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Feature Scaling: Why Feature Scaling Affects Model Training

Feature scaling is often overlooked because it seems like just another data preprocessing step. However, in practice, it often helps models train faster and more stably. Imagine one feature has values ranging from 0 to 1, while another has values ranging from 0 to 10,000. Although both features may be equally important for prediction, it's more difficult for the optimizer to work with such data.

This means it has to take more steps to find a good solution. Additionally, regularization becomes less effective because features with different scales require coefficients of different magnitudes. Let's look at how this looks in a simple example.

Install dependencies:

pip install numpy scikit-learn

Import libraries:

import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import roc_auc_score

Let's create a small synthetic dataset. It will have two features: the first has a normal scale, and the second is about a thousand times larger.

Importantly, both features actually influence the target variable. That is, the only difference between them is the scale.

np.random.seed(42)
x_small = np.random.normal(0, 1, 300)
x_large = np.random.normal(0, 1000, 300)

X = np.vstack([x_small, x_large]).T

y = (x_small + 0.001 * x_large > 0).astype(int)

Now, let's split the data into training and testing sets. We won't scale anything yet—first, let's see how the model behaves on the original data.

X_train, X_test, y_train, y_test = train_test_split(
    X, y,
    test_size=0.3,
    random_state=42,
    stratify=y
)

Let's train a logistic regression model without scaling.

In addition to the model's quality, let's also look at the number of iterations (n_iter_). This metric shows how much work the optimizer had to do to find the coefficients.

model = LogisticRegression()
model.fit(X_train, y_train)

pred = model.predict_proba(X_test)[:, 1]

print("ROC-AUC:", roc_auc_score(y_test, pred))
print("Iterations:", model.n_iter_)

Now, let's scale the features to the same scale using StandardScaler.

It calculates the mean and standard deviation only for the training set and then uses the same values for the test set. This is important because the model should not "peek" at the test data during training.

After this transformation, both features are approximately on the same scale, and it becomes easier for the optimizer to work with them.

scaler = StandardScaler()

X_train_scaled = scaler.fit_transform(X_train)
X_test_scaled = scaler.transform(X_test)

Now, let's retrain the model.

We're using the same model, the same data, and the same parameters. The only difference is that the features are now scaled.

model = LogisticRegression()
model.fit(X_train_scaled, y_train)

pred = model.predict_proba(X_test_scaled)[:, 1]

print("ROC-AUC (scaled):", roc_auc_score(y_test, pred))
print("Iterations (scaled):", model.n_iter_)

Most often, the ROC-AUC doesn't change much. However, the number of iterations becomes smaller. This means that the optimizer found a solution faster, and the training was more stable.

🔥 Feature scaling is a simple data preprocessing step that, in many cases, allows the model to train faster and more stably. For logistic regression, SVMs, neural networks, and other algorithms that use numerical optimization, it's best not to skip it.

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▎Understanding Overfitting in Machine Learning

Overfitting is a common challenge in machine learning that can confuse both beginners and experienced practitioners. In this lesson, we'll break down what overfitting is, why it occurs, how to identify it, and strategies to prevent it.

▎1. What is Overfitting?

Overfitting occurs when a machine learning model learns not only the underlying patterns in the training data but also the noise and outliers. As a result, the model performs exceptionally well on the training dataset but poorly on unseen data (test dataset). Essentially, the model becomes too complex and tailored to the training data, losing its ability to generalize.

Key Characteristics of Overfitting:

• High accuracy on the training set.
• Poor accuracy on the validation/test set.
• The model captures noise rather than the actual signal.


▎2. Why Does Overfitting Happen?

Overfitting can happen due to several reasons:

• Complex Models: Using highly complex algorithms (e.g., deep neural networks) with many parameters can lead to overfitting, especially if the dataset is small.
• Insufficient Data: When there isn’t enough data to represent the underlying distribution, models can latch onto random noise.
• Too Many Features: Including too many irrelevant features can confuse the model and lead to overfitting.


▎3. Identifying Overfitting

To identify overfitting, you can use the following techniques:

A. Train/Test Split

Divide your dataset into a training set and a test set (often a 70/30 or 80/20 split). Train your model on the training set and evaluate it on the test set. If you see a significant difference in performance (high training accuracy vs. low test accuracy), your model may be overfitting.

B. Cross-Validation

Use k-fold cross-validation to assess model performance across different subsets of your data. This method provides a more reliable estimate of how well your model will perform on unseen data.

C. Learning Curves

Plot learning curves that show training and validation error as a function of the number of training examples. If the training error continues to decrease while validation error increases, it indicates overfitting.


▎4. Preventing Overfitting

There are several strategies to mitigate overfitting:

A. Simplifying the Model

Choose a simpler model that is less likely to overfit. For example, if you’re using a polynomial regression model, consider reducing the degree of the polynomial.

B. Regularization

Apply regularization techniques like L1 (Lasso) or L2 (Ridge) regularization, which add a penalty for large coefficients in the model. This discourages complexity and helps improve generalization.

C. Pruning (for Decision Trees)

If you’re using decision trees, consider pruning them by removing branches that have little importance. This reduces complexity while retaining essential patterns.

D. Data Augmentation

If you have limited data, consider augmenting your dataset through techniques like rotation, scaling, or flipping images. This increases the diversity of your training data without requiring additional data collection.

E. Early Stopping

In iterative algorithms like gradient descent, monitor validation performance and stop training when performance begins to degrade.


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