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Logistic Regression and Classification

Despite its name, Logistic Regression is a classification algorithm. It's the foundation of all modern classification models.

The Sigmoid Function

Logistic Regression applies the sigmoid function to convert any number into a probability between 0 and 1:

σ(z) = 1 / (1 + e^(-z))

If σ(z) ≥ 0.5 → Class 1; otherwise → Class 0.

Evaluation Metrics

Accuracy: Overall correctness — misleading with imbalanced data
Precision: Of predicted positives, how many were correct?
Recall: Of actual positives, how many did we catch?
F1 Score: Harmonic mean of Precision and Recall

When to Prioritize

| Application | Priority | Reason | |-------------|---------|--------| | Cancer detection | High Recall | Don't miss sick patients | | Spam filtering | High Precision | Don't delete important emails | | Fraud detection | Both | Both errors are costly |

python

import numpy as np
import pandas as pd
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import (accuracy_score, precision_score,
                              recall_score, f1_score,
                              confusion_matrix, classification_report)

print("=" * 55)
print("Logistic Regression: كشف البريد المزعج")
print("=" * 55)

# ─────────────────────────────────────────
# بيانات مصطنعة للبريد الإلكتروني
# ─────────────────────────────────────────
np.random.seed(42)
n = 1000

# ميزات تميّز البريد المزعج
has_free_word  = np.random.binomial(1, 0.6, n)   # كلمة "مجاني"
num_links      = np.random.poisson(3, n)          # عدد الروابط
caps_ratio     = np.random.beta(2, 5, n)          # نسبة الأحرف الكبيرة
sender_known   = np.random.binomial(1, 0.7, n)   # المرسل معروف؟
email_length   = np.random.normal(300, 150, n)   # طول الرسالة

# spam = دالة للميزات
spam_score = (1.5 * has_free_word + 0.3 * num_links
              + 2.0 * caps_ratio - 2.5 * sender_known
              + np.random.normal(0, 0.5, n))
is_spam = (spam_score > 0.2).astype(int)

print(f"نسبة البريد المزعج: {is_spam.mean():.1%}")

df = pd.DataFrame({
    "has_free_word": has_free_word,
    "num_links": num_links,
    "caps_ratio": caps_ratio,
    "sender_known": sender_known,
    "email_length": email_length,
    "is_spam": is_spam
})

# ─────────────────────────────────────────
# تحضير وتدريب
# ─────────────────────────────────────────
features = ["has_free_word", "num_links", "caps_ratio",
            "sender_known", "email_length"]
X = df[features]
y = df["is_spam"]

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, stratify=y, random_state=42
)

scaler = StandardScaler()
X_train_s = scaler.fit_transform(X_train)
X_test_s  = scaler.transform(X_test)

model = LogisticRegression(random_state=42)
model.fit(X_train_s, y_train)

# ─────────────────────────────────────────
# التقييم الكامل
# ─────────────────────────────────────────
y_pred = model.predict(X_test_s)
y_prob = model.predict_proba(X_test_s)[:, 1]  # احتمال كونه spam

print("\n" + "=" * 55)
print("نتائج التقييم:")
print(f"  Accuracy  = {accuracy_score(y_test, y_pred):.3f}")
print(f"  Precision = {precision_score(y_test, y_pred):.3f}")
print(f"  Recall    = {recall_score(y_test, y_pred):.3f}")
print(f"  F1 Score  = {f1_score(y_test, y_pred):.3f}")

print("\nConfusion Matrix:")
cm = confusion_matrix(y_test, y_pred)
print(f"  TN={cm[0,0]}  FP={cm[0,1]}")
print(f"  FN={cm[1,0]}  TP={cm[1,1]}")

print("\nتقرير مفصل:")
print(classification_report(y_test, y_pred,
      target_names=["حقيقي", "مزعج"]))

# ─────────────────────────────────────────
# أهمية الميزات
# ─────────────────────────────────────────
coef_df = pd.DataFrame({
    "feature": features,
    "coefficient": model.coef_[0]
}).sort_values("coefficient", ascending=False)

print("أهمية الميزات:")
for _, row in coef_df.iterrows():
    bar = "█" * int(abs(row["coefficient"]) * 5)
    sign = "+" if row["coefficient"] > 0 else "-"
    print(f"  {row['feature']:15s}: {sign}{abs(row['coefficient']):.2f} {bar}")

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Logistic Regression and Classification

Despite its name, Logistic Regression is a classification algorithm. It's the foundation of all modern classification models.

The Sigmoid Function

Logistic Regression applies the sigmoid function to convert any number into a probability between 0 and 1:

σ(z) = 1 / (1 + e^(-z))

If σ(z) ≥ 0.5 → Class 1; otherwise → Class 0.

Evaluation Metrics

Accuracy: Overall correctness — misleading with imbalanced data

Precision: Of predicted positives, how many were correct?

Recall: Of actual positives, how many did we catch?

F1 Score: Harmonic mean of Precision and Recall

When to Prioritize

import numpy as np import pandas as pd from sklearn.linear_model import LogisticRegression from sklearn.model_selection import train_test_split from sklearn.preprocessing import StandardScaler from sklearn.metrics import (accuracy_score, precision_score, recall_score, f1_score, confusion_matrix, classification_report) print("=" * 55) print("Logistic Regression: كشف البريد المزعج") print("=" * 55) # ───────────────────────────────────────── # بيانات مصطنعة للبريد الإلكتروني # ───────────────────────────────────────── np.random.seed(42) n = 1000 # ميزات تميّز البريد المزعج has_free_word = np.random.binomial(1, 0.6, n) # كلمة "مجاني" num_links = np.random.poisson(3, n) # عدد الروابط caps_ratio = np.random.beta(2, 5, n) # نسبة الأحرف الكبيرة sender_known = np.random.binomial(1, 0.7, n) # المرسل معروف؟ email_length = np.random.normal(300, 150, n) # طول الرسالة # spam = دالة للميزات spam_score = (1.5 * has_free_word + 0.3 * num_links + 2.0 * caps_ratio - 2.5 * sender_known + np.random.normal(0, 0.5, n)) is_spam = (spam_score > 0.2).astype(int) print(f"نسبة البريد المزعج: {is_spam.mean():.1%}") df = pd.DataFrame({ "has_free_word": has_free_word, "num_links": num_links, "caps_ratio": caps_ratio, "sender_known": sender_known, "email_length": email_length, "is_spam": is_spam }) # ───────────────────────────────────────── # تحضير وتدريب # ───────────────────────────────────────── features = ["has_free_word", "num_links", "caps_ratio", "sender_known", "email_length"] X = df[features] y = df["is_spam"] X_train, X_test, y_train, y_test = train_test_split( X, y, test_size=0.2, stratify=y, random_state=42 ) scaler = StandardScaler() X_train_s = scaler.fit_transform(X_train) X_test_s = scaler.transform(X_test) model = LogisticRegression(random_state=42) model.fit(X_train_s, y_train) # ───────────────────────────────────────── # التقييم الكامل # ───────────────────────────────────────── y_pred = model.predict(X_test_s) y_prob = model.predict_proba(X_test_s)[:, 1] # احتمال كونه spam print("\n" + "=" * 55) print("نتائج التقييم:") print(f" Accuracy = {accuracy_score(y_test, y_pred):.3f}") print(f" Precision = {precision_score(y_test, y_pred):.3f}") print(f" Recall = {recall_score(y_test, y_pred):.3f}") print(f" F1 Score = {f1_score(y_test, y_pred):.3f}") print("\nConfusion Matrix:") cm = confusion_matrix(y_test, y_pred) print(f" TN={cm[0,0]} FP={cm[0,1]}") print(f" FN={cm[1,0]} TP={cm[1,1]}") print("\nتقرير مفصل:") print(classification_report(y_test, y_pred, target_names=["حقيقي", "مزعج"])) # ───────────────────────────────────────── # أهمية الميزات # ───────────────────────────────────────── coef_df = pd.DataFrame({ "feature": features, "coefficient": model.coef_[0] }).sort_values("coefficient", ascending=False) print("أهمية الميزات:") for _, row in coef_df.iterrows(): bar = "█" * int(abs(row["coefficient"]) * 5) sign = "+" if row["coefficient"] > 0 else "-" print(f" {row['feature']:15s}: {sign}{abs(row['coefficient']):.2f} {bar}")