p(y|\lambda) = \frac{\lambda^y \exp(-\lambda)}{y!}
L = \log\left(\prod_i p(y_i|\lambda_i)\right)
L = \sum_i \log( p(y_i|\lambda_i) )
L = \sum_i y_i \log(\lambda_i) - \lambda_i + \mbox{cont}
\log(\lambda) = {\bf w} \cdot {\bf x} + b
L = \sum_i y_i ({\bf w} \cdot {\bf x}_i + b) - \exp({\bf w} \cdot {\bf x}_i + b) + \mbox{cont}
Gaussian prior
wにgaussian priorを入れる
L = \sum_i y_i ({\bf w} \cdot {\bf x}_i + b) - \exp({\bf w} \cdot {\bf x}_i + b)
- c \ |{\bf w}|^2
オフセット項を入れる
L = \sum_i y_i ({\bf w} \cdot {\bf x}_i + b + \log A_i) - \exp({\bf w} \cdot {\bf x}_i + b + \log A_i)
- c \ |{\bf w}|^2
で
Lを最大化