Importance Sampling 的权重

\[E_p [f(z)] = \int p(z)f(z) dz = \int \frac {p(z)}{q(z)} q(z) f(z) dz = \int \frac{p(z)}{q(z)} f(z) q(z) dz \approx \frac{1}{N}\sum_{i=1}^Nf(z_i)\frac{p(z_i)}{q(z_i)} \]

\[z_i \sim q(z) , i = 1, \dots ,N \]

用\(q(z_i)\)采样，得到\(z_i\), 然后用\(\frac{1}{N}\sum_{i=1}^Nf(z_i)\frac{p(z_i)}{q(z_i)}\),近似原来的期望。当\(p(z_i)\)和它的近似分布\(q(z_i)\)的比值越大时，表明如果按照\(q(z_i)\)来采样时，这个样本点越难采到，其权重\(\frac{p(z_i)}{q(z_i)}\)就要越大。

标签：采样,frac,权重,Importance,sum,Nf,Sampling,int,dz
来源： https://www.cnblogs.com/urcjzz/p/16454185.html