Sigmoid
Maps any real number into (0, 1).
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07
Supervised learning
Classification
Predicting categories with probabilities: logistic regression, its boundary and its multiclass extension.
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What you’ll take away
- Logistic regression = linear score → sigmoid → probability, trained with cross-entropy.
- Its decision boundary is a hyperplane; non-linear features curve it.
- Thresholds trade precision against recall; calibrated probabilities make them meaningful.
- Softmax extends the idea to many classes.
Major concepts (syllabus)
Logistic regression, decision boundaries, probability-based classification, binary and multiclass classification
Lessons
- From regression to classificationWhy a straight line is a poor model for yes/no targets.7 min
- Logistic regressionA linear score passed through the sigmoid to get a probability.10 min
- Decision boundariesWhere the predicted class flips; linear for logistic regression.8 min
- Probability-based classificationThresholds, calibrated probabilities and cross-entropy loss.8 min
- Binary classificationTwo classes, one probability.7 min
- Multiclass classificationOne-vs-rest and the softmax function.9 min
Key formulas
Logistic model
Probability of the positive class.
Binary cross-entropy
Negative log-likelihood of Bernoulli labels.
Softmax
K scores to K probabilities that sum to 1.
Key terms
- Cross-entropy
- Loss for probabilistic classification: −log of the probability assigned to the true class.
- Decision boundary
- The surface in feature space where a classifier's prediction changes class.
- Logistic regression
- Linear score passed through a sigmoid to model a class probability.
- Sigmoid
- 1 / (1 + e⁻ᶻ): squashes any number into (0, 1).
- Softmax
- Turns a vector of scores into probabilities that sum to 1.
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