### Update 2021JUL21.md

parent d8839946
 ... ... @@ -4,7 +4,7 @@ ### Model formulation Suppose $\mathbf{X}^{H}, \mathbf{X}^{L}$ are $N \times V$ feature matrices (e.g. connectivity between $N$ thalamus voxels and $V$ whole brain voxels). Note that they can have different dimensions in practice. To keep notations uncluttered, we suppose the number of voxels in high- and low-quality images are the same for a given subject. Now we assume $\mathbf{X}^{H}, \mathbf{X}^{L}$ share the same latent variable $Y$, which is a $N \times K$ binary matrix representing the voxels' classes. For a single voxel, suppose $\mathbf{y}_{n} \sim \text{multinomial}(\mathcal{\pi})$, and $p(\mathbf{x}^{L}_{n}|y_{nk}=1) = \mathcal{N}(\mu_{k}, \Sigma_{k}^{L})$. For a single voxel, suppose $\mathbf{y}_{n} \sim \text{multinomial}(\mathcal{\pi})$, and $p(\mathbf{x}^{L}_{n}|y_{nk}=1) = \mathcal{N}(\mu_{k}, \Sigma_{k}^{L})$. To use high-quality data to inform the inference on low-quality data, we assume $p(\mathbf{x}^{H}_{n}|y_{nk}=1, \mathbf{U}) = \mathcal{N}(\mathbf{U}\mathbf{x}^{H}_{n}|\mu_{k}, \Sigma_{k}^{H})$. ... ...
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