Trick 小记

1.
\[
P(A|BC) = \frac{P(AB|C)}{P(B|C)}
\]

2.

In EM algorithm, the usual expectation function can be written as follows:
\[
\begin{split}
Q(\theta,\theta^0) &= E_{h}\left[P(\mathbf{x},h|\theta)|\mathbf{x},\theta^0\right] \\
& = \sum_{h}P(\mathbf{x},h|\theta)P(h|\mathbf{x},\theta^0)
\end{split}
\]

where

$h$ : the hidden varible.

$\theta$ : the obvious varible.

$\mathbf{x}$ : the observed data.

$\theta^0$ : the obvious varible calculated on the last.

3.

The　inverse of a symmetrical matrix is still symmetrical.

That is because
\[
(A^{-1})^T = (A^T)^{-1} = A^{-1}
\]