Repository: scikit-learn/scikit-learn
File: examples/semi_supervised/plot_semi_supervised_versus_svm_iris.py (Python)

Code before:
# We observe that the decision boundaries are already quite similar to those
# using the full labeled data available for training, even when using a very
# small subset of the labels.
#
# Interpretation of `predict_proba`
# =================================
#
# `predict_proba` in `LabelSpreading`
# -----------------------------------
#
# :class:`~sklearn.semi_supervised.LabelSpreading` constructs a similarity graph
# from the data, by default using an RBF kernel. This means each sample is
# connected to every other with a weight that decays with their squared
# Euclidean distance, scaled by a parameter `gamma`.
#
# Once you have that weighted graph, labels are propagated along the graph
# edges. Each sample gradually takes on a soft label distribution that reflects
# a weighted average of the labels of its neighbors until the process converges.
# These per-sample distributions are stored in `label_distributions_`.
#
# `predict_proba` computes the class probabilities for a new point by taking a
# weighted average of the rows in `label_distributions_`, where the weights come
# from the RBF kernel similarities between the new point and the training
# samples. The averaged values are then renormalized so that they sum to one.
#
# Just keep into account that these "probabilities" are graph-based scores, not
# calibrated posteriors. Don't over-interpret their absolute values.

from sklearn.metrics.pairwise import rbf_kernel

ls = ls100[0]  # fitted LabelSpreading instance
x_query = np.array([3.5, 1.5]).reshape(1, -1)  # point in the soft blue region

# Step 1: similarities between query and all training samples
W = rbf_kernel(x_query, X, gamma=ls.gamma)  # `gamma=20` by default

# Step 2: weighted average of label distributions
probs = np.dot(W, ls.label_distributions_)

# Step 3: normalize to sum to 1
probs /= probs.sum(axis=1, keepdims=True)

print("Manual:", probs)
print("API   :", ls.predict_proba(x_query))

# %%
# `predict_proba` in `SelfTrainingClassifier`
# ----------------------------------------------
#
# :class:`~sklearn.semi_supervised.SelfTrainingClassifier` works by repeatedly
# fitting its base estimator on the currently labeled data, then adding

Review comment (suggestion):
```suggestion
# Just keep in mind that these "probabilities" are graph-based scores, not
```

I think it is either "to take into account" or "to keep in mind".

Code after:
        response_method="predict_proba",
        plot_method="contourf",
        ax=ax,
    )
    colors = [color_map[label] for label in y_train]
    ax.scatter(X[:, 0], X[:, 1], c=colors, edgecolor="black")
    ax.set_title(title)
fig.suptitle(
    "Semi-supervised decision boundaries with varying fractions of labeled data", y=1
)
fig.legend(
    handles=handles, loc="lower center", ncol=len(handles), bbox_to_anchor=(0.5, 0.0)
)
fig.tight_layout(rect=[0, 0.03, 1, 1])
plt.show()

# %%
# We observe that the decision boundaries are already quite similar to those
# using the full labeled data available for training, even when using a very
# small subset of the labels.
#
# Interpretation of `predict_proba`
# =================================
#
# `predict_proba` in `LabelSpreading`
# -----------------------------------
#
# :class:`~sklearn.semi_supervised.LabelSpreading` constructs a similarity graph
# from the data, by default using an RBF kernel. This means each sample is
# connected to every other with a weight that decays with their squared
# Euclidean distance, scaled by a parameter `gamma`.
#
# Once we have that weighted graph, labels are propagated along the graph
# edges. Each sample gradually takes on a soft label distribution that reflects
# a weighted average of the labels of its neighbors until the process converges.
# These per-sample distributions are stored in `label_distributions_`.
#
# `predict_proba` computes the class probabilities for a new point by taking a
# weighted average of the rows in `label_distributions_`, where the weights come
# from the RBF kernel similarities between the new point and the training
# samples. The averaged values are then renormalized so that they sum to one.
#
# Just keep in mind that these "probabilities" are graph-based scores, not
# calibrated posteriors. Don't over-interpret their absolute values.

from sklearn.metrics.pairwise import rbf_kernel

ls = ls100[0]  # fitted LabelSpreading instance
x_query = np.array([[3.5, 1.5]])  # point in the soft blue region

# Step 1: similarities between query and all training samples