FOCISelector: T_n progression

This example fits the FOCISelector on synthetic data and plots the cumulative T_n values along the selection path.

import matplotlib.pyplot as plt
import numpy as np

from pyFOCI import FOCISelector

random_state = np.random.RandomState(0)
n, p = 1000, 30
X = random_state.normal(size=(n, p))

# Additive signal across multiple features
# -> incremental improvements with each addition
y = (
    np.sin(2.0 * X[:, 0])
    + X[:, 1]
    + (X[:, 2] ** 2 - 1.0)
    + np.tanh(X[:, 3])
    + (X[:, 4] > 0).astype(float)
    + 0.1 * random_state.normal(size=n)  # small noise
)

selector = FOCISelector(max_features=6, random_state=0)
selector.fit(X, y)

feat_idx = list(selector.selected_indices_)
Tn_vals = list(selector.Tn_path_)

# Labels: directly prepend "x" to the indices
labels = [f"step {i+1}: x{j}" for i, j in enumerate(feat_idx)]

m = len(Tn_vals)
plt.figure(figsize=(8, 4))
plt.bar(range(m), Tn_vals, color="tab:orange", edgecolor="black", linewidth=0.5)
plt.title("FOCISelector: cumulative T_n over selection steps")
plt.ylabel("T_n(S_k)")
plt.xlabel("Selection steps")
plt.xticks(ticks=range(m), labels=labels, rotation=45, ha="right", fontsize=9)
plt.tight_layout()
plt.show()