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Variational Inference的一些问题 #9

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lujun2445 opened this issue May 5, 2019 · 0 comments
Open

Variational Inference的一些问题 #9

lujun2445 opened this issue May 5, 2019 · 0 comments

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@lujun2445
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在求ln⁡(q_j^* (Z_j))时,
ln⁡(q_j^* (Z_j))=E_(i≠j) [ln⁡(p(X,Z))]
在右侧计算时为什么只考虑与Zj有关的项,而将其他项直接去掉?例如,对于高斯函数,推导了:
ln⁡(q_μ^* (μ))=E_(q_τ ) [ln⁡(p(μ,τ│D)) ]
=-(E_(q_τ ) [τ])/2 [∑_(i=1)^n▒〖(x_i-μ)^2+λ_0 (μ-μ_0 )〗^2 ]+const
这个常数项其实是关于τ的函数,即可以写成:
ln⁡(q_μ^* (μ))=-(E_(q_τ ) [τ])/2 [∑_(i=1)^n▒〖(x_i-μ)^2+λ_0 (μ-μ_0 )〗^2 ]+f(τ)
我觉得这个常数项不能直接忽略,因为:
ln⁡(q_τ^* (τ))=E_(q_μ ) [ln⁡(p(μ,τ│D)) ]
在求解ln⁡(q_τ^* (τ))时用到q_μ^* (μ),则q_μ^* (μ)中含有τ的项不能忽略,这样理解有什么问题吗。

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