Régression logistique en 2D

Prédire la couleur d’un vin à partir de ses composants.

%matplotlib inline

from teachpyx.datasets import load_wines_dataset

data = load_wines_dataset()
X = data.drop(["quality", "color"], axis=1)
y = data["color"]

from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(X, y)

from statsmodels.discrete.discrete_model import Logit

model = Logit(y_train == "white", X_train)
res = model.fit()

Optimization terminated successfully.
         Current function value: 0.048414
         Iterations 11

res.summary2()

Model:	Logit	Method:	MLE
Dependent Variable:	color	Pseudo R-squared:	0.913
Date:	2024-01-23 00:52	AIC:	493.7476
No. Observations:	4872	BIC:	565.1515
Df Model:	10	Log-Likelihood:	-235.87
Df Residuals:	4861	LL-Null:	-2717.5
Converged:	1.0000	LLR p-value:	0.0000
No. Iterations:	11.0000	Scale:	1.0000

	Coef.	Std.Err.	z	P>|z|	[0.025	0.975]
fixed_acidity	-1.4541	0.1515	-9.5981	0.0000	-1.7511	-1.1572
volatile_acidity	-11.3716	0.9995	-11.3771	0.0000	-13.3306	-9.4126
citric_acid	1.7492	1.1280	1.5507	0.1210	-0.4616	3.9599
residual_sugar	0.1246	0.0600	2.0756	0.0379	0.0069	0.2422
chlorides	-32.7390	3.9560	-8.2758	0.0000	-40.4926	-24.9854
free_sulfur_dioxide	-0.0505	0.0134	-3.7724	0.0002	-0.0768	-0.0243
total_sulfur_dioxide	0.0632	0.0050	12.6896	0.0000	0.0534	0.0730
density	42.0110	4.2093	9.9806	0.0000	33.7610	50.2610
pH	-8.7417	0.9800	-8.9204	0.0000	-10.6624	-6.8210
sulphates	-8.8918	1.0237	-8.6857	0.0000	-10.8983	-6.8853
alcohol	0.4150	0.1233	3.3656	0.0008	0.1733	0.6567

On ne garde que les deux premières.

X_train2 = X_train.iloc[:, :2]

import pandas

df = pandas.DataFrame(X_train2.copy())
df["y"] = y_train

import matplotlib.pyplot as plt

fig, ax = plt.subplots(1, 1, figsize=(4, 4))
df[df.y == "white"].plot(
    x="fixed_acidity", y="volatile_acidity", ax=ax, kind="scatter", label="white"
)
df[df.y == "red"].plot(
    x="fixed_acidity",
    y="volatile_acidity",
    ax=ax,
    kind="scatter",
    label="red",
    color="red",
    s=2,
)
ax.set_title("Vins rouges et white selon deux composantes");

from sklearn.linear_model import LogisticRegression

model = LogisticRegression()
model.fit(X_train2, y_train == "white")

LogisticRegression()

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model.coef_, model.intercept_

(array([[ -1.11120776, -11.79383309]]), array([13.83313405]))

On trace cette droite sur le graphique.

x0 = 3
y0 = -(model.coef_[0, 0] * x0 + model.intercept_) / model.coef_[0, 1]
x1 = 14
y1 = -(model.coef_[0, 0] * x1 + model.intercept_) / model.coef_[0, 1]
x0, y0, x1, y1

(3, array([0.89025431]), 14, array([-0.14615898]))

import matplotlib.pyplot as plt

fig, ax = plt.subplots(1, 1, figsize=(4, 4))
df[df.y == "white"].plot(
    x="fixed_acidity", y="volatile_acidity", ax=ax, kind="scatter", label="white"
)
df[df.y == "red"].plot(
    x="fixed_acidity",
    y="volatile_acidity",
    ax=ax,
    kind="scatter",
    label="red",
    color="red",
    s=2,
)
ax.plot(
    [x0, x1],
    [y0, y1],
    "y--",
    lw=4,
    label="frontière trouvée\npar la régression\nlogistique",
)
ax.legend()
ax.set_title("Vins rouges et blancs\nselon deux composantes");

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