Turn a score into a probability

Logistic regression forms a weighted score and sends it through sigmoid to produce a 0-to-1 output.

The idea

First combine the clues into one score, then squeeze that score into a number between 0 and 1 so it can be read as a probability-like output.

z = w·x + b, then p = σ(z). The sigmoid is monotonic: larger z means larger p. A chosen threshold converts p into a binary class decision.

How it works

  1. Scale/encode features as required by the solver and data.
  2. Compute the linear logit z = w·x + b.
  3. Apply sigmoid for binary probability or softmax/multinomial formulation for multiclass settings.
  4. Fit coefficients by minimizing penalized log loss; choose an operating threshold using validation evidence and application costs.

Logit, sigmoid, and log loss

The logit is linear in the features; sigmoid makes it bounded; log loss strongly penalizes confident wrong probabilities.

z = w·x + b, p = 1/(1+e⁻ᶻ), ℓ = −[y log p + (1−y) log(1−p)]

Check your understanding

What happens immediately before sigmoid in logistic regression?

Answer and explanation

The model first computes the linear score z = w·x + b. Sigmoid then maps that score into the 0-to-1 range.

A common misconception

The sigmoid output is not ‘confidence’ in a universal sense. It is the model’s probability estimate under its fitted assumptions and may require calibration checks.

Open Logistic Regression visualizer

ML Basics

Learn the learning loop before diving into individual models: data, splits, regression, and probabilities.

  1. Clues in, answer out
  2. Practice is not the exam
  3. Fit a straight-line rule
  4. Turn a score into a probability