03 Logistic Regression Optimization

Last updated on 2025-07-10 | Edit this page

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Optimising a Logistic Regression Classifier

In this notebook, we demonstrate how to tune hyperparameters in a Logistic Regression model to improve performance.

Step 1: Load Breast Cancer Data

PYTHON 

from sklearn.datasets import load_breast_cancer
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
import pandas as pd

# Load dataset
data = load_breast_cancer()
X = data.data
y = data.target

# Split dataset
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.3, random_state=31
)

# Normalize (Standardize) features
scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

Step 2: Define a Function to Train and Evaluate

This function will: - Train the model - Return training and test accuracy

PYTHON 

from sklearn.linear_model import LogisticRegression
from sklearn.metrics import accuracy_score
import numpy as np

def train_and_evaluate(max_iter=5000, C=1, penalty='l2', solver='liblinear'):
    model = LogisticRegression(max_iter=max_iter, C=C, penalty=penalty, solver=solver)
    model.fit(X_train, y_train)
    train_acc = accuracy_score(y_train, model.predict(X_train))
    test_acc = accuracy_score(y_test, model.predict(X_test))
    return train_acc, test_acc

Step 3: Explore Effect of C (Inverse of Regularization Strength)

Controls the amount of regularization. Effect:

Smaller C → Stronger regularization → Prevents overfitting but may underfit.

Larger C → Weaker regularization → Better fit but may overfit.

PYTHON 

import matplotlib.pyplot as plt

values = [ 1e-3, 1e-2, 1e-1, 1, 10, 100, 1000 ]
train_scores, test_scores = [], []

for v in values:
    tr, te = train_and_evaluate(C=v)
    train_scores.append(tr)
    test_scores.append(te)

labels = [str(s) for s in values]

plt.plot(labels, train_scores, marker='o', label='Train Acc')
plt.plot(labels, test_scores, marker='s', label='Test Acc')
plt.xlabel('Values')
plt.ylabel('Accuracy')
plt.legend()
plt.grid(True)
plt.xticks(rotation=90, ha='right')
plt.show()
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png

Step 4: Explore Effect of penalty (L1, L2 Regularization)

Penalty Key Effect When to Use
L1 Sparsity, feature selection You want simpler models or auto-feature selection
L2 Shrinkage, no sparsity You want to reduce overfitting without dropping features

PYTHON 

import matplotlib.pyplot as plt

values = [ 'l1', 'l2' ]
train_scores, test_scores = [], []

for v in values:
    tr, te = train_and_evaluate(penalty=v)
    train_scores.append(tr)
    test_scores.append(te)

labels = [str(s) for s in values]

plt.plot(labels, train_scores, marker='o', label='Train Acc')
plt.plot(labels, test_scores, marker='s', label='Test Acc')
plt.xlabel('Values')
plt.ylabel('Accuracy')
plt.legend()
plt.grid(True)
plt.xticks(rotation=90, ha='right')
plt.show()
png
png

Step 5: Explore Effect of max_iter

Scenario Effect
Too low Model may not converge → You’ll see warnings like “STOP: TOTAL NO. OF F, G EVALUATIONS EXCEEDS LIMIT”. Model coefficients may be inaccurate or unstable.
Sufficient (or slightly high) Model converges properly. No warnings. Coefficients stabilize at optimal values.
Very high (but converges early) No harm—most solvers stop automatically once convergence is reached (before hitting max_iter). However, unnecessarily large values can increase training time for very large datasets.

PYTHON 

import matplotlib.pyplot as plt

values = [3, 4, 5, 6, 7, 10, 100 ]
train_scores, test_scores = [], []

for v in values:
    tr, te = train_and_evaluate(max_iter=v)
    train_scores.append(tr)
    test_scores.append(te)

labels = [str(s) for s in values]

plt.plot(labels, train_scores, marker='o', label='Train Acc')
plt.plot(labels, test_scores, marker='s', label='Test Acc')
plt.xlabel('Values')
plt.ylabel('Accuracy')
plt.legend()
plt.grid(True)
plt.xticks(rotation=90, ha='right')
plt.show()

SH 

C:\Users\moji1\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.13_qbz5n2kfra8p0\LocalCache\local-packages\Python313\site-packages\sklearn\svm\_base.py:1250: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.
  warnings.warn(
C:\Users\moji1\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.13_qbz5n2kfra8p0\LocalCache\local-packages\Python313\site-packages\sklearn\svm\_base.py:1250: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.
  warnings.warn(
C:\Users\moji1\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.13_qbz5n2kfra8p0\LocalCache\local-packages\Python313\site-packages\sklearn\svm\_base.py:1250: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.
  warnings.warn(
C:\Users\moji1\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.13_qbz5n2kfra8p0\LocalCache\local-packages\Python313\site-packages\sklearn\svm\_base.py:1250: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.
  warnings.warn(
C:\Users\moji1\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.13_qbz5n2kfra8p0\LocalCache\local-packages\Python313\site-packages\sklearn\svm\_base.py:1250: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.
  warnings.warn(
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png

Changing the Classification Threshold

Most classifiers output probabilities between 0 and 1. By default, the threshold for classification is 0.5. This means:

  • If predicted probability ≥ 0.5 → classify as positive
  • Else → classify as negative

Changing the Threshold:

  • Lower threshold → more positives predicted → higher recall, more false positives
  • Higher threshold → fewer positives predicted → higher precision, more false negatives

Choosing the right threshold depends on your application’s goals.

We’ll now visualize how the confusion matrix changes for two different thresholds.

PYTHON 

from sklearn.metrics import ConfusionMatrixDisplay

thresholds = [0.3, 0.5, 0.7]         # List of three thresholds to compare

# Retrain model
manual_model = LogisticRegression()
manual_model.fit(X_train, y_train)

# Predict probabilities
y_proba = manual_model.predict_proba(X_test)[:, 1]

# Plot side-by-side confusion matrices
fig, axs = plt.subplots(1, 3, figsize=(12, 5))
for i, thresh in enumerate(thresholds):
    y_pred = (y_proba >= thresh).astype(int)
    ConfusionMatrixDisplay.from_predictions(y_test, y_pred, ax=axs[i])
    axs[i].set_title(f"Threshold = {thresh}")
plt.tight_layout()
plt.show()
png
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