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切片采样01

[00:00.000]	作词 : -L1-
[00:01.000]	作曲 : -L1-
[00:04.191]	重要性采样(importance sampling)给出对某个分布p(z)p(z)的数字特征的估计
[00:09.442]	，而绕过了对p(z)p(z)的直接采样。其大致原理如下，
[00:16.442]	首先构造提议分布(proposal distribution)q(z)q(z)，
[00:20.692]从而利用在q(z)q(z)上的采样估计E[f]E[f]	，即
[00:26.191]E[f]	=∫f(z)p(z)dz
[00:31.192]	=∫f(z)p(z)q(z)q(z)dz
[00:36.691]	≃1L∑l=1Lp(z(l))q(z(l))f(z(l))
[00:41.942]	其中p(z(l))/q(z(l))p(z(l))/q(z(l))，简记为rlrl，称为重要性权值。显然，若q(z)≡p(z)q(z)≡p(z)，有rl≡1rl≡1。
[00:47.192]	与取舍采样相同，
[00:52.691]	重要性采样的效果依赖于选取的提议分布在多大程度上与原始分布相似，

[00:00.000]	zuò cí : L1
[00:01.000]	zuò qǔ : L1
[00:04.191]	zhòng yào xìng cǎi yàng importance sampling gěi chū duì mǒu gè fēn bù p z p z de shù zì tè zhēng de gū jì
[00:09.442]	, ér rào guò le duì p z p z de zhí jiē cǎi yàng. qí dà zhì yuán lǐ rú xià,
[00:16.442]	shǒu xiān gòu zào tí yì fēn bù proposal distribution q z q z,
[00:20.692]从而利用在q(z)q(z)上的采样估计E[f]E[f]	, jí
[00:26.191]E[f]	f z p z dz
[00:31.192]	f z p z q z q z dz
[00:36.691]	1L l 1Lp z l q z l f z l
[00:41.942]	qí zhōng p z l q z l p z l q z l, jiǎn jì wéi rlrl, chēng wéi zhòng yào xìng quán zhí. xiǎn rán, ruò q z p z q z p z, yǒu rl 1rl 1.
[00:47.192]	yǔ qǔ shě cǎi yàng xiāng tóng,
[00:52.691]	zhòng yào xìng cǎi yàng de xiào guǒ yī lài yú xuǎn qǔ de tí yì fēn bù zài duō dà chéng dù shàng yǔ yuán shǐ fēn bù xiāng sì,