  We propose a method that meta-learns a knowledge on matrix factorization from
various matrices, and uses the knowledge for factorizing unseen matrices. The
proposed method uses a neural network that takes a matrix as input, and
generates prior distributions of factorized matrices of the given matrix. The
neural network is meta-learned such that the expected imputation error is
minimized when the factorized matrices are adapted to each matrix by a maximum
a posteriori (MAP) estimation. We use a gradient descent method for the MAP
estimation, which enables us to backpropagate the expected imputation error
through the gradient descent steps for updating neural network parameters since
each gradient descent step is written in a closed form and is differentiable.
The proposed method can meta-learn from matrices even when their rows and
columns are not shared, and their sizes are different from each other. In our
experiments with three user-item rating datasets, we demonstrate that our
proposed method can impute the missing values from a limited number of
observations in unseen matrices after being trained with different matrices.
