I've been trying to derive the marginalized likelihood, which I think I have done successfully. The problem is that I've ended up with an expression that I can't really explain, my expression is like this:

$$L(W) = -\frac{1}{2}\sum_{i=1}^{N}y_i^{T}(WW^{T} + \sigma^{2}I)^{-1}y_i$$

The problem is to explain the terms, for the "normal" Maximum Likelihood as well as the MAP, it's fairly straight forward, but I have a hard time understanding what this really means, is there anyone who can provide and explanation?


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