---
tags:
- ai
- classification
*Given an observation, determine one class from a set of classes that best explains the observation*
***Features are discrete or continuous***
- 2 category classifier
- Dichotomiser
# Argmax
Argument that gives the maximum value from a target function
# Gaussian Classifier
[Training](Supervised/Supervised.md)
- Each class $i$ has it's own Gaussian $N_i=N(m_i,v_i)$
$$\hat i=\text{argmax}_i\left(p(o_t|N_i)\cdot P(N_i)\right)$$
$$\hat i=\text{argmax}_i\left(p(o_t|N_i)\right)$$
- With equal priors
# Discrete Classifier
- Each class $i$ has it's own histogram $H_i$
- Describes the probability of each observation type $k$
- $P(o_t=k|H_i)$, based on class-specific type counts
$$\hat i=\text{argmax}_i\left(P(o_t=k|H_i)\right)$$
- Nothing else known about classes
$$\hat i=\text{argmax}_i\left(P(o_t=k|H_i)\cdot P(H_i)\right)$$
- Given class priors $P(H_i)$
- Maximum posterior probability
- Bayes
