Introduction

sklearn.linear_model.LogisticRegression is a linear classifier. It does not accept a kernel parameter the way SVC does, so there is no built-in “kernel logistic regression” switch in scikit-learn’s standard logistic regression estimator.

That does not mean you are stuck with only straight-line decision boundaries. It means you create non-linear decision boundaries by transforming the features before they reach logistic regression.

Why LogisticRegression Has No Kernel Argument

A kernel method works by replacing the original feature representation with an implicit similarity computation in another space. In scikit-learn, that pattern is exposed directly in estimators such as SVC(kernel="rbf").

LogisticRegression, by contrast, is implemented as a linear model over the feature matrix you give it. So if you want non-linearity, you must change the input features rather than expecting the classifier to do kernel expansion internally.

Use Polynomial Features for a Simple Non-Linear Boundary

One practical option is explicit feature expansion with PolynomialFeatures.

1from sklearn.datasets import make_moons
2from sklearn.pipeline import make_pipeline
3from sklearn.preprocessing import PolynomialFeatures
4from sklearn.linear_model import LogisticRegression
5
6X, y = make_moons(noise=0.15, random_state=42)
7
8model = make_pipeline(
9    PolynomialFeatures(degree=3, include_bias=False),
10    LogisticRegression(max_iter=2000)
11)
12
13model.fit(X, y)
14print(model.score(X, y))

This is still logistic regression, but now the classifier sees richer feature interactions that allow curved decision boundaries.

Use Kernel Approximation When You Want RBF-Like Behavior

If your mental model is “I want something closer to an RBF kernel,” scikit-learn offers approximation transformers such as RBFSampler and Nystroem.

1from sklearn.datasets import make_circles
2from sklearn.kernel_approximation import RBFSampler
3from sklearn.linear_model import LogisticRegression
4from sklearn.pipeline import make_pipeline
5from sklearn.preprocessing import StandardScaler
6
7X, y = make_circles(noise=0.1, factor=0.4, random_state=42)
8
9model = make_pipeline(
10    StandardScaler(),
11    RBFSampler(gamma=1.0, n_components=300, random_state=42),
12    LogisticRegression(max_iter=2000)
13)
14
15model.fit(X, y)
16print(model.score(X, y))

This is not true built-in kernel logistic regression, but it is often the closest workflow inside scikit-learn when you want logistic loss with non-linear transformed features.

When SVC May Be the Better Tool

Sometimes the honest answer is that you should use a support vector classifier if you specifically want a native kernelized classifier.

from sklearn.svm import SVC

model = SVC(kernel="rbf", gamma="scale")

That changes the learning objective, so it is not interchangeable with logistic regression. But if the main goal is a strong non-linear classifier and not calibrated log-odds interpretation, SVC may be the cleaner choice.

Keep the Reason for Logistic Regression in Mind

Logistic regression remains attractive because it gives:

• simple linear decision logic in the transformed feature space
• probability estimates
• interpretable coefficients in some settings
• fast training on many tabular problems

If those properties matter, feature engineering plus logistic regression can be a better fit than switching models immediately.

Regularization becomes more important once you expand features. If you move from a small raw feature space to hundreds of polynomial or sampled kernel features, tune C carefully and validate on held-out data instead of trusting the default. Otherwise the model may appear to solve the training set while generalizing poorly.

Common Pitfalls

• Looking for a kernel= parameter on LogisticRegression and assuming you missed an option.
• Assuming polynomial expansion and true kernel methods are exactly the same thing in cost and behavior.
• Forgetting feature scaling before kernel approximation methods.
• Comparing kernelized SVC and logistic regression without noticing that they optimize different objectives.
• Adding huge feature expansions without regularization or validation, which leads to overfitting.

Summary

• Scikit-learn LogisticRegression does not support kernels directly.
• To get non-linear behavior, transform the features before fitting logistic regression.
• 'PolynomialFeatures is a simple explicit approach.'
• 'RBFSampler or Nystroem can approximate kernel-style behavior while keeping logistic regression as the classifier.'
• If you specifically need a native kernel classifier, SVC is often the more direct tool.