Timeline for Prior for a linear transformation matrix: Matrix Normal Distribution
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Nov 6, 2015 at 23:56 | comment | added | user16776 | Yes it seems so. But if you assume $vec(A) \sim \mathcal{N}(\mu, sI)$ with $s$ being some number, and $I$ is the identity matrix -- I don't know if there is a way to specify $V$ and $U$ (they will be constant times identity, but constants are not easy to say I guess). | |
| Nov 5, 2015 at 18:24 | comment | added | Luca | May I ask a subsequent clarification? So, if the elements of my matrix $A$ are modelled to be independent than what would the matrix-normal prior look like to allow for a wide range of values? So, in a normal Gaussian case, the equivalant of having a wide prior. I guess I can have both $V$ and $U$ matrices to be diagonal with large values for the diagonal entries? | |
| Nov 4, 2015 at 15:23 | comment | added | Luca | yes, I also have these independence assumptions. I would be happy to get something working with a simple model in the first instance :) | |
| Nov 4, 2015 at 15:22 | comment | added | user16776 | and note also that I also assume $\Sigma = \lambda \otimes I$ (meaning $\lambda I$ informally). This also has effect on tractability in my case. I wonder about what happens with general observation covariance and prior covariance as well. | |
| Nov 4, 2015 at 15:18 | comment | added | user16776 | Assuming a special covariance structure on MVN prior on $vec(A)$ enabled me to go back to the matrix form (and you see in the Wikipedia, it also corresponds to assume a Matrix-normal prior with $U=I$). If you assume a MVN prior with full covariance on $vec(A)$, I suspect posterior is not tractable in matrix-form. I wanted to avoid vectorising and de-vectorising after each observation, and wanted to keep matrix-form along updates. (I will try to obtain a direct matrix-form as well!). | |
| Nov 4, 2015 at 15:08 | comment | added | Luca | I am going through the paper now and will update the thread on my progress! Since, we are putting a prior over $vec(A)$, is it not enough to use a MVN prior rather than a matrix-normal? | |
| Nov 4, 2015 at 15:05 | comment | added | user16776 | My motivation comes from converting $Ax$ to some model over $A$. It seemed easy to do so. I am not sure what will happen if you derive everything in directly matrix form. If you do, please post here the derivation! :) | |
| Nov 4, 2015 at 14:34 | comment | added | Luca | One thing I am confused about is why is the matrix-normal prior on $vec(A)$ rather than $A$ itself? | |
| Nov 4, 2015 at 13:33 | vote | accept | Luca | ||
| Nov 4, 2015 at 11:53 | history | answered | user16776 | CC BY-SA 3.0 |