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Logistic Regression, Interactively

Build intuition for logistic regression by training one live in your browser — adjust the learning rate, watch the decision boundary move, no backend required.

@shvinn

Machine Learning Engineer

1 min readJun 1, 2026

Logistic regression is the simplest model that still teaches almost everything: a linear boundary, a nonlinear squashing function, and gradient descent.

The model

It predicts the probability of the positive class by passing a linear score through the sigmoid:

p=σ(w⋅x+b),σ(z)=11+e−zp = \sigma(\mathbf{w}\cdot\mathbf{x} + b), \qquad \sigma(z) = \frac{1}{1 + e^{-z}}

Training minimizes the binary cross-entropy loss L=−1m∑i=1m[yilog⁡pi+(1−yi)log⁡(1−pi)]\mathcal{L} = -\frac{1}{m}\sum_{i=1}^{m}\big[y_i \log p_i + (1-y_i)\log(1-p_i)\big] by gradient descent.

Train it yourself

The playground below trains a logistic regression model entirely in your browser on a synthetic two-class dataset. Adjust the learning rate and epochs, hit train, and watch the decision boundary converge.

Loading playground…

What to notice

  • A too-high learning rate makes the loss bounce or diverge.
  • A too-low rate converges slowly — many epochs for little progress.
  • The boundary is always a straight line: logistic regression is linear in feature space. Curved boundaries require feature engineering or a nonlinear model.

This same training loop — forward pass, loss, gradient, update — is the kernel inside every deep network.