Introduction

If you want an artificial dataset for binary classification, the cleanest approach is to simulate the features first and then generate the binary response from a probability model. A logistic model is a natural choice because it turns a linear combination of features into values between 0 and 1, which you can interpret as class probabilities.

A Simple Simulation Strategy

The general pattern is:

1. generate 4 or 5 features from chosen distributions
2. combine them into a linear score
3. pass that score through the logistic function
4. sample a binary response from the resulting probabilities

This is useful because you control the signal strength, class balance, feature correlation, and noise level.

Generate Features

Suppose we want 5 predictors:

• 'x1, x2, x3 as continuous variables'
• 'x4 as a binary indicator'
• 'x5 as another continuous feature with different scale'

1import numpy as np
2import pandas as pd
3
4rng = np.random.default_rng(42)
5n = 1000
6
7x1 = rng.normal(0, 1, n)
8x2 = rng.normal(1, 2, n)
9x3 = rng.uniform(-1, 1, n)
10x4 = rng.binomial(1, 0.4, n)
11x5 = rng.normal(10, 3, n)

At this point we have features, but no label yet.

Build a Logistic Probability Model

Now define a linear predictor. This is the hidden score that controls the probability of class 1.

1linear_score = (
2    -0.8
3    + 1.2 * x1
4    - 0.7 * x2
5    + 1.5 * x3
6    + 0.9 * x4
7    + 0.15 * x5
8)
9
10prob = 1 / (1 + np.exp(-linear_score))

prob is now a vector of probabilities between 0 and 1. Higher values mean the observation is more likely to belong to the positive class.

Sample the Binary Response

Turn probabilities into labels by drawing from a Bernoulli distribution:

y = rng.binomial(1, prob)

That produces a realistic binary response because examples with high probability usually become 1, but not deterministically every time.

Now assemble the dataset:

1df = pd.DataFrame({
2    "x1": x1,
3    "x2": x2,
4    "x3": x3,
5    "x4": x4,
6    "x5": x5,
7    "y": y,
8})
9
10print(df.head())
11print(df["y"].mean())

The mean of y gives the approximate positive-class rate.

Why This Is Better Than Random Labels

If you generate features and then assign completely random labels, the classification problem has no real signal. Most models will perform near chance because there is nothing to learn.

By generating labels from a model tied to the features, you create a dataset where:

• some features are informative
• some effects can be strong or weak
• the class boundary is noisy but structured

That is much better for testing classifiers.

Add Correlation or Noise If Needed

Real datasets often have correlated predictors. You can simulate that too:

z = rng.normal(0, 1, n)
x1 = z + rng.normal(0, 0.2, n)
x2 = z * 0.8 + rng.normal(0, 0.5, n)

Now x1 and x2 share common structure.

You can also add extra noise to the score:

linear_score = linear_score + rng.normal(0, 0.5, n)

More noise makes the classification task harder and less separable.

Fit a Model to Check the Simulation

It is good practice to confirm the dataset behaves the way you intended:

1from sklearn.linear_model import LogisticRegression
2from sklearn.model_selection import train_test_split
3from sklearn.metrics import accuracy_score
4
5X = df[["x1", "x2", "x3", "x4", "x5"]]
6y = df["y"]
7
8X_train, X_test, y_train, y_test = train_test_split(
9    X, y, test_size=0.3, random_state=42
10)
11
12model = LogisticRegression(max_iter=1000)
13model.fit(X_train, y_train)
14
15pred = model.predict(X_test)
16print(accuracy_score(y_test, pred))

If the accuracy is far above random guessing, the simulation contains usable signal.

Alternative: Use make_classification

If you just need a quick synthetic dataset and do not care about controlling the exact probability model, scikit-learn has a helper:

1from sklearn.datasets import make_classification
2
3X, y = make_classification(
4    n_samples=1000,
5    n_features=5,
6    n_informative=4,
7    n_redundant=0,
8    n_classes=2,
9    random_state=42,
10)

This is convenient, but the manual logistic simulation is usually easier to explain and tune.

Common Pitfalls

The biggest pitfall is generating the response independently of the features. That creates a classification task with no learnable structure.

Another common mistake is choosing coefficient values so large that the probabilities collapse near 0 or 1 for almost every observation. That can make the simulated problem unrealistically easy.

People also often forget class balance. If the intercept is too extreme, nearly all rows end up in one class. Adjust the intercept until the positive rate is sensible for your experiment.

Finally, if you want realism, think beyond marginal distributions. Correlation, interaction effects, and noise level matter more than simply drawing five unrelated columns.

Summary

• Simulate features first, then generate the binary response from a probability model.
• Logistic probability generation is a natural choice for binary classification data.
• Use coefficients, intercept, and noise to control difficulty and class balance.
• Fit a classifier afterward to verify the simulated data contains real signal.
• Use make_classification for convenience, but manual simulation gives more control.