Exercise 12.9 - Imputation in a FA model

Answers

In this context, 𝐱 h and 𝐱 v are complementary components of the data space. Recall that:

p ( 𝐱 v , 𝐱 h | 𝜃 ) = 𝒩 ( 𝐱 v , 𝐱 h | 0 , Ψ + 𝐖 𝐖 T ) .

Now we use (4.69):

p ( 𝐱 h | 𝐱 v , 𝜃 ) = 𝒩 ( μ , Σ ) ,

where:

μ = Σ h𝑣 Σ 𝑣𝑣 − 1 𝐱 v , Σ = Σ hh − Σ h𝑣 Σ 𝑣𝑣 − 1 Σ 𝑣h ,

in which Σ h𝑣 corresponding to the submatrix in Ψ + 𝐖 𝐖 T .

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2021-03-24 13:42
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