# Meta-learning for Matrix Factorization without Shared Rows or Columns

arXiv: https://arxiv.org/abs/2106.15133 · HTML: https://mlsanity.com/paper/2106.15133/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 58 references that are in the map.
- First posted on arXiv 29 Jun 2021.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Meta-Learning with Latent Embedding Optimization](https://mlsanity.com/paper/1807.05960/) (2018)
- [Meta-Learning with Differentiable Convex Optimization](https://mlsanity.com/paper/1904.03758/) (2019)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Meta-SGD: Learning to Learn Quickly for Few-Shot Learning](https://mlsanity.com/paper/1707.09835/) (2017)
- [Attentive Neural Processes](https://mlsanity.com/paper/1901.05761/) (2019)
- [Probabilistic Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1806.02817/) (2018)
- [Bayesian Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1806.03836/) (2018)
- [Towards a Neural Statistician](https://mlsanity.com/paper/1606.02185/) (2016)
- [Deep Models of Interactions Across Sets](https://mlsanity.com/paper/1803.02879/) (2018)
- [Hierarchically Structured Meta-learning](https://mlsanity.com/paper/1905.05301/) (2019)
- [One-Shot Generalization in Deep Generative Models](https://mlsanity.com/paper/1603.05106/) (2016)
- [MetaFun: Meta-Learning with Iterative Functional Updates](https://mlsanity.com/paper/1912.02738/) (2019)
- [Few-shot Autoregressive Density Estimation: Towards Learning to Learn Distributions](https://mlsanity.com/paper/1710.10304/) (2017)
- [The Variational Homoencoder: Learning to learn high capacity generative models from few examples](https://mlsanity.com/paper/1807.08919/) (2018)
- [Variational Memory Addressing in Generative Models](https://mlsanity.com/paper/1709.07116/) (2017)
- [Tensor Factorization via Matrix Factorization](https://mlsanity.com/paper/1501.07320/) (2015)

## Built on by (most cited first, 1 of 1)

- [Meta-learning of semi-supervised learning from tasks with heterogeneous attribute spaces](https://mlsanity.com/paper/2311.05088/) (2023)

## Abstract (arXiv)

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.