Meta-learning for Matrix Factorization without Shared Rows or Columns

TL;DR

This paper introduces a meta-learning approach for matrix factorization that can generalize to unseen matrices with different sizes and no shared rows or columns, using a neural network to generate priors and gradient-based adaptation.

Contribution

It presents a novel meta-learning method that enables matrix factorization across diverse matrices without shared dimensions, improving imputation with limited data.

Findings

Effective imputation on user-item datasets

Can handle matrices with different sizes and no shared structure

Meta-learning reduces the need for extensive training data

Abstract

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.