Probabilistic matrix factorization¶
Is an colaborative filtering agorithm where we assume that each rating in \(R\) are draws from a Gaussian distribution where the mean for
\[R_{ij} = U_iV_j^T\]
The precision of this distribution \((1/\sigma^2)\) We also put a Gaussian prior with mean 0 on \(U\) and \(V\) for regularization. This means that each row of U and V are drawn from a Gaussian with mean 0 and where the precision of these gaussian is a multiple of the Identiy matrix. If the precission of these parameters is not to far from 0 that ensures that the latent variables wont grow to much.
This prevents learning to strong user preferences and item factor compositions from being learned.