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Ying-Qiu Zheng
archive
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16c25085
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16c25085
authored
Jul 28, 2021
by
Ying-Qiu Zheng
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Update 2021JUN20.md
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@@ -113,4 +113,4 @@ The posterior of $`\mathbf{U}`$ is
```
math
P(\mathbf{U}|\mathbf{t}, \mathbf{H}^{L}, \mathbf{w}, \beta_1,...\beta_d) \propto P(\mathbf{t}|\mathbf{X}^{L},\mathbf{U}, \mathbf{w})P(\mathbf{U} | \mathbf{w}, \beta_1,...\beta_d)
```
where $
`P(\mathbf{t}|\mathbf{X}^{L},\mathbf{U}, \mathbf{w}) = \sigma(\mathbf{X}^{L}\mathbf{Uw})`
$ and $
`P(\mathbf{U} | \mathbf{w}, \beta_1,...\beta_d) = \mathcal{N}(\mathbf{U
W
} | \mathbf{0}, \text{diag}(\beta_1,...\beta_d))`
$, s.t. $
`\mathbf{U}^{T}\mathbf{U} = \mathbf{I}`
$.
where $
`P(\mathbf{t}|\mathbf{X}^{L},\mathbf{U}, \mathbf{w}) = \sigma(\mathbf{X}^{L}\mathbf{Uw})`
$ and $
`P(\mathbf{U} | \mathbf{w}, \beta_1,...\beta_d) = \mathcal{N}(\mathbf{U
w
} | \mathbf{0}, \text{diag}(\beta_1,...\beta_d))`
$, s.t. $
`\mathbf{U}^{T}\mathbf{U} = \mathbf{I}`
$.
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