Supervised Learning

Gaussian Classifier

• With $T$ labelled data

  $$q_t(i)= \begin{cases} 1 & \text{if class } i \\ 0 & \text{otherwise} \end{cases}$$

• Indicator function

• Mean parameter

  $$\hat m_i=\frac{\sum_tq_t(i)o_t}{\sum_tq_t(i)}$$

• Variance parameter

  $$\hat v_i=\frac{\sum_tq_t(i)(o_t-\hat m_i)^2}{\sum_tq_t(i)}$$

• Distribution weight

  • Class prior
  • $P(N_i)$ $\hat c_i=\frac 1 T \sum_tq_t(i)$

• For K-dimensional