# valued
`valued` method is like the mapping $\mathcal{F}$ such that
$$
\mathcal{F}: p(a \mid b) \mapsto p(f(c) \mid b)
$$
with mapping $f$ such that
$$
f: C \mapsto A
$$
Log
$$
\log{p(\mathbf{a} \mid f(c))}
$$
Log Value Difference
（ use `ConditionDifferentiableConditionedDistribution` ）
$$
\frac{\partial \log {p(f(c) \mid \mathbf{b})}}{\partial c} = \frac{\partial \log {p(f(c) \mid \mathbf{b})}}{\partial f(c)} \times \frac{\partial f(c)}{\partial c}
$$
`ConditionDifferentiableConditionedDistribution` has
Valued Distribution : $ p(f(c) \mid \mathbf{b})$ ,
and
Differentiated Value ( not $\log$ ) : $\frac{\partial f(c)}{\partial c}$ ( Matrix )
Log Condition Difference
$$
\frac{\partial \log{p(f(c) \mid \mathbf{b})}}{\partial \mathbf{b}}
$$