Chapter 4: Composition-based vs GNN Quantitative Comparison

In this chapter, we quantitatively compare the performance of composition-based features (Magpie) and GNN structure-based features (CGCNN) using the Matbench standard benchmark. We conduct empirical analysis from multiple perspectives including not only prediction accuracy, but also statistical significance, computational cost, data requirements, and interpretability.

4.1 Overview of Matbench Benchmark

Matbench (Materials Benchmark) is a standardized evaluation platform for machine learning models in materials science. It defines 13 material property prediction tasks, with training, validation, and test data pre-split for each task. This enables fair performance comparison across different research studies.

4.1.1 Main Matbench Tasks

In this chapter, we compare the performance of Random Forest (Magpie features) and CGCNN on two tasks: matbench_mp_e_form (formation energy prediction) and matbench_mp_gap (band gap prediction).

4.1.2 Evaluation Protocol

In Matbench, 5-fold cross-validation is the standard evaluation protocol. The entire dataset is split into 5 folds, and the following evaluation is performed for each fold:

1. Training: Train the model on the remaining 4 folds
2. Validation: Use for hyperparameter tuning (optional)
3. Testing: Evaluate performance on the corresponding fold (calculate MAE, RMSE, R²)

By averaging the evaluation metrics across the 5 folds, we obtain a reliable estimate of generalization performance.

4.2 Matbench Benchmark Implementation

In this section, we implement Random Forest (Magpie) and CGCNN on the Matbench mp_e_form task and quantitatively compare their prediction accuracy.

4.2.1 Environment Setup and Data Loading

# Requirements:
# - Python 3.9+
# - numpy>=1.24.0, <2.0.0
# - pandas>=2.0.0, <2.2.0

"""
Example: 4.2.1 Environment Setup and Data Loading

Purpose: Demonstrate core concepts and implementation patterns
Target: Advanced
Execution time: ~5 seconds
Dependencies: None
"""

# Load and preprocess Matbench dataset
import numpy as np
import pandas as pd
from matbench.bench import MatbenchBenchmark
from pymatgen.core import Structure
from matminer.featurizers.composition import ElementProperty
from sklearn.ensemble import RandomForestRegressor
from sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score
import warnings
warnings.filterwarnings('ignore')

# Initialize Matbench benchmark
mb = MatbenchBenchmark(autoload=False)

# Load mp_e_form task (formation energy prediction)
task = mb.matbench_mp_e_form
task.load()

print(f"Task name: {task.metadata['task_type']}")
print(f"Data size: {len(task.df)}")
print(f"Input: {task.metadata['input_type']}")
print(f"Output: {task.metadata['target']}")

# Check data structure
print("\nData sample:")
print(task.df.head(3))

# Output example:
# Task name: regression
# Data size: 132752
# Input: structure
# Output: e_form (eV/atom)
#
# Data sample:
#                                           structure  e_form
# 0  Structure: Fe2 O3 ...                    -2.54
# 1  Structure: Mn2 O3 ...                    -2.89
# 2  Structure: Co2 O3 ...                    -2.31

4.2.2 Random Forest (Magpie Features) Implementation

# Random Forest + Magpie features implementation
from matminer.featurizers.composition import ElementProperty

def extract_magpie_features(structures):
    """
    Extract Magpie features from Pymatgen Structure

    Parameters:
    -----------
    structures : list of Structure
        List of crystal structures

    Returns:
    --------
    features : np.ndarray, shape (n_samples, 145)
        Magpie features (145 dimensions)
    """
    # Initialize Magpie feature extractor
    featurizer = ElementProperty.from_preset("magpie")

    features = []
    for struct in structures:
        # Get Composition from Structure
        comp = struct.composition
        # Calculate Magpie features (145 dimensions)
        feat = featurizer.featurize(comp)
        features.append(feat)

    return np.array(features)

# 5-fold cross-validation evaluation
rf_results = []

for fold_idx, fold in enumerate(task.folds):
    print(f"\n=== Fold {fold_idx + 1}/5 ===")

    # Get training and test data
    train_inputs, train_outputs = task.get_train_and_val_data(fold)
    test_inputs, test_outputs = task.get_test_data(fold, include_target=True)

    # Extract Magpie features
    print("Extracting Magpie features...")
    X_train = extract_magpie_features(train_inputs)
    X_test = extract_magpie_features(test_inputs)
    y_train = train_outputs.values
    y_test = test_outputs.values

    print(f"Training data: {X_train.shape}, Test data: {X_test.shape}")

    # Train Random Forest model
    print("Training Random Forest...")
    rf_model = RandomForestRegressor(
        n_estimators=100,
        max_depth=30,
        min_samples_split=5,
        random_state=42,
        n_jobs=-1
    )
    rf_model.fit(X_train, y_train)

    # Predict on test data
    y_pred = rf_model.predict(X_test)

    # Calculate evaluation metrics
    mae = mean_absolute_error(y_test, y_pred)
    rmse = np.sqrt(mean_squared_error(y_test, y_pred))
    r2 = r2_score(y_test, y_pred)

    print(f"MAE:  {mae:.4f} eV/atom")
    print(f"RMSE: {rmse:.4f} eV/atom")
    print(f"R²:   {r2:.4f}")

    rf_results.append({
        'fold': fold_idx + 1,
        'mae': mae,
        'rmse': rmse,
        'r2': r2
    })

# Calculate 5-fold average scores
rf_df = pd.DataFrame(rf_results)
print("\n=== Random Forest (Magpie) Overall Results ===")
print(f"MAE:  {rf_df['mae'].mean():.4f} ± {rf_df['mae'].std():.4f} eV/atom")
print(f"RMSE: {rf_df['rmse'].mean():.4f} ± {rf_df['rmse'].std():.4f} eV/atom")
print(f"R²:   {rf_df['r2'].mean():.4f} ± {rf_df['r2'].std():.4f}")

# Output example:
# === Random Forest (Magpie) Overall Results ===
# MAE:  0.0325 ± 0.0012 eV/atom
# RMSE: 0.0678 ± 0.0019 eV/atom
# R²:   0.9321 ± 0.0045

4.2.3 CGCNN Implementation

# Requirements:
# - Python 3.9+
# - torch>=2.0.0, <2.3.0

"""
Example: 4.2.3 CGCNN Implementation

Purpose: Demonstrate data manipulation and preprocessing
Target: Advanced
Execution time: 1-5 minutes
Dependencies: None
"""

# CGCNN on Matbench implementation
import torch
import torch.nn as nn
from torch_geometric.data import Data, DataLoader
from torch_geometric.nn import CGConv, global_mean_pool
import time

# Define CGCNN for Matbench (using model from Chapter 2)
class CGCNNMatbench(nn.Module):
    def __init__(self, atom_fea_len=92, nbr_fea_len=41, hidden_dim=128, n_conv=3):
        super(CGCNNMatbench, self).__init__()

        # Atom embedding
        self.atom_embedding = nn.Linear(atom_fea_len, hidden_dim)

        # Convolution layers
        self.conv_layers = nn.ModuleList([
            CGConv(hidden_dim, nbr_fea_len) for _ in range(n_conv)
        ])
        self.bn_layers = nn.ModuleList([
            nn.BatchNorm1d(hidden_dim) for _ in range(n_conv)
        ])

        # Readout
        self.fc1 = nn.Linear(hidden_dim, 64)
        self.fc2 = nn.Linear(64, 1)
        self.activation = nn.Softplus()

    def forward(self, data):
        x, edge_index, edge_attr, batch = data.x, data.edge_index, data.edge_attr, data.batch

        # Atom embedding
        x = self.atom_embedding(x)

        # Graph convolutions
        for conv, bn in zip(self.conv_layers, self.bn_layers):
            x = conv(x, edge_index, edge_attr)
            x = bn(x)
            x = self.activation(x)

        # Global pooling
        x = global_mean_pool(x, batch)

        # Fully connected layers
        x = self.fc1(x)
        x = self.activation(x)
        x = self.fc2(x)

        return x.squeeze()

def structure_to_pyg_data(structure, target, cutoff=8.0):
    """
    Convert Pymatgen Structure to PyTorch Geometric data

    Parameters:
    -----------
    structure : Structure
        Crystal structure
    target : float
        Target value (formation energy)
    cutoff : float
        Cutoff radius (Å)

    Returns:
    --------
    data : Data
        PyTorch Geometric data object
    """
    # Node features (element one-hot encoding, 92 dimensions)
    atom_types = [site.specie.Z for site in structure]
    x = torch.zeros(len(atom_types), 92)
    for i, z in enumerate(atom_types):
        x[i, z - 1] = 1.0

    # Edge construction (atom pairs within cutoff radius)
    neighbors = structure.get_all_neighbors(cutoff)
    edge_index = []
    edge_attr = []

    for i, neighbors_i in enumerate(neighbors):
        for neighbor in neighbors_i:
            j = neighbor.index
            distance = neighbor.nn_distance

            # Gaussian distance expansion (41 dimensions)
            distances = torch.linspace(0, cutoff, 41)
            sigma = 0.5
            edge_feature = torch.exp(-((distance - distances) ** 2) / (2 * sigma ** 2))

            edge_index.append([i, j])
            edge_attr.append(edge_feature)

    edge_index = torch.tensor(edge_index, dtype=torch.long).t().contiguous()
    edge_attr = torch.stack(edge_attr)
    y = torch.tensor([target], dtype=torch.float)

    return Data(x=x, edge_index=edge_index, edge_attr=edge_attr, y=y)

# 5-fold cross-validation evaluation
cgcnn_results = []

device = torch.device('cuda' if torch.cuda.is_available() else 'cpu')
print(f"Using device: {device}")

for fold_idx, fold in enumerate(task.folds):
    print(f"\n=== Fold {fold_idx + 1}/5 ===")

    # Get training and test data
    train_inputs, train_outputs = task.get_train_and_val_data(fold)
    test_inputs, test_outputs = task.get_test_data(fold, include_target=True)

    # Convert to PyTorch Geometric data
    print("Building graph data...")
    train_data = [structure_to_pyg_data(s, t) for s, t in zip(train_inputs, train_outputs.values)]
    test_data = [structure_to_pyg_data(s, t) for s, t in zip(test_inputs, test_outputs.values)]

    train_loader = DataLoader(train_data, batch_size=32, shuffle=True)
    test_loader = DataLoader(test_data, batch_size=32, shuffle=False)

    # Initialize CGCNN model
    model = CGCNNMatbench().to(device)
    optimizer = torch.optim.Adam(model.parameters(), lr=0.001)
    criterion = nn.L1Loss()  # MAE loss

    # Training
    print("Training CGCNN...")
    model.train()
    for epoch in range(50):  # Should use early stopping in practice
        total_loss = 0
        for batch in train_loader:
            batch = batch.to(device)
            optimizer.zero_grad()
            out = model(batch)
            loss = criterion(out, batch.y)
            loss.backward()
            optimizer.step()
            total_loss += loss.item()

        if (epoch + 1) % 10 == 0:
            print(f"Epoch {epoch+1}/50, Loss: {total_loss/len(train_loader):.4f}")

    # Testing
    model.eval()
    y_true = []
    y_pred = []

    with torch.no_grad():
        for batch in test_loader:
            batch = batch.to(device)
            out = model(batch)
            y_true.extend(batch.y.cpu().numpy())
            y_pred.extend(out.cpu().numpy())

    y_true = np.array(y_true)
    y_pred = np.array(y_pred)

    # Calculate evaluation metrics
    mae = mean_absolute_error(y_true, y_pred)
    rmse = np.sqrt(mean_squared_error(y_true, y_pred))
    r2 = r2_score(y_true, y_pred)

    print(f"MAE:  {mae:.4f} eV/atom")
    print(f"RMSE: {rmse:.4f} eV/atom")
    print(f"R²:   {r2:.4f}")

    cgcnn_results.append({
        'fold': fold_idx + 1,
        'mae': mae,
        'rmse': rmse,
        'r2': r2
    })

# Calculate 5-fold average scores
cgcnn_df = pd.DataFrame(cgcnn_results)
print("\n=== CGCNN Overall Results ===")
print(f"MAE:  {cgcnn_df['mae'].mean():.4f} ± {cgcnn_df['mae'].std():.4f} eV/atom")
print(f"RMSE: {cgcnn_df['rmse'].mean():.4f} ± {cgcnn_df['rmse'].std():.4f} eV/atom")
print(f"R²:   {cgcnn_df['r2'].mean():.4f} ± {cgcnn_df['r2'].std():.4f}")

# Output example:
# === CGCNN Overall Results ===
# MAE:  0.0286 ± 0.0009 eV/atom
# RMSE: 0.0592 ± 0.0014 eV/atom
# R²:   0.9524 ± 0.0032

4.2.4 Quantitative Comparison of Prediction Accuracy

We integrate the 5-fold cross-validation results and compare the prediction accuracy of Random Forest (Magpie) and CGCNN.

# Requirements:
# - Python 3.9+
# - matplotlib>=3.7.0
# - seaborn>=0.12.0

"""
Example: We integrate the 5-fold cross-validation results and compare

Purpose: Demonstrate data visualization techniques
Target: Beginner to Intermediate
Execution time: 2-5 seconds
Dependencies: None
"""

# Visualization of prediction accuracy comparison
import matplotlib.pyplot as plt
import seaborn as sns

# Integrate results
comparison_df = pd.DataFrame({
    'Model': ['RF (Magpie)'] * 5 + ['CGCNN'] * 5,
    'Fold': list(range(1, 6)) * 2,
    'MAE': list(rf_df['mae']) + list(cgcnn_df['mae']),
    'RMSE': list(rf_df['rmse']) + list(cgcnn_df['rmse']),
    'R²': list(rf_df['r2']) + list(cgcnn_df['r2'])
})

# Visualization
fig, axes = plt.subplots(1, 3, figsize=(15, 5))

# MAE comparison
sns.barplot(data=comparison_df, x='Model', y='MAE', ax=axes[0], palette=['#667eea', '#764ba2'])
axes[0].set_title('MAE Comparison (Lower is Better)', fontsize=14, fontweight='bold')
axes[0].set_ylabel('MAE (eV/atom)', fontsize=12)
axes[0].axhline(0.03, color='red', linestyle='--', linewidth=1, label='Target: 0.03')
axes[0].legend()

# RMSE comparison
sns.barplot(data=comparison_df, x='Model', y='RMSE', ax=axes[1], palette=['#667eea', '#764ba2'])
axes[1].set_title('RMSE Comparison (Lower is Better)', fontsize=14, fontweight='bold')
axes[1].set_ylabel('RMSE (eV/atom)', fontsize=12)

# R² comparison
sns.barplot(data=comparison_df, x='Model', y='R²', ax=axes[2], palette=['#667eea', '#764ba2'])
axes[2].set_title('R² Comparison (Higher is Better)', fontsize=14, fontweight='bold')
axes[2].set_ylabel('R²', fontsize=12)
axes[2].axhline(0.95, color='red', linestyle='--', linewidth=1, label='Target: 0.95')
axes[2].legend()

plt.tight_layout()
plt.savefig('accuracy_comparison.png', dpi=300, bbox_inches='tight')
plt.show()

# Statistical summary
print("=== Statistical Summary of Prediction Accuracy ===")
print(comparison_df.groupby('Model').agg({
    'MAE': ['mean', 'std'],
    'RMSE': ['mean', 'std'],
    'R²': ['mean', 'std']
}).round(4))

# Calculate relative improvement rates
mae_improvement = (rf_df['mae'].mean() - cgcnn_df['mae'].mean()) / rf_df['mae'].mean() * 100
rmse_improvement = (rf_df['rmse'].mean() - cgcnn_df['rmse'].mean()) / rf_df['rmse'].mean() * 100
r2_improvement = (cgcnn_df['r2'].mean() - rf_df['r2'].mean()) / rf_df['r2'].mean() * 100

print(f"\n=== Relative Improvement Rate of CGCNN ===")
print(f"MAE improvement:  {mae_improvement:.2f}%")
print(f"RMSE improvement: {rmse_improvement:.2f}%")
print(f"R² improvement:   {r2_improvement:.2f}%")

# Output example:
# === Relative Improvement Rate of CGCNN ===
# MAE improvement:  12.00%
# RMSE improvement: 12.68%
# R² improvement:   2.18%

Interpretation of Results:

• MAE improvement: 12.00% - CGCNN achieves approximately 12% lower error than Magpie+RF in formation energy prediction
• R² improvement: 2.18% - Although RF already achieves a high R² (0.932), CGCNN achieves an extremely high coefficient of determination of 0.952, so the relative improvement rate is small
• Statistical significance testing is required - In the next section, we will test whether this accuracy difference is statistically significant

4.3 Statistical Significance Testing

In the previous section, we confirmed that CGCNN achieves approximately 12% lower MAE than Random Forest (Magpie). However, to verify whether this accuracy difference is statistically significant, we cannot rule out the possibility that it is merely by chance. In this section, we evaluate statistical significance using paired t-test and 95% confidence interval.

4.3.1 Principle of Paired t-Test

In 5-fold cross-validation, both RF and CGCNN are evaluated on the same data splits. Therefore, the MAE differences for each fold can be treated as paired data. The paired t-test tests the following null hypothesis:

$$H_0: \mu_{\text{diff}} = 0 \quad \text{(The average MAE difference between RF and CGCNN is zero)}$$

$$H_1: \mu_{\text{diff}} \neq 0 \quad \text{(The average MAE difference is not zero)}$$

The test statistic t is calculated as follows:

$$t = \frac{\bar{d}}{s_d / \sqrt{n}}$$

Where $\bar{d}$ is the mean of the differences, $s_d$ is the standard deviation of the differences, and $n$ is the sample size (number of folds = 5).

4.3.2 t-Test Implementation

# Requirements:
# - Python 3.9+
# - numpy>=1.24.0, <2.0.0
# - scipy>=1.11.0

"""
Example: 4.3.2 t-Test Implementation

Purpose: Demonstrate core concepts and implementation patterns
Target: Intermediate
Execution time: 5-10 seconds
Dependencies: None
"""

# Paired t-test implementation
from scipy import stats
import numpy as np

# MAE for Random Forest and CGCNN (results from 5 folds)
rf_mae = np.array([0.0325, 0.0338, 0.0312, 0.0329, 0.0321])  # Example data
cgcnn_mae = np.array([0.0286, 0.0293, 0.0279, 0.0288, 0.0284])  # Example data

# Calculate MAE differences
mae_diff = rf_mae - cgcnn_mae

print("=== Paired t-Test ===")
print(f"RF MAE:     {rf_mae}")
print(f"CGCNN MAE:  {cgcnn_mae}")
print(f"MAE diff:   {mae_diff}")
print(f"Mean diff:  {mae_diff.mean():.4f} eV/atom")
print(f"Std dev:    {mae_diff.std(ddof=1):.4f} eV/atom")

# Perform paired t-test
t_statistic, p_value = stats.ttest_rel(rf_mae, cgcnn_mae)

print(f"\nt-statistic: {t_statistic:.4f}")
print(f"p-value:     {p_value:.4f}")

# Judge with significance level α=0.05
alpha = 0.05
if p_value < alpha:
    print(f"\nJudgment: p-value ({p_value:.4f}) < α ({alpha}) → Reject null hypothesis")
    print("Conclusion: The accuracy difference between CGCNN and RF is statistically significant.")
else:
    print(f"\nJudgment: p-value ({p_value:.4f}) ≥ α ({alpha}) → Cannot reject null hypothesis")
    print("Conclusion: The accuracy difference between CGCNN and RF is not statistically significant.")

# Calculate effect size (Cohen's d)
cohens_d = mae_diff.mean() / mae_diff.std(ddof=1)
print(f"\nEffect size (Cohen's d): {cohens_d:.4f}")
if abs(cohens_d) < 0.2:
    print("Effect size magnitude: Small")
elif abs(cohens_d) < 0.5:
    print("Effect size magnitude: Medium")
elif abs(cohens_d) < 0.8:
    print("Effect size magnitude: Large")
else:
    print("Effect size magnitude: Very large")

# Output example:
# === Paired t-Test ===
# RF MAE:     [0.0325 0.0338 0.0312 0.0329 0.0321]
# CGCNN MAE:  [0.0286 0.0293 0.0279 0.0288 0.0284]
# MAE diff:   [0.0039 0.0045 0.0033 0.0041 0.0037]
# Mean diff:  0.0039 eV/atom
# Std dev:    0.0004 eV/atom
#
# t-statistic: 20.5891
# p-value:     0.0001
#
# Judgment: p-value (0.0001) < α (0.05) → Reject null hypothesis
# Conclusion: The accuracy difference between CGCNN and RF is statistically significant.
#
# Effect size (Cohen's d): 9.1894
# Effect size magnitude: Very large

4.3.3 Calculation of 95% Confidence Interval

The 95% confidence interval indicates the range that contains the true mean difference with 95% probability. If the confidence interval does not include zero, we can conclude that there is a statistically significant difference.

# Requirements:
# - Python 3.9+
# - matplotlib>=3.7.0
# - scipy>=1.11.0

"""
Example: The 95% confidence interval indicates therange that contains

Purpose: Demonstrate data visualization techniques
Target: Beginner to Intermediate
Execution time: 2-5 seconds
Dependencies: None
"""

# Calculation and visualization of 95% confidence interval
from scipy import stats
import matplotlib.pyplot as plt

# Calculate 95% confidence interval
confidence_level = 0.95
degrees_freedom = len(mae_diff) - 1
t_critical = stats.t.ppf((1 + confidence_level) / 2, degrees_freedom)

mean_diff = mae_diff.mean()
se_diff = mae_diff.std(ddof=1) / np.sqrt(len(mae_diff))
margin_error = t_critical * se_diff

ci_lower = mean_diff - margin_error
ci_upper = mean_diff + margin_error

print("=== 95% Confidence Interval ===")
print(f"Mean difference:     {mean_diff:.4f} eV/atom")
print(f"Standard error:      {se_diff:.4f} eV/atom")
print(f"t-critical (df={degrees_freedom}): {t_critical:.4f}")
print(f"Margin of error:     ±{margin_error:.4f} eV/atom")
print(f"95% CI:              [{ci_lower:.4f}, {ci_upper:.4f}] eV/atom")

if ci_lower > 0:
    print("\nJudgment: CI does not include 0 → Statistically significant difference exists")
else:
    print("\nJudgment: CI includes 0 → No statistically significant difference")

# Visualization
fig, ax = plt.subplots(figsize=(10, 6))

# Plot MAE differences for each fold
ax.scatter(range(1, 6), mae_diff, s=100, color='#764ba2', zorder=3, label='MAE diff per fold')

# Mean line
ax.axhline(mean_diff, color='#667eea', linestyle='--', linewidth=2, label=f'Mean diff: {mean_diff:.4f}')

# 95% confidence interval
ax.axhspan(ci_lower, ci_upper, alpha=0.2, color='#667eea', label=f'95% CI: [{ci_lower:.4f}, {ci_upper:.4f}]')

# Zero line
ax.axhline(0, color='red', linestyle='-', linewidth=1, label='No difference (H₀)')

ax.set_xlabel('Fold number', fontsize=12)
ax.set_ylabel('MAE diff (RF - CGCNN) [eV/atom]', fontsize=12)
ax.set_title('MAE Difference and 95% Confidence Interval in 5-Fold Cross-Validation', fontsize=14, fontweight='bold')
ax.set_xticks(range(1, 6))
ax.legend(fontsize=10)
ax.grid(alpha=0.3)

plt.tight_layout()
plt.savefig('statistical_significance.png', dpi=300, bbox_inches='tight')
plt.show()

# Output example:
# === 95% Confidence Interval ===
# Mean difference:     0.0039 eV/atom
# Standard error:      0.0002 eV/atom
# t-critical (df=4):  2.7764
# Margin of error:     ±0.0005 eV/atom
# 95% CI:              [0.0034, 0.0044] eV/atom
#
# Judgment: CI does not include 0 → Statistically significant difference exists

4.3.4 Summary of Statistical Testing Results

Conclusion:

• CGCNN showed statistically significant accuracy improvement over Random Forest (Magpie) (p=0.0001 << 0.05)
• The 95% confidence interval [0.0034, 0.0044] eV/atom does not include zero, so the existence of the accuracy difference is statistically supported
• Cohen's d = 9.19, a very large effect size, indicates the practical superiority of CGCNN
• The 12% relative improvement rate has practical merit directly related to improving the efficiency of materials discovery

4.4 Quantitative Comparison of Computational Cost

Not only accuracy, but also computational cost (training time, inference time, memory usage) is an important factor in model selection. In this section, we measure and quantitatively compare the computational cost of Random Forest and CGCNN.

4.4.1 Measurement of Training Time

# Measurement of training and inference time
import time
import psutil
import os

def measure_training_time_and_memory(model_type='rf'):
    """
    Measure model training time and memory usage

    Parameters:
    -----------
    model_type : str
        'rf' (Random Forest) or 'cgcnn'

    Returns:
    --------
    results : dict
        Training time, inference time, memory usage
    """
    # Get process memory usage
    process = psutil.Process(os.getpid())
    mem_before = process.memory_info().rss / (1024 ** 2)  # MB

    # Training and test data (use only Fold 1)
    train_inputs, train_outputs = task.get_train_and_val_data(task.folds[0])
    test_inputs, test_outputs = task.get_test_data(task.folds[0], include_target=True)

    if model_type == 'rf':
        # Measure Random Forest training time
        X_train = extract_magpie_features(train_inputs)
        X_test = extract_magpie_features(test_inputs)
        y_train = train_outputs.values

        # Start training
        start_train = time.time()
        rf_model = RandomForestRegressor(
            n_estimators=100,
            max_depth=30,
            random_state=42,
            n_jobs=-1
        )
        rf_model.fit(X_train, y_train)
        train_time = time.time() - start_train

        # Measure inference time
        start_infer = time.time()
        _ = rf_model.predict(X_test)
        infer_time = time.time() - start_infer

        mem_after = process.memory_info().rss / (1024 ** 2)
        memory_usage = mem_after - mem_before

    elif model_type == 'cgcnn':
        # Measure CGCNN training time
        train_data = [structure_to_pyg_data(s, t) for s, t in zip(train_inputs, train_outputs.values)]
        test_data = [structure_to_pyg_data(s, t) for s, t in zip(test_inputs, test_outputs.values)]

        train_loader = DataLoader(train_data, batch_size=32, shuffle=True)
        test_loader = DataLoader(test_data, batch_size=32, shuffle=False)

        model = CGCNNMatbench().to(device)
        optimizer = torch.optim.Adam(model.parameters(), lr=0.001)
        criterion = nn.L1Loss()

        # Start training
        start_train = time.time()
        model.train()
        for epoch in range(50):
            for batch in train_loader:
                batch = batch.to(device)
                optimizer.zero_grad()
                out = model(batch)
                loss = criterion(out, batch.y)
                loss.backward()
                optimizer.step()
        train_time = time.time() - start_train

        # Measure inference time
        model.eval()
        start_infer = time.time()
        with torch.no_grad():
            for batch in test_loader:
                batch = batch.to(device)
                _ = model(batch)
        infer_time = time.time() - start_infer

        mem_after = process.memory_info().rss / (1024 ** 2)
        memory_usage = mem_after - mem_before

    return {
        'train_time': train_time,
        'infer_time': infer_time,
        'memory_usage': memory_usage
    }

# Measure Random Forest computational cost
print("=== Measuring Random Forest Computational Cost... ===")
rf_cost = measure_training_time_and_memory('rf')

print(f"Training time:  {rf_cost['train_time']:.2f} seconds")
print(f"Inference time: {rf_cost['infer_time']:.2f} seconds")
print(f"Memory usage:   {rf_cost['memory_usage']:.2f} MB")

# Measure CGCNN computational cost (when using GPU)
print("\n=== Measuring CGCNN Computational Cost... ===")
cgcnn_cost = measure_training_time_and_memory('cgcnn')

print(f"Training time:  {cgcnn_cost['train_time']:.2f} seconds")
print(f"Inference time: {cgcnn_cost['infer_time']:.2f} seconds")
print(f"Memory usage:   {cgcnn_cost['memory_usage']:.2f} MB")

# Comparison
print("\n=== Computational Cost Comparison ===")
print(f"Training time ratio (CGCNN/RF): {cgcnn_cost['train_time'] / rf_cost['train_time']:.2f}x")
print(f"Inference time ratio (CGCNN/RF): {cgcnn_cost['infer_time'] / rf_cost['infer_time']:.2f}x")
print(f"Memory ratio (CGCNN/RF):         {cgcnn_cost['memory_usage'] / rf_cost['memory_usage']:.2f}x")

# Output example:
# === Measuring Random Forest Computational Cost... ===
# Training time:  45.32 seconds
# Inference time: 0.18 seconds
# Memory usage:   1250.45 MB
#
# === Measuring CGCNN Computational Cost... ===
# Training time:  1832.56 seconds
# Inference time: 2.34 seconds
# Memory usage:   3450.23 MB
#
# === Computational Cost Comparison ===
# Training time ratio (CGCNN/RF): 40.45x
# Inference time ratio (CGCNN/RF): 13.00x
# Memory ratio (CGCNN/RF):         2.76x

4.4.2 Visualization of Computational Cost

# Requirements:
# - Python 3.9+
# - matplotlib>=3.7.0
# - numpy>=1.24.0, <2.0.0

"""
Example: 4.4.2 Visualization of Computational Cost

Purpose: Demonstrate data visualization techniques
Target: Beginner to Intermediate
Execution time: 1-5 minutes
Dependencies: None
"""

# Visualization of computational cost comparison
import matplotlib.pyplot as plt
import numpy as np

# Prepare data
models = ['RF (Magpie)', 'CGCNN']
train_times = [45.32, 1832.56]
infer_times = [0.18, 2.34]
memory_usage = [1250.45, 3450.23]

fig, axes = plt.subplots(1, 3, figsize=(15, 5))

# Training time comparison (log scale)
axes[0].bar(models, train_times, color=['#667eea', '#764ba2'])
axes[0].set_ylabel('Training time (seconds)', fontsize=12)
axes[0].set_title('Training Time Comparison', fontsize=14, fontweight='bold')
axes[0].set_yscale('log')
for i, v in enumerate(train_times):
    axes[0].text(i, v, f'{v:.1f}s', ha='center', va='bottom', fontsize=10)

# Inference time comparison (log scale)
axes[1].bar(models, infer_times, color=['#667eea', '#764ba2'])
axes[1].set_ylabel('Inference time (seconds)', fontsize=12)
axes[1].set_title('Inference Time Comparison', fontsize=14, fontweight='bold')
axes[1].set_yscale('log')
for i, v in enumerate(infer_times):
    axes[1].text(i, v, f'{v:.2f}s', ha='center', va='bottom', fontsize=10)

# Memory usage comparison
axes[2].bar(models, memory_usage, color=['#667eea', '#764ba2'])
axes[2].set_ylabel('Memory usage (MB)', fontsize=12)
axes[2].set_title('Memory Usage Comparison', fontsize=14, fontweight='bold')
for i, v in enumerate(memory_usage):
    axes[2].text(i, v, f'{v:.1f}MB', ha='center', va='bottom', fontsize=10)

plt.tight_layout()
plt.savefig('computational_cost_comparison.png', dpi=300, bbox_inches='tight')
plt.show()

4.4.3 Summary of Computational Cost Analysis

Interpretation of Computational Cost:

• Training time: 40x difference - CGCNN requires approximately 30 minutes of training time (when using GPU). With CPU only, it could be 10-20x slower
• Inference time: 13x difference - RF is advantageous when real-time prediction is required
• Memory: 2.8x difference - CGCNN also requires additional GPU memory (approximately 2GB in this example)
• Accuracy-cost tradeoff - Whether the 40x computational time can be tolerated for a 12% accuracy improvement depends on the use case

4.5 Analysis of Data Requirements

In evaluating the practicality of machine learning models, how much training data is required is an important factor. In this section, we visualize the difference in data requirements between Random Forest and CGCNN using learning curves.

4.5.1 Concept of Learning Curves

Learning curves are graphs that plot changes in model performance as the amount of training data varies. They typically have the following characteristics:

• Small data region: Model performance strongly depends on the amount of training data and improves rapidly with increasing data
• Sufficient data region: Performance saturates and improvement from additional data becomes small
• Data-efficient models: Reach high performance with less data, with curves saturating early
• Data-inefficient models: Require more data, with late saturation of curves

4.5.2 Learning Curve Implementation

# Requirements:
# - Python 3.9+
# - matplotlib>=3.7.0
# - numpy>=1.24.0, <2.0.0

"""
Example: 4.5.2 Learning Curve Implementation

Purpose: Demonstrate data visualization techniques
Target: Advanced
Execution time: 30-60 seconds
Dependencies: None
"""

# Generation of learning curves
import numpy as np
import matplotlib.pyplot as plt
from sklearn.model_selection import learning_curve

# Training and test data (use Fold 1)
train_inputs, train_outputs = task.get_train_and_val_data(task.folds[0])
test_inputs, test_outputs = task.get_test_data(task.folds[0], include_target=True)

# Extract Magpie features
X_train = extract_magpie_features(train_inputs)
X_test = extract_magpie_features(test_inputs)
y_train = train_outputs.values
y_test = test_outputs.values

# Set training data sizes (10%, 20%, ..., 100%)
train_sizes = np.linspace(0.1, 1.0, 10)

# Learning curve for Random Forest
print("=== Calculating Learning Curve for Random Forest... ===")
rf_train_scores = []
rf_test_scores = []

for train_size in train_sizes:
    # Sample training data
    n_samples = int(len(X_train) * train_size)
    indices = np.random.choice(len(X_train), n_samples, replace=False)
    X_train_subset = X_train[indices]
    y_train_subset = y_train[indices]

    # Train model
    rf_model = RandomForestRegressor(
        n_estimators=100,
        max_depth=30,
        random_state=42,
        n_jobs=-1
    )
    rf_model.fit(X_train_subset, y_train_subset)

    # Calculate training and test errors
    train_mae = mean_absolute_error(y_train_subset, rf_model.predict(X_train_subset))
    test_mae = mean_absolute_error(y_test, rf_model.predict(X_test))

    rf_train_scores.append(train_mae)
    rf_test_scores.append(test_mae)

    print(f"Training size: {train_size*100:.0f}% ({n_samples} samples) - Train MAE: {train_mae:.4f}, Test MAE: {test_mae:.4f}")

# Learning curve for CGCNN (simplified version: only 3 points due to computational time)
print("\n=== Calculating Learning Curve for CGCNN... ===")
cgcnn_train_sizes = [0.2, 0.5, 1.0]  # 20%, 50%, 100%
cgcnn_train_scores = []
cgcnn_test_scores = []

for train_size in cgcnn_train_sizes:
    n_samples = int(len(train_inputs) * train_size)
    sampled_inputs = train_inputs[:n_samples]
    sampled_outputs = train_outputs.values[:n_samples]

    # Build graph data
    train_data = [structure_to_pyg_data(s, t) for s, t in zip(sampled_inputs, sampled_outputs)]
    test_data = [structure_to_pyg_data(s, t) for s, t in zip(test_inputs, test_outputs.values)]

    train_loader = DataLoader(train_data, batch_size=32, shuffle=True)
    test_loader = DataLoader(test_data, batch_size=32, shuffle=False)

    # CGCNN training (simplified version: 30 epochs)
    model = CGCNNMatbench().to(device)
    optimizer = torch.optim.Adam(model.parameters(), lr=0.001)
    criterion = nn.L1Loss()

    model.train()
    for epoch in range(30):
        for batch in train_loader:
            batch = batch.to(device)
            optimizer.zero_grad()
            out = model(batch)
            loss = criterion(out, batch.y)
            loss.backward()
            optimizer.step()

    # Evaluation
    model.eval()
    train_preds, train_true = [], []
    test_preds, test_true = [], []

    with torch.no_grad():
        # Training error
        for batch in train_loader:
            batch = batch.to(device)
            out = model(batch)
            train_preds.extend(out.cpu().numpy())
            train_true.extend(batch.y.cpu().numpy())

        # Test error
        for batch in test_loader:
            batch = batch.to(device)
            out = model(batch)
            test_preds.extend(out.cpu().numpy())
            test_true.extend(batch.y.cpu().numpy())

    train_mae = mean_absolute_error(train_true, train_preds)
    test_mae = mean_absolute_error(test_true, test_preds)

    cgcnn_train_scores.append(train_mae)
    cgcnn_test_scores.append(test_mae)

    print(f"Training size: {train_size*100:.0f}% ({n_samples} samples) - Train MAE: {train_mae:.4f}, Test MAE: {test_mae:.4f}")

# Visualize learning curves
fig, ax = plt.subplots(figsize=(12, 7))

# Random Forest
ax.plot(train_sizes * len(X_train), rf_test_scores, 'o-', color='#667eea', linewidth=2,
        markersize=8, label='RF (Magpie) - Test error')
ax.plot(train_sizes * len(X_train), rf_train_scores, 's--', color='#667eea', linewidth=1.5,
        markersize=6, alpha=0.5, label='RF (Magpie) - Train error')

# CGCNN
cgcnn_train_sizes_abs = [s * len(train_inputs) for s in cgcnn_train_sizes]
ax.plot(cgcnn_train_sizes_abs, cgcnn_test_scores, 'o-', color='#764ba2', linewidth=2,
        markersize=8, label='CGCNN - Test error')
ax.plot(cgcnn_train_sizes_abs, cgcnn_train_scores, 's--', color='#764ba2', linewidth=1.5,
        markersize=6, alpha=0.5, label='CGCNN - Train error')

ax.set_xlabel('Number of training samples', fontsize=12)
ax.set_ylabel('MAE (eV/atom)', fontsize=12)
ax.set_title('Learning Curve: Relationship between Training Data Size and Prediction Accuracy', fontsize=14, fontweight='bold')
ax.legend(fontsize=10)
ax.grid(alpha=0.3)

plt.tight_layout()
plt.savefig('learning_curve.png', dpi=300, bbox_inches='tight')
plt.show()

# Output example:
# === Calculating Learning Curve for Random Forest... ===
# Training size: 10% (10601 samples) - Train MAE: 0.0089, Test MAE: 0.0521
# Training size: 20% (21202 samples) - Train MAE: 0.0085, Test MAE: 0.0428
# ...
# Training size: 100% (106012 samples) - Train MAE: 0.0078, Test MAE: 0.0325
#
# === Calculating Learning Curve for CGCNN... ===
# Training size: 20% (21202 samples) - Train MAE: 0.0234, Test MAE: 0.0389
# Training size: 50% (53006 samples) - Train MAE: 0.0198, Test MAE: 0.0312
# Training size: 100% (106012 samples) - Train MAE: 0.0176, Test MAE: 0.0286

4.5.3 Interpretation of Data Requirements

Insights from learning curves:

• Small data region (<20%): Random Forest is superior. CGCNN has low performance due to insufficient training data
• Medium data region (20-50%): CGCNN performance improves rapidly and approaches RF
• Large data region (>50%): CGCNN surpasses RF, with the gap widening as data increases
• Data efficiency: RF performance saturates at around 20% of data, while CGCNN maintains an upward trend even at 100% of data

Practical implications:

• When data is limited (<10,000 samples): Random Forest (Magpie) is recommended
• When data is sufficient (>50,000 samples): CGCNN achieves high accuracy
• When data collection cost is high: A hybrid strategy is effective - start with RF in the initial stage, then migrate to CGCNN after data accumulation

4.6 Comparison of Interpretability

The interpretability of machine learning models is essential for understanding prediction rationale and improving reliability. In this section, we compare the interpretability of both methods using SHAP values for Random Forest (Magpie) and Attention mechanism for CGCNN.

4.6.1 Interpretation of Composition-based Features using SHAP Values

SHAP (SHapley Additive exPlanations) is a method that quantifies the contribution of each feature to the prediction. Based on Shapley value theory, it achieves fair distribution of contributions.

# Requirements:
# - Python 3.9+
# - shap>=0.42.0

"""
Example: SHAP (SHapley Additive exPlanations) is a method that quanti

Purpose: Demonstrate data visualization techniques
Target: Beginner to Intermediate
Execution time: 1-5 minutes
Dependencies: None
"""

# Feature importance analysis using SHAP values
import shap

# Train Random Forest model (use already trained rf_model)
# Sample a portion of test data (to reduce computational time)
X_test_sample = X_test[:100]
y_test_sample = y_test[:100]

# Calculate SHAP values
print("=== Calculating SHAP values... ===")
explainer = shap.TreeExplainer(rf_model)
shap_values = explainer.shap_values(X_test_sample)

# SHAP value summary plot
shap.summary_plot(shap_values, X_test_sample,
                  feature_names=[f'Magpie_{i}' for i in range(145)],
                  max_display=20, show=False)
plt.title('Feature Importance by SHAP Values (Random Forest + Magpie)', fontsize=14, fontweight='bold')
plt.tight_layout()
plt.savefig('shap_summary.png', dpi=300, bbox_inches='tight')
plt.show()

# Prediction interpretation for a specific sample
sample_idx = 0
print(f"\n=== Prediction Interpretation for Sample {sample_idx} ===")
print(f"True value: {y_test_sample[sample_idx]:.4f} eV/atom")
print(f"Predicted:  {rf_model.predict(X_test_sample[sample_idx:sample_idx+1])[0]:.4f} eV/atom")

# SHAP Force Plot (interpretation of individual samples)
shap.force_plot(explainer.expected_value,
                shap_values[sample_idx],
                X_test_sample[sample_idx],
                feature_names=[f'Magpie_{i}' for i in range(145)],
                matplotlib=True, show=False)
plt.savefig('shap_force_plot.png', dpi=300, bbox_inches='tight')
plt.show()

# Display top 10 important features
feature_importance = np.abs(shap_values).mean(axis=0)
top_features = np.argsort(feature_importance)[-10:][::-1]

print("\n=== Top 10 Important Features ===")
for i, feat_idx in enumerate(top_features):
    print(f"{i+1}. Magpie_{feat_idx}: SHAP importance = {feature_importance[feat_idx]:.4f}")

# Output example:
# === Top 10 Important Features ===
# 1. Magpie_34: SHAP importance = 0.0087  # Average electronegativity
# 2. Magpie_12: SHAP importance = 0.0065  # Average atomic radius
# 3. Magpie_78: SHAP importance = 0.0054  # Std dev of valence electrons
# ...

4.6.2 GNN Interpretation using Attention Mechanism

In CGCNN, Attention mechanisms can be used to visualize atom-atom interactions important for prediction (strictly speaking, standard CGCNN doesn't have Attention, so comparison with Attention-based GNNs like GAT is more appropriate, but here we visualize CGCNN convolution weights for educational purposes).

# Requirements:
# - Python 3.9+
# - matplotlib>=3.7.0
# - torch>=2.0.0, <2.3.0

"""
Example: Standard CGCNN does not have an Attention mechanism, so inte

Purpose: Demonstrate data visualization techniques
Target: Advanced
Execution time: 2-5 seconds
Dependencies: None
"""

# CGCNN activation visualization (simplified version)
import torch
import matplotlib.pyplot as plt
from pymatgen.core import Structure

# Extract 1 sample from test data
sample_structure = test_inputs[0]
sample_target = test_outputs.values[0]

# Convert to PyTorch Geometric data
sample_data = structure_to_pyg_data(sample_structure, sample_target).to(device)

# Predict with CGCNN (get intermediate layer activations)
model.eval()
with torch.no_grad():
    # Initialize node features
    x = sample_data.x
    x = model.atom_embedding(x)

    # Record activations from each convolution layer
    activations = []
    for conv, bn in zip(model.conv_layers, model.bn_layers):
        x = conv(x, sample_data.edge_index, sample_data.edge_attr)
        x = bn(x)
        x = model.activation(x)
        activations.append(x.cpu().numpy())

    # Final prediction
    x = global_mean_pool(x.unsqueeze(0), torch.zeros(x.size(0), dtype=torch.long))
    prediction = model.fc2(model.activation(model.fc1(x))).item()

print(f"=== CGCNN Prediction Interpretation ===")
print(f"True value: {sample_target:.4f} eV/atom")
print(f"Predicted:  {prediction:.4f} eV/atom")

# Visualize activation for each atom
fig, axes = plt.subplots(1, 3, figsize=(15, 5))

for layer_idx, activation in enumerate(activations):
    # Calculate average activation for each atom
    atom_importance = activation.mean(axis=1)

    # Get atom types
    atom_types = [site.specie.symbol for site in sample_structure]

    # Plot importance for each atom
    axes[layer_idx].bar(range(len(atom_types)), atom_importance)
    axes[layer_idx].set_xlabel('Atom index', fontsize=12)
    axes[layer_idx].set_ylabel('Average activation', fontsize=12)
    axes[layer_idx].set_title(f'Convolution Layer {layer_idx+1}', fontsize=12, fontweight='bold')
    axes[layer_idx].set_xticks(range(len(atom_types)))
    axes[layer_idx].set_xticklabels(atom_types, rotation=45)

plt.tight_layout()
plt.savefig('cgcnn_activation.png', dpi=300, bbox_inches='tight')
plt.show()

print("\nImportance of each atom (Layer 3 activation):")
for i, (atom_type, importance) in enumerate(zip(atom_types, activations[-1].mean(axis=1))):
    print(f"{i+1}. {atom_type}: {importance:.4f}")

4.6.3 Summary of Interpretability Comparison

Practical selection:

• Composition-level insights needed (e.g., which elements are important) → Random Forest + SHAP
• Structure-level insights needed (e.g., which atom-atom interactions are important) → CGCNN + GAT/GNNExplainer
• Explanation to domain experts → SHAP values are more intuitive
• Detailed analysis for research purposes → GNN Attention mechanisms are useful

4.7 Decision Flowchart for Method Selection

We integrate the quantitative comparison results from this chapter and construct a decision flowchart to support practical method selection using Mermaid.

4.7.1 Usage Guide for Decision Flowchart

Details of each decision point:

1. Evaluation of Training Data Size
   • <10,000 samples: Random Forest performs stably and well (insights from learning curves)
   • 10,000-50,000 samples: Choose according to computational resources
   • >50,000 samples: CGCNN superiority is significant
2. Confirmation of Computational Resources
   • GPU available: CGCNN training time reduced to about 30 minutes
   • CPU only: CGCNN training time may take 5-10 hours
3. Accuracy vs Speed Tradeoff
   • Evaluate the value of 12% MAE improvement vs the cost of 40x training time
   • Check if 13x difference in inference speed affects real-time prediction
4. Verification of Statistical Significance
   • Perform paired t-test with 5-fold cross-validation
   • Confirm p-value<0.05 and 95% confidence interval does not include 0
5. Interpretability Requirements
   • SHAP values: Composition-level insights (which element properties are important)
   • Attention/GNNExplainer: Structure-level insights (which atom-atom interactions are important)

4.8 Chapter Summary

In this chapter, we quantitatively compared Random Forest (Magpie) and CGCNN from 7 perspectives using the Matbench benchmark.

Key Findings

Practical Recommendations

Exercises

# Requirements:
# - Python 3.9+
# - numpy>=1.24.0, <2.0.0
# - scipy>=1.11.0

"""
Example: Answer:

Purpose: Demonstrate core concepts and implementation patterns
Target: Beginner to Intermediate
Execution time: ~5 seconds
Dependencies: None
"""

import numpy as np
from scipy import stats

mae_diff = np.array([0.003, 0.004, 0.003, 0.005, 0.004])
mean_diff = mae_diff.mean()  # 0.00380
std_diff = mae_diff.std(ddof=1)  # 0.00084
se_diff = std_diff / np.sqrt(len(mae_diff))  # 0.00037
t_critical = 2.776

margin_error = t_critical * se_diff  # 0.00104
ci_lower = mean_diff - margin_error  # 0.00276
ci_upper = mean_diff + margin_error  # 0.00484

print(f"95% CI: [{ci_lower:.5f}, {ci_upper:.5f}] eV/atom")
# Output: 95% CI: [0.00276, 0.00484] eV/atom

# Comparison of monthly computational time
# Random Forest
rf_train_time = 45  # sec/month
rf_infer_time = 0.18 * 10 * 30  # 0.18 sec/1000 samples × 10 × 30 days
rf_total = rf_train_time + rf_infer_time
print(f"RF monthly total: {rf_total:.1f}sec = {rf_total/60:.2f}min")

# CGCNN
cgcnn_train_time = 1833  # sec/month
cgcnn_infer_time = 2.34 * 10 * 30
cgcnn_total = cgcnn_train_time + cgcnn_infer_time
print(f"CGCNN monthly total: {cgcnn_total:.1f}sec = {cgcnn_total/60:.2f}min")

print(f"\nTime ratio (CGCNN/RF): {cgcnn_total/rf_total:.2f}x")

# Output:
# RF monthly total: 99.0sec = 1.65min
# CGCNN monthly total: 2535.0sec = 42.25min
# Time ratio (CGCNN/RF): 25.61x

# Requirements:
# - Python 3.9+
# - matplotlib>=3.7.0
# - numpy>=1.24.0, <2.0.0
# - shap>=0.42.0

"""
Example: Answer:

Purpose: Demonstrate data visualization techniques
Target: Beginner to Intermediate
Execution time: 30-60 seconds
Dependencies: None
"""

import shap
import numpy as np

# Train Random Forest model (assume Exercise 2 code example is used)
# Assume X_train, y_train, X_test, y_test are already prepared

# Train Random Forest
rf_model = RandomForestRegressor(
    n_estimators=100,
    max_depth=30,
    random_state=42,
    n_jobs=-1
)
rf_model.fit(X_train, y_train)

# Calculate SHAP values (50 test samples)
X_test_sample = X_test[:50]
explainer = shap.TreeExplainer(rf_model)
shap_values = explainer.shap_values(X_test_sample)

# Calculate mean absolute SHAP value for each feature
mean_abs_shap = np.abs(shap_values).mean(axis=0)

# Indices of top 5 important features
top_5_indices = np.argsort(mean_abs_shap)[-5:][::-1]

# Magpie feature name mapping (partial examples)
magpie_names = {
    34: "Average electronegativity",
    12: "Average atomic radius",
    78: "Std dev of valence electrons",
    # ... define other feature names
}

print("=== Top 5 Important Features (SHAP Values) ===")
for rank, feat_idx in enumerate(top_5_indices, 1):
    feat_name = magpie_names.get(feat_idx, f"Magpie_{feat_idx}")
    shap_importance = mean_abs_shap[feat_idx]
    print(f"{rank}. {feat_name} (Index {feat_idx}): SHAP importance = {shap_importance:.4f}")

# Visualization
import matplotlib.pyplot as plt
plt.figure(figsize=(10, 6))
plt.barh(range(5), mean_abs_shap[top_5_indices][::-1], color='#764ba2')
plt.yticks(range(5), [magpie_names.get(i, f"Magpie_{i}") for i in top_5_indices][::-1])
plt.xlabel('Mean Absolute SHAP Value', fontsize=12)
plt.title('Top 5 Important Features (by SHAP Values)', fontsize=14, fontweight='bold')
plt.tight_layout()
plt.savefig('top5_features_shap.png', dpi=300, bbox_inches='tight')
plt.show()

# Output example:
# === Top 5 Important Features (SHAP Values) ===
# 1. Average electronegativity (Index 34): SHAP importance = 0.0087
# 2. Average atomic radius (Index 12): SHAP importance = 0.0065
# 3. Std dev of valence electrons (Index 78): SHAP importance = 0.0054
# 4. Magpie_45: SHAP importance = 0.0048
# 5. Magpie_89: SHAP importance = 0.0042

References

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