Add plot to compare noise-free and noisy sigma

BLcourse2.3/gp_intro.py

@@ -324,7 +324,10 @@ with torch.no_grad():
     post_pred_y = likelihood(model(X_pred))
 
     fig, axs = plt.subplots(ncols=2, figsize=(12, 5))
-    for ii, (ax, post_pred) in enumerate(zip(axs, [post_pred_f, post_pred_y])):
+    fig_sigmas, ax_sigmas = plt.subplots()
+    for ii, (ax, post_pred, name) in enumerate(
+        zip(axs, [post_pred_f, post_pred_y], ["f", "y"])
+    ):
         yf_mean = post_pred.mean
         yf_samples = post_pred.sample(sample_shape=torch.Size((10,)))
 
@@ -354,6 +357,23 @@ with torch.no_grad():
             color="tab:orange",
             alpha=0.3,
         )
+        if name == "f":
+            sigma_label = r"$\pm 2\sqrt{\mathrm{diag}(\Sigma)}$"
+            zorder = 1
+        else:
+            sigma_label = (
+                r"$\pm 2\sqrt{\mathrm{diag}(\Sigma + \sigma_n^2\,I)}$"
+            )
+            zorder = 0
+        ax_sigmas.fill_between(
+            X_pred.numpy(),
+            lower.numpy(),
+            upper.numpy(),
+            label="confidence " + sigma_label,
+            color="tab:orange" if name == "f" else "tab:blue",
+            alpha=0.5,
+            zorder=zorder,
+        )
         y_min = y_train.min()
         y_max = y_train.max()
         y_span = y_max - y_min
@@ -361,6 +381,7 @@ with torch.no_grad():
         plot_samples(ax, X_pred, yf_samples, label="posterior pred. samples")
         if ii == 1:
             ax.legend()
+    ax_sigmas.legend()
 
 # When running as script
 if not is_interactive():