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Probabilistic Classifier

Last updated Oct 28, 2022 Edit Source

We want a model of $P(y_i = \textrm{important} | x_i )$ for use in decision theory.

The most common choice is to use the sigmoid function:

$$h(z_i) = \frac{1}{1+\exp(-z_i)}$$

# Multi-class Probabilities

See also: multi-class classification

The softmax function allows us to map $k$ real numbers $z_i = w_c^Tx_i$ to probabilities

$$P(y | z_1, z_2, \dots, z_k) = \frac{\exp(z_y)}{\sum_{c=1}^k \exp(z_c))}$$