--- tags: - ai --- # 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 - $P(N_i)$ $$\hat c_i=\frac 1 T \sum_tq_t(i)$$ $$\hat \mu_i=\frac{\sum_{t=1}^Tq_t(i)o_t}{\sum_{t=1}^Tq_t(i)}$$ $$\hat\sum_i=\frac{\sum_{t=1}^Tq_t(i)(o_t-\mu_i)(o_t-\mu_i)^T}{\sum_{t=1}^Tq_t(i)}$$ - For K-dimensional