Add illustration for creating and vanishing MI with mixtures

scripts/Mixtures/plot_appearing_and_vanishing_mi.py

@@ -0,0 +1,59 @@
+"""Appearing and vanishing mutual information illustration."""
+import matplotlib.pyplot as plt
+import numpy as np
+
+
+def plot_density(ax: plt.Axes, array: np.ndarray, title: str) -> None:
+    """Plots density in `array` on `ax`."""
+    ax.imshow(array, origin="lower", extent=[0, 2, 0, 2], cmap="Blues", vmin=0, vmax=1)
+    ax.set_xticks([])
+    ax.set_yticks([])
+    ax.set_xlabel("$x$")
+    ax.set_ylabel("$y$")
+    ax.set_title(title)
+
+
+def main() -> None:
+    x = np.linspace(0, 2)
+    y = np.linspace(0, 2)
+
+    X, Y = np.meshgrid(x, y)
+
+    fig, axs = plt.subplots(2, 3, dpi=300)
+
+    # First row: appearing MI
+    # Component 1 (bottom left)
+    ax = axs[0, 0]
+    mask1 = (0 < X) & (X < 1) & (0 < Y) & (Y < 1)
+    plot_density(ax, mask1, "$I=0$")
+
+    # Component 2 (top right)
+    ax = axs[0, 1]
+    mask2 = (1 < X) & (X < 2) & (1 < Y) & (Y < 2)
+    plot_density(ax, mask2, "$I=0$")
+
+    # Mixture
+    ax = axs[0, 2]
+    mask3 = mask1 | mask2
+    plot_density(ax, 0.5 * mask3, "$I=\\log 2$")
+
+    # Second row
+    # Component 1: mixture from first row
+    ax = axs[1, 0]
+    plot_density(ax, 0.5 * mask3, "$I=\\log 2$")
+
+    # Component 2: symmetric mixture
+    ax = axs[1, 1]
+    mask4 = (0 < X) & (X < 1) & (1 < Y) & (Y < 2) | (1 < X) & (X < 2) & (0 < Y) & (Y < 1)
+    plot_density(ax, 0.5 * mask4, "$I=\\log 2$")
+
+    # Mixture: independent
+    ax = axs[1, 2]
+    plot_density(ax, 0.25 * (mask3 | mask4), "$I=0$")
+
+    fig.tight_layout()
+    fig.savefig("appearing_and_vanishing_mi.pdf")
+
+
+if __name__ == "__main__":
+    main()