# Scalable Bayesian Non-linear Matrix Completion

arXiv: https://arxiv.org/abs/1908.01009 · HTML: https://mlsanity.com/paper/1908.01009/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2019.

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

- [Incremental Ensemble Gaussian Processes](https://mlsanity.com/paper/2110.06777/) (2021)

## Abstract (arXiv)

Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization, which predicts unobserved entries as linear combinations of latent variables. We generalize to non-linear combinations in massive-scale matrices. Bayesian approaches have been proven beneficial in linear matrix completion, but not applied in the more general non-linear case, due to limited scalability. We introduce a Bayesian non-linear matrix completion algorithm, which is based on a recent Bayesian formulation of Gaussian process latent variable models. To solve the challenges regarding scalability and computation, we propose a data-parallel distributed computational approach with a restricted communication scheme. We evaluate our method on challenging out-of-matrix prediction tasks using both simulated and real-world data.