

Causal modeling offers statistical tools to address such limitations. The Structural Causal Model (SCM) formalizes the relationships between variables on a directed graph, encoding the causal nature of each connection.

At this point, Judea Pearl’s do-operator becomes essential. The do-operator, denoted as do(X), was introduced in causal inference theory to mathematically represent the concept of intervention on a variable.

Observational Prediction: P(Y | X) — “The probability of Y given that X is observed” — represents correlation.
Interventional Prediction: P(Y | do(X)) — “The probability of Y given that X is intervened upon” — represents causation.

The do(X) operator enables us to model how a system behaves when a variable is externally manipulated, as in the earlier examples. But why do we need the do-operator in the first place? To understand this, we must first examine a classic case known as Simpson’s Paradox.

Formalized by Edward Simpson in 1951, Simpson’s Paradox refers to a situation where a trend or correlation present in a dataset reverses or disappears when the data is divided into subgroups.

Core Principle:
- In the aggregate data, it appears that A > B
- But within subgroups, B > A

This is not truly a mathematical paradox, but rather a mistake in causal interpretation.

Classical Example: The University of California, Berkeley Gender Discrimination Case (1973)

Aggregate Data:

Total Applications:
- Men: 8,442 applications → 3,714 accepted (44% acceptance rate)
- Women: 4,321 applications → 1,512 accepted (35% acceptance rate)
- At First Glance: "The university is discriminating against women!"

Segmented Data;

import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
# Simplified version of the real Berkeley admissions data
data = {
    'Department': ['A', 'A', 'B', 'B', 'C', 'C', 'D', 'D', 'E', 'E', 'F', 'F'],
    'Gender': ['Male', 'Female'] * 6,
    'Applications': [825, 108, 560, 25, 325, 593, 417, 375, 191, 393, 373, 341],
    'Admissions': [512, 89, 353, 17, 120, 202, 138, 131, 53, 94, 22, 24],
    'Acceptance_Rate': [0.62, 0.82, 0.63, 0.68, 0.37, 0.34, 0.33, 0.35, 0.28, 0.24, 0.06, 0.07]
}
df = pd.DataFrame(data)
# Visualization
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 6))
# Acceptance rates by department
dept_data = df.pivot(index='Department', columns='Gender', values='Acceptance_Rate')
dept_data.plot(kind='bar', ax=ax1)
ax1.set_title('Acceptance Rates by Department')
ax1.set_ylabel('Acceptance Rate')
ax1.axhline(y=0.5, color='gray', linestyle='--', alpha=0.5)
# Application counts by department
apply_data = df.pivot(index='Department', columns='Gender', values='Applications')
apply_data.plot(kind='bar', ax=ax2)
ax2.set_title('Number of Applications by Department')
ax2.set_ylabel('Application Count')
plt.tight_layout()
plt.show()

Explanation of the Paradox:

The Actual Situation:
1. Women tend to apply more to competitive departments (with lower acceptance rates)
2. Men tend to apply more to less competitive departments (with higher acceptance rates)
3. In each department, women have equal or higher acceptance rates compared to men
4. Yet overall, women appear to have a lower acceptance rate!

When we examine this paradox through mathematical formulation:

import numpy as np

# Example of two hospitals
def simpson_example():
    # Hospital A (Smaller, handles simpler cases)
    male_A = {'treated': 80, 'recovered': 70}   # 87.5%
    female_A = {'treated': 20, 'recovered': 19} # 95%
    
    # Hospital B (Larger, handles more complex cases)
    male_B = {'treated': 20, 'recovered': 10}   # 50%
    female_B = {'treated': 80, 'recovered': 45} # 56.25%
    
    # Totals
    total_male = 80  # 80/100 = 80% recovery
    total_female = 64  # 64/100 = 64% recovery
    
    print("Hospital A: Female (95%) > Male (87.5%)")
    print("Hospital B: Female (56.25%) > Male (50%)")
    print("OVERALL: Male (80%) > Female (64%) – PARADOX!")
    
    return {
        'hospital_A': {'male': 0.875, 'female': 0.95},
        'hospital_B': {'male': 0.50, 'female': 0.5625},
        'total': {'male': 0.80, 'female': 0.64}
    }results = simpson_example()

In this case, the paradox arises under the following condition:

a1/b1 < c1/d1  ve  a2/b2 < c2/d2
AMA
(a1+a2)/(b1+b2) > (c1+c2)/(d1+d2)

Now, let us examine how this paradox is addressed within a causal diagram framework:

import networkx as nx
import matplotlib.pyplot as plt
def draw_causal_diagram():
    G = nx.DiGraph()
    
    # Nodes
    nodes = ['Gender', 'Department Choice', 'Admission', 'Department Difficulty']
    G.add_nodes_from(nodes)
    
    # Edges (causal relationships)
    edges = [
        ('Gender', 'Department Choice'),
        ('Department Choice', 'Admission'),
        ('Department Difficulty', 'Admission'),
        ('Department Difficulty', 'Department Choice')
    ]
    G.add_edges_from(edges)
    
    pos = {
        'Gender': (0, 1),
        'Department Choice': (1, 1),
        'Admission': (2, 0),
        'Department Difficulty': (1, 0)
    }
    
    plt.figure(figsize=(10, 6))
    nx.draw(G, pos, with_labels=True, node_color='lightblue', 
            node_size=3000, font_size=10, font_weight='bold',
            arrows=True, arrowsize=20, edge_color='gray')
    
    plt.title('Causal Diagram of the Berkeley Case')
    plt.axis('off')
    plt.show()

draw_causal_diagram()

This is precisely why Simpson’s Paradox serves as a powerful example demonstrating that statistical analysis cannot rely on numbers alone — it must be grounded in causal reasoning. Cases like this highlight the importance of thinking causally in data science and underscore why tools such as Judea Pearl’s do-operator are critical for uncovering true cause-effect relationships.

Returning to the do-operator, let us now take a look at the rules of do-calculus. Judea Pearl introduced three fundamental rules to transform expressions involving the do-operator into equivalent expressions based on observational data:

Rule 1 — Insertion/Deletion:
If Y is independent of Z given X and W, then:

P(Y|do(X), Z, W) = P(Y|do(X), W)

Rule 2 — Action/Observation Exchange:
If Y is independent of Z given X and W, then:

P(Y|do(X), do(Z), W) = P(Y|do(X), Z, W)

Rule 3 — Insertion/Deletion (Alternative Form):
Under certain specific conditions:

P(Y|do(X), do(Z), W) = P(Y|do(X), W)

An Example Simulation of the Do-Operator:

import numpy as np
import pandas as pd
class CausalModel:
    def __init__(self):
        self.n = 10000  # Number of data points
        
    def generate_observational_data(self):
        # Confounding variable: Socioeconomic status
        socioeconomic = np.random.normal(0, 1, self.n)
        
        # Education level (influenced by socioeconomic status)
        education = 0.7 * socioeconomic + np.random.normal(0, 0.5, self.n)
        
        # Income (influenced by both education and socioeconomic status)
        income = 0.5 * education + 0.5 * socioeconomic + np.random.normal(0, 0.3, self.n)
        
        return pd.DataFrame({
            'socioeconomic': socioeconomic,
            'education': education,
            'income': income
        })
    
    def observational_effect(self, data):
        # Estimating P(income | education)
        high_edu = data[data['education'] > data['education'].median()]
        low_edu = data[data['education'] <= data['education'].median()]
        
        effect = high_edu['income'].mean() - low_edu['income'].mean()
        return effect
    
    def causal_effect_do_operator(self, data):
        # Estimating P(income | do(education))
        # Using backdoor adjustment by stratifying on socioeconomic status
        
        effects = []
        for ses_level in np.percentile(data['socioeconomic'], [25, 50, 75]):
            subset = data[np.abs(data['socioeconomic'] - ses_level) < 0.5]
            
            high_edu = subset[subset['education'] > subset['education'].median()]
            low_edu = subset[subset['education'] <= subset['education'].median()]
            
            effect = high_edu['income'].mean() - low_edu['income'].mean()
            effects.append(effect)
        
        # Weighted average of effects across strata
        return np.mean(effects)
    
# Simulation
model = CausalModel()
data = model.generate_observational_data()

obs_effect = model.observational_effect(data)
causal_effect = model.causal_effect_do_operator(data)print(f"Observational Effect P(Y|X): {obs_effect:.3f}")
print(f"Causal Effect P(Y|do(X)): {causal_effect:.3f}")
print(f"Confounding Bias (Difference): {obs_effect - causal_effect:.3f}")

As we have seen, the do-operator provides the mathematical foundation of causal inference. It formally defines the concept of intervention and, thanks to its formulation, it allows us to:

Clearly distinguish between correlation and causation,
Isolate the effects of confounding variables,
Make reliable predictions for policy decisions,
Theoretically anticipate the outcomes of scientific experiments.

When GNNs Lack Causal Reasoning: Failure Cases

Let us now consider scenarios where GNNs, in the absence of causal reasoning, are prone to making erroneous decisions.

A critical example is the Out-of-Distribution (OOD) generalization problem. Standard GNNs often overfit to spurious patterns in the training data. Numerous academic studies — such as those referenced in the context of the OGB molecular datasets — have shown that when training is stratified by molecular scaffold types (rather than randomized), the performance of conventional GNNs significantly deteriorates.

This degradation occurs because the model mistakenly infers that frequently occurring scaffolds during training are causally relevant to the molecule’s effect. However, when confronted with novel scaffolds during testing, this illusory correlation fails to generalize.

Why the GNN × Causal Reasoning Hybrid Matters

The importance of combining GNNs with causal reasoning can be summarized as follows:

GNNs, due to their correlation-based learning, struggle to capture true causal mechanisms. This leads to failures under distribution shifts, interventions, or unexpected scenarios.
Causal modeling, through SCMs and the do-operator, helps eliminate confounding influences and isolate true cause-effect relationships.
For instance, causal models can identify which neighboring node features are genuinely responsible for an outcome — something traditional GNNs may overlook.
Therefore, the hybrid approach enables filtering out spurious correlations and learning invariant relationships, enhancing the robustness, generalizability, and interpretability of AI systems.

Real-World Applications: Drug Discovery and Beyond

In practical domains such as pharmacology, causal GNNs are increasingly used to understand drug–response mechanisms. When assessing the effect of a drug on a disease, correlation alone is often insufficient, as underlying biological processes and confounding variables may obscure true causal pathways.

Structural Causal Models (SCMs) are particularly effective in modeling such complex scenarios. For instance, in a study cited below, Xia et al. proposed a novel approach by integrating a specific form of SCM — termed the Neural Causal Model — with neural networks to predict combination treatment effects, offering new insights in therapeutic strategy design.

Combinatorial prediction of therapeutic perturbations using causally-inspired neural networks

Phenotype-driven approaches identify disease-counteracting compounds by analyzing the phenotypic signatures that…

pmc.ncbi.nlm.nih.gov

Therefore, when evaluating hybrid models in drug discovery and biomedical applications, we observe several key advantages:

More accurate effect analysis: Causal GNNs can identify which molecular or biological interactions truly influence therapeutic outcomes. This enables more precise predictions regarding the success of drug candidates, ultimately increasing the likelihood of favorable results in clinical trials.
Side-effect and safety profiling: By analyzing causal relationships within graph structures, these models can predict which off-target interactions may lead to undesired or adverse effects, helping to assess drug safety in earlier stages.

The Necessity of Hybrid Models

Hybrid models are essential because they form complementary relationships between correlation-based learning and causal inference, thereby providing robust decision support. This synergy enhances the reliability of AI systems in high-stakes domains such as medicine, where understanding why a decision is made is as critical as what decision is made.

GNN: “What is connected to what?” → Structural relationships
Causal Reasoning: “What causes what?” → Causal relationships
Hybrid Approach: “Which connections are causal, and how do they influence outcomes?”

The other essential motivation arises from the demand for robust reasoning in high-stakes, error-intolerant domains. When we examine critical application scenarios, the need becomes evident — especially in fields like healthcare and medicine, where hybrid reasoning is vital for:

Personalizing treatment effects,
Anticipating adverse side effects,
Understanding disease propagation dynamics.

For example:

# COVID-19 intervention strategy
def optimize_intervention(city_network, resources):
    # GNN: Analyze inter-city connectivity
    connectivity = gnn.analyze_network(city_network)
    
    # Causal: Estimate effects of interventions
    intervention_effects = causal.compute_do_calculus(
        intervention="lockdown",
        target_cities=high_risk_cities
    )
    
    # Optimal strategy selection
    return minimize_spread_with_minimal_economic_impact()

In financial risk management, the need for hybrid reasoning arises from the importance of:

Understanding systemic risks,
Predicting domino effects across interconnected entities,
Identifying optimal intervention points to prevent cascading failures.

In the context of social media and disinformation, the challenges call for:

Uncovering the mechanisms of misinformation spread,
Designing effective intervention strategies,
Minimizing unintended side effects of content moderation or suppression.

Thank you for reading.

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