# Gaussian Processes for Missing Value Imputation

arXiv: https://arxiv.org/abs/2204.04648 · HTML: https://mlsanity.com/paper/2204.04648/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 34 references that are in the map.
- First posted on arXiv 10 Apr 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [MCMC for Variationally Sparse Gaussian Processes](https://mlsanity.com/paper/1506.04000/) (2015)
- [Deep Gaussian Processes for Regression using Approximate Expectation Propagation](https://mlsanity.com/paper/1602.04133/) (2016)
- [Computational Graph Completion](https://mlsanity.com/paper/2110.10323/) (2021)
- [Multi-class Gaussian Process Classification with Noisy Inputs](https://mlsanity.com/paper/2001.10523/) (2020)
- [Recurrent Gaussian Processes](https://mlsanity.com/paper/1511.06644/) (2015)
- [Filling the gaps: Gaussian mixture models from noisy, truncated or incomplete samples](https://mlsanity.com/paper/1611.05806/) (2016)
- [Scalable Multi-Class Gaussian Process Classification using Expectation Propagation](https://mlsanity.com/paper/1706.07258/) (2017)

## Built on by (most cited first, 5 of 5)

- [RedCore: Relative Advantage Aware Cross-modal Representation Learning for Missing Modalities with Imbalanced Missing Rates](https://mlsanity.com/paper/2312.10386/) (2023)
- [Explainability of Machine Learning Models under Missing Data](https://mlsanity.com/paper/2407.00411/) (2024)
- [JoLT: Joint Probabilistic Predictions on Tabular Data Using LLMs](https://mlsanity.com/paper/2502.11877/) (2025)
- [Integrative Analysis and Imputation of Multiple Data Streams via Deep Gaussian Processes](https://mlsanity.com/paper/2505.12076/) (2025)
- [IBMA: An Imputation-Based Mixup Augmentation Using Self-Supervised Learning for Time Series Data](https://mlsanity.com/paper/2511.07930/) (2025)

## Abstract (arXiv)

Missing values are common in many real-life datasets. However, most of the current machine learning methods can not handle missing values. This means that they should be imputed beforehand. Gaussian Processes (GPs) are non-parametric models with accurate uncertainty estimates that combined with sparse approximations and stochastic variational inference scale to large data sets. Sparse GPs can be used to compute a predictive distribution for missing data. Here, we present a hierarchical composition of sparse GPs that is used to predict missing values at each dimension using all the variables from the other dimensions. We call the approach missing GP (MGP). MGP can be trained simultaneously to impute all observed missing values. Specifically, it outputs a predictive distribution for each missing value that is then used in the imputation of other missing values. We evaluate MGP in one private clinical data set and four UCI datasets with a different percentage of missing values. We compare the performance of MGP with other state-of-the-art methods for imputing missing values, including variants based on sparse GPs and deep GPs. The results obtained show a significantly better performance of MGP.