Meta-learning for Matrix Factorization without Shared Rows or Columns

2021/06/29 by Tomoharu Iwata, Iwata, Tomoharu
Computer Science · #Advanced Graph Neural Networks #Artificial Intelligence (cs.AI) #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Recommender Systems and Techniques

paper · pdf · doi:10.48550/arxiv.2106.15133

openalex publication_date 2021/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Some Mathematical Notes on Three-Mode Factor Analysis
• Analysis of Individual Differences in Multidimensional Scaling Via an N-way Generalization of “Eckart-Young” Decomposition
• Matrix Factorization Techniques for Recommender Systems
• Independent component analysis: algorithms and applications
• Collaborative Filtering and the Missing at Random Assumption
• One-Shot Generalization in Deep Generative Models
• Prototypical Networks for Few-shot Learning
• Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks
• Meta-SGD: Learning to Learn Quickly for Few-Shot Learning
• Hierarchically Structured Meta-learning

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