🏋️ Log-Odds

Log-Odds#

The logarithm of the odds, the natural scale for logistic models.

Important

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What it is#

The log-odds (or logit) is the natural logarithm of the odds of an event — the ratio of its probability to its complement:

\[\text{logit}(p) = \log\!\left(\frac{p}{1 - p}\right), \qquad p = \sigma(z) = \frac{1}{1 + e^{-z}}.\]

Odds run from 0 (at \(p=0\)) through 1 (at \(p=0.5\)) to \(\infty\) (at \(p=1\)); taking the log spreads them onto the full line, from \(-\infty\) to \(+\infty\).

Why models use it#

A probability is trapped in \([0,1]\), awkward to model with a linear function; the log-odds is unbounded, so logistic regression (and the final layer of many classifiers) models the log-odds as a linear combination of features — the raw “score” before conversion.

Back to probability#

The sigmoid \(\sigma\) is the inverse of the logit — it maps a log-odds score \(z\) back to a probability. So the pipeline runs linear score → log-odds → sigmoid → classification probability → threshold → class.

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Classification Probability · Binary Classification · Sigmoid Function · Softmax Function · Logistic Regression · Neural Networks

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Active Learning · Binary Cross-Entropy (BCE) · Deep Ensembles · Early Stopping · Ensemble · Epochs · FLOPs · Full Annotation · Hyperparameter · Label Noise · Logit Space · Logits · Loss Functions · Model Distillation (Knowledge Distillation)