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

Meta-learning for Matrix Factorization without Shared Rows or Columns