understand how this lambda function works

Question

I thought I understood how lambda functions work, though I don't use them myself. But the lambda below from this tutorial totally stumps me:

import matplotlib.pyplot as plt
import numpy as np
import sklearn
import sklearn.datasets
import sklearn.linear_model
import matplotlib

That was easy. More:

# Generate a dataset and plot it
np.random.seed(0)
X, y = sklearn.datasets.make_moons(200, noise=0.20)
plt.scatter(X[:,0], X[:,1], s=40, c=y, cmap=plt.cm.Spectral)
clf = sklearn.linear_model.LogisticRegressionCV()
clf.fit(X, y)

# Helper function to plot a decision boundary.
# If you don't fully understand this function don't worry, it just generates the contour plot below.

def plot_decision_boundary(pred_func):

    # Set min and max values and give it some padding
    x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5
    y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5
    h = 0.01

    # Generate a grid of points with distance h between them
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))

    # Predict the function value for the whole gid
    Z = pred_func(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)

    # Plot the contour and training examples
    plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
    plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Spectral)

Now the line I don't understand:

plot_decision_boundary(lambda x: clf.predict(x))

I've read many times how lambdas work, but I just don't get how the x here passing the correct values from before. How is the x mapped to the relevant values?

Answer 1

lambdas are just anonymous functions. lambda bodies can only be an expression (as subset of what you can put into a function) because they have to fit inline with other code.

plot_decision_boundary(lambda x: clf.predict(x)) could be rewritten as

def call_clf_predict(x):
    return clf.predict(x)
plot_decision_boundary(call_clf_predict)

Here, its more clear what is going on. plot_decision_boundary gets a callable and calls it with the single parameter np.c_[xx.ravel(), yy.ravel()].

But lambda shouldn't have been used here in the first place. You could just do

plot_decision_boundary(clf.predict)

In the grand tradition of python tutorials, lambda is abused once again.

Answer 2

plot_decision_boundary(lambda x: clf.predict(x))

This line is passing a function that takes a single argument into the method. When the lambda is evaluated, or the method is "called" with an argument x, it'll do clf.predict(x)

Within the method, that function is named pred_func and it is called with its single argument at

Z = pred_func(np.c_[xx.ravel(), yy.ravel()])

So the code that is ran is

Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])