classifying-using-logarithmic-regression.py

"""
Logarithmic regression solves a different problem to ordinary linear regression.
It is commonly used for classification problems where, typically, we wish to
classify data into two distinct groups, according to a number of predictor
variables. Underlying this technique is a transformation that's performed using
logarithms. The original classification problem is transformed into a problem of
constructing a model for the log-odds. This model can be completed with simple
linear regression. We apply the inverse transformation to the linear model,
which leaves us with a model of the probability that the desired outcome will
occur, given the predictor data. The transform we apply here is called the
logistic function, which gives its name to the method. The probability we obtain
can then be used in the classification problem we originally aimed to solve.

This module illustrates how to perform logistic regression and use this
technique in classification problems.
"""
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

from numpy.random import default_rng
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import classification_report, roc_curve

rng = default_rng(12345)
df = pd.DataFrame({
    "var1": np.concatenate([rng.normal(3.0, 1.5, size=50),
                            rng.normal(-4.0, 2.0, size=50)]),
    "var2": rng.uniform(size=100),
    "var3": np.concatenate([rng.normal(-2.0, 2.0, size=50),
                            rng.normal(1.5, 0.8, size=50)])
})

score = 4.0 + df["var1"] - df["var3"]
Y = score >= 0

fig1, ax1 = plt.subplots()
ax1.plot(df.loc[Y, "var1"], df.loc[Y, "var3"], "bo", label="True data")
ax1.plot(df.loc[~Y, "var1"], df.loc[~Y, "var3"], "rx", label="False data")
ax1.legend()
ax1.set_xlabel("var1")
ax1.set_ylabel("var2")
ax1.set_title("Scatter plot of var3 agains var1")

plt.show()

model = LogisticRegression()
model.fit(df, Y)

test_df = pd.DataFrame({
    "var1": np.concatenate([rng.normal(3.0, 1.5, size=25),
                            rng.normal(-4.0, 2.0, size=25)]),
    "var2": rng.uniform(size=50),
    "var3": np.concatenate([rng.normal(-2.0, 2.0, size=25),
                            rng.normal(1.5, 0.8, size=25)])
})

test_scores = 4.0 + test_df["var1"] - test_df["var3"]
test_Y = test_scores >= 0
test_predicts = model.predict(test_df)

plt.show()

print(classification_report(test_Y, test_predicts))