plot_piecewise_classification.py

"""
Piecewise classification with scikit-learn predictors
=====================================================

Piecewise regression is easier to understand but the concept can be
extended to classification. That's what this notebook explores.



Iris dataset and first logistic regression
------------------------------------------
"""

import matplotlib.pyplot as plt
import seaborn
import numpy
import pandas
from sklearn import datasets
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression
from sklearn.dummy import DummyClassifier
from sklearn.preprocessing import KBinsDiscretizer
from sklearn.metrics import auc, roc_curve
from mlinsights.mlmodel import PiecewiseClassifier

iris = datasets.load_iris()
X = iris.data[:, :2]  # we only take the first two features.
Y = iris.target
X_train, X_test, y_train, y_test = train_test_split(X, Y)

########################################
#


def graph(X, Y, model):
    x_min, x_max = X[:, 0].min() - 0.5, X[:, 0].max() + 0.5
    y_min, y_max = X[:, 1].min() - 0.5, X[:, 1].max() + 0.5
    h = 0.02  # step size in the mesh
    xx, yy = numpy.meshgrid(
        numpy.arange(x_min, x_max, h), numpy.arange(y_min, y_max, h)
    )
    Z = model.predict(numpy.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)

    # Put the result into a color plot
    _fig, ax = plt.subplots(1, 1, figsize=(4, 3))
    ax.pcolormesh(xx, yy, Z, cmap=plt.cm.Paired)

    # Plot also the training points
    ax.scatter(X[:, 0], X[:, 1], c=Y, edgecolors="k", cmap=plt.cm.Paired)
    ax.set_xlabel("Sepal length")
    ax.set_ylabel("Sepal width")

    ax.set_xlim(xx.min(), xx.max())
    ax.set_ylim(yy.min(), yy.max())
    ax.set_xticks(())
    ax.set_yticks(())
    return ax


logreg = LogisticRegression()
logreg.fit(X_train, y_train)
ax = graph(X_test, y_test, logreg)
ax.set_title("LogisticRegression")


######################################################################
# Piecewise classication
# ----------------------


dummy = DummyClassifier(strategy="most_frequent")
piece4 = PiecewiseClassifier(KBinsDiscretizer(n_bins=2), estimator=dummy, verbose=True)
piece4.fit(X_train, y_train)


######################################################################
# We look into the bucket given to each point.


bucket = piece4.transform_bins(X_test)
df = pandas.DataFrame(X_test, columns=("x1", "x2"))
df["bucket"] = bucket
df["label"] = y_test
df = df.set_index(bucket)
df.head(n=5)

########################################
#


ax = seaborn.scatterplot(x="x1", y="x2", hue="bucket", data=df, palette="Set1", s=400)
seaborn.scatterplot(
    x="x1", y="x2", hue="label", data=df, palette="Set1", marker="o", ax=ax, s=100
)
ax.set_title("buckets")


######################################################################
# We see there are four buckets. Two buckets only contains one label. The
# dummy classifier maps every bucket to the most frequent class in the
# bucket.


ax = graph(X_test, y_test, piece4)
ax.set_title("Piecewise Classification\n4 buckets")


######################################################################
# We can increase the number of buckets.


dummy = DummyClassifier(strategy="most_frequent")
piece9 = PiecewiseClassifier(KBinsDiscretizer(n_bins=3), estimator=dummy, verbose=True)
piece9.fit(X_train, y_train)

########################################
#


ax = graph(X_test, y_test, piece9)
ax.set_title("Piecewise Classification\n9 buckets")


######################################################################
# Let's compute the ROC curve.


def plot_roc_curve(models, X, y):
    if not isinstance(models, dict):
        return plot_roc_curve({models.__class__.__name__: models}, X, y)

    ax = None
    colors = "bgrcmyk"
    for ic, (name, model) in enumerate(models.items()):
        fpr, tpr, roc_auc = dict(), dict(), dict()
        nb = len(model.classes_)
        y_score = model.predict_proba(X)
        for i in range(nb):
            c = model.classes_[i]
            fpr[i], tpr[i], _ = roc_curve(y_test == c, y_score[:, i])
            roc_auc[i] = auc(fpr[i], tpr[i])

        if ax is None:
            lw = 2
            _, ax = plt.subplots(1, nb, figsize=(4 * nb, 4))
            for i in range(nb):
                ax[i].plot([0, 1], [0, 1], color="navy", lw=lw, linestyle="--")
        plotname = "".join(c for c in name if "A" <= c <= "Z" or "0" <= c <= "9")
        for i in range(nb):
            ax[i].plot(
                fpr[i],
                tpr[i],
                color=colors[ic],
                lw=lw,
                label="%0.2f %s" % (roc_auc[i], plotname),
            )
            ax[i].set_title("class {}".format(model.classes_[i]))
    for k in range(ax.shape[0]):
        ax[k].legend()
    return ax


plot_roc_curve({"LR": logreg, "P4": piece4, "P9": piece9}, X_test, y_test)


######################################################################
# Let's use the decision tree to create buckets.


dummy = DummyClassifier(strategy="most_frequent")
pieceT = PiecewiseClassifier("tree", estimator=dummy, verbose=True)
pieceT.fit(X_train, y_train)

########################################
#


ax = graph(X_test, y_test, pieceT)
ax.set_title("Piecewise Classification\n%d buckets (tree)" % len(pieceT.estimators_))

########################################
#

plot_roc_curve({"LR": logreg, "P4": piece4, "P9": piece9, "DT": pieceT}, X_test, y_test)