I have a question about imposing identification constraints on the matrix normal covariances. In fitting the multi-output Gaussian process, it is recommended to fix \alpha to unity.
We should set α to 1.0 because the parameter is not identified unless we constrain
trace(C) = 1 .
I will like to find out if there’s a justification for this, an article I can cite. This is because, articles I have reviewed suggest either fixing the trace of a covariance matrix to the the length of the diagonals, or fixing the first entry of a covariance matrix to 1. For example, https://arxiv.org/pdf/1703.08882.pdf.