Dyn_corr

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Thu May  8 20:21:13 2025

@author: fvera
"""
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from scipy.stats import pearsonr
import matplotlib.pyplot as plt
import pandas as pd

# Simulate dynamic ground-truth adjacency matrices (OU process)
def generate_dynamic_adjacency(N, T, tau=20, sigma=0.05):
    A = np.zeros((T, N, N))
    A[0] = np.random.rand(N, N) * 0.1
    for t in range(1, T):
        dA = -(A[t-1] - A[0]) / tau + sigma * np.random.randn(N, N)
        A[t] = A[t-1] + dA
        A[t] = np.clip(A[t], 0, 1)
    return A

# Simulate DyGAT-predicted adjacency matrices with noise
def simulate_prediction(A_true, noise_level=0.1):
    return np.clip(A_true + np.random.randn(*A_true.shape) * noise_level, 0, 1)

# Compute edge-wise Pearson correlations
def edge_correlations(A_true, A_pred):
    T, N, _ = A_true.shape
    corrs = []
    for i in range(N):
        for j in range(N):
            if i != j:
                r, _ = pearsonr(A_true[:, i, j], A_pred[:, i, j])
                corrs.append(r)
    return np.mean(corrs), corrs

# Parameters
N, T = 100, 300
A_true = generate_dynamic_adjacency(N, T)
A_pred = simulate_prediction(A_true)

# Correlation computation
mean_r, all_r = edge_correlations(A_true, A_pred)

# Plot
plt.figure(figsize=(8, 5))
sns.histplot(all_r, kde=True, bins=30, color='royalblue')
plt.axvline(mean_r, color='red', linestyle='--', label=f'Mean ρ = {mean_r:.2f}')
plt.xlabel('Pearson Correlation (ρ)')
plt.ylabel('Edge Count')
plt.title('Edge-wise Correlation Between True and Predicted Dynamics')
plt.legend()
plt.tight_layout()
plt.savefig("dyn_corr.png")
plt.show()


def generate_synthetic_dygat_data(N=50, T=100, noise_std=0.05, seed=42):
    np.random.seed(seed)
    A_true = np.zeros((N, N, T))
    for i in range(N):
        for j in range(N):
            if i != j:
                x = np.zeros(T)
                for t in range(1, T):
                    x[t] = 0.9 * x[t-1] + 0.05 * np.random.randn()
                A_true[i, j, :] = np.tanh(x)
    alpha_pred = A_true + noise_std * np.random.randn(N, N, T)
    return A_true, alpha_pred

# Generate synthetic data
A_true, alpha_pred = generate_synthetic_dygat_data()

# Compute edge-wise correlation
N, _, T = A_true.shape
correlations = []
for i in range(N):
    for j in range(N):
        if i != j:
            corr, _ = pearsonr(A_true[i, j, :], alpha_pred[i, j, :])
            correlations.append(corr)

# Plot the correlation histogram
plt.figure(figsize=(8, 5))
plt.hist(correlations, bins=30, color='steelblue', edgecolor='black', alpha=0.7)
plt.axvline(np.mean(correlations), color='red', linestyle='--', label=f"Mean ρ = {np.mean(correlations):.3f}")
plt.xlabel("Pearson Correlation per Edge")
plt.ylabel("Count")
plt.title("Distribution of Edge-wise Temporal Correlation (DyGAT Simulation)")
plt.legend()
plt.grid(True)
plt.tight_layout()
plt.show()

mean_correlation = np.mean(correlations)
mean_correlation


stats = pd.Series(correlations).describe()
print(stats[['mean', 'std', 'min', 'max']])