Refactor bayesian neural network example (#670)

- Improve axis labels
- Remove `mutable=True` argument (will get deprecated)
- Fix shape warning
- Fix minibatch sampling issue (cf. #654)

Author: ElisabethBrockhausQC

examples/variational_inference/bayesian_neural_network_advi.ipynb

@@ -69,7 +69,6 @@ import matplotlib.pyplot as plt
 import numpy as np
 import pymc as pm
 import pytensor
-import pytensor.tensor as pt
 import seaborn as sns
 
 from sklearn.datasets import make_moons
@@ -103,7 +102,7 @@ ax.scatter(X[Y == 0, 0], X[Y == 0, 1], color="C0", label="Class 0")
 ax.scatter(X[Y == 1, 0], X[Y == 1, 1], color="C1", label="Class 1")
 sns.despine()
 ax.legend()
-ax.set(xlabel="X", ylabel="Y", title="Toy binary classification data set");
+ax.set(xlabel="X1", ylabel="X2", title="Toy binary classification data set");
 ```
 
 ### Model specification
@@ -127,11 +126,11 @@ def construct_nn(ann_input, ann_output):
         "hidden_layer_1": np.arange(n_hidden),
         "hidden_layer_2": np.arange(n_hidden),
         "train_cols": np.arange(X_train.shape[1]),
-        # "obs_id": np.arange(X_train.shape[0]),
+        "obs_id": np.arange(X_train.shape[0]),
     }
     with pm.Model(coords=coords) as neural_network:
-        ann_input = pm.Data("ann_input", X_train, mutable=True, dims=("obs_id", "train_cols"))
-        ann_output = pm.Data("ann_output", Y_train, mutable=True, dims="obs_id")
+        ann_input = pm.Data("ann_input", X_train, dims=("obs_id", "train_cols"))
+        ann_output = pm.Data("ann_output", Y_train, dims="obs_id")
 
         # Weights from input to hidden layer
         weights_in_1 = pm.Normal(
@@ -215,14 +214,15 @@ pred = ppc.posterior_predictive["out"].mean(("chain", "draw")) > 0.5
 
 ```{code-cell} ipython3
 fig, ax = plt.subplots()
-ax.scatter(X_test[pred == 0, 0], X_test[pred == 0, 1], color="C0")
-ax.scatter(X_test[pred == 1, 0], X_test[pred == 1, 1], color="C1")
+ax.scatter(X_test[pred == 0, 0], X_test[pred == 0, 1], color="C0", label="Predicted 0")
+ax.scatter(X_test[pred == 1, 0], X_test[pred == 1, 1], color="C1", label="Predicted 1")
 sns.despine()
-ax.set(title="Predicted labels in testing set", xlabel="X", ylabel="Y");
+ax.legend()
+ax.set(title="Predicted labels in testing set", xlabel="X1", ylabel="X2");
 ```
 
 ```{code-cell} ipython3
-print(f"Accuracy = {(Y_test == pred.values).mean() * 100}%")
+print(f"Accuracy = {(Y_test == pred.values).mean() * 100:.2f}%")
 ```
 
 Hey, our neural network did all right!
@@ -240,16 +240,21 @@ jupyter:
 ---
 grid = pm.floatX(np.mgrid[-3:3:100j, -3:3:100j])
 grid_2d = grid.reshape(2, -1).T
-dummy_out = np.ones(grid.shape[1], dtype=np.int8)
+dummy_out = np.ones(grid_2d.shape[0], dtype=np.int8)
 ```
 
 ```{code-cell} ipython3
 ---
 jupyter:
   outputs_hidden: true
 ---
+coords_eval = {
+    "train_cols": np.arange(grid_2d.shape[1]),
+    "obs_id": np.arange(grid_2d.shape[0]),
+}
+
 with neural_network:
-    pm.set_data(new_data={"ann_input": grid_2d, "ann_output": dummy_out})
+    pm.set_data(new_data={"ann_input": grid_2d, "ann_output": dummy_out}, coords=coords_eval)
     ppc = pm.sample_posterior_predictive(trace)
 ```
 
@@ -268,7 +273,7 @@ contour = ax.contourf(
 ax.scatter(X_test[pred == 0, 0], X_test[pred == 0, 1], color="C0")
 ax.scatter(X_test[pred == 1, 0], X_test[pred == 1, 1], color="C1")
 cbar = plt.colorbar(contour, ax=ax)
-_ = ax.set(xlim=(-3, 3), ylim=(-3, 3), xlabel="X", ylabel="Y")
+_ = ax.set(xlim=(-3, 3), ylim=(-3, 3), xlabel="X1", ylabel="X2")
 cbar.ax.set_ylabel("Posterior predictive mean probability of class label = 0");
 ```
 
@@ -285,7 +290,7 @@ contour = ax.contourf(
 ax.scatter(X_test[pred == 0, 0], X_test[pred == 0, 1], color="C0")
 ax.scatter(X_test[pred == 1, 0], X_test[pred == 1, 1], color="C1")
 cbar = plt.colorbar(contour, ax=ax)
-_ = ax.set(xlim=(-3, 3), ylim=(-3, 3), xlabel="X", ylabel="Y")
+_ = ax.set(xlim=(-3, 3), ylim=(-3, 3), xlabel="X1", ylabel="X2")
 cbar.ax.set_ylabel("Uncertainty (posterior predictive standard deviation)");
 ```
 
@@ -300,8 +305,7 @@ So far, we have trained our model on all data at once. Obviously this won't scal
 Fortunately, ADVI can be run on mini-batches as well. It just requires some setting up:
 
 ```{code-cell} ipython3
-minibatch_x = pm.Minibatch(X_train, batch_size=50)
-minibatch_y = pm.Minibatch(Y_train, batch_size=50)
+minibatch_x, minibatch_y = pm.Minibatch(X_train, Y_train, batch_size=50)
 neural_network_minibatch = construct_nn(minibatch_x, minibatch_y)
 with neural_network_minibatch:
     approx = pm.fit(40000, method=pm.ADVI())