# Multiple imputation for continuous variables using a Bayesian principal component analysis

arXiv: https://arxiv.org/abs/1401.5747 · HTML: https://mlsanity.com/paper/1401.5747/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jan 2014.

## Built on by (most cited first, 11 of 11)

- [EMFlow: Data Imputation in Latent Space via EM and Deep Flow Models](https://mlsanity.com/paper/2106.04804/) (2021)
- [Explainability of Machine Learning Models under Missing Data](https://mlsanity.com/paper/2407.00411/) (2024)
- [Understanding Generative AI Content with Embedding Models](https://mlsanity.com/paper/2408.10437/) (2024)
- [Principal Component Analysis based frameworks for efficient missing data imputation algorithms](https://mlsanity.com/paper/2205.15150/) (2022)
- [Conditional expectation with regularization for missing data imputation](https://mlsanity.com/paper/2302.00911/) (2023)
- [Blockwise Principal Component Analysis for monotone missing data imputation and dimensionality reduction](https://mlsanity.com/paper/2305.06042/) (2023)
- [Principal Components for Neural Network Initialization](https://mlsanity.com/paper/2501.19114/) (2025)
- [Data Imputation from the Perspective of Graph Dirichlet Energy](https://mlsanity.com/paper/2304.04474/) (2023)
- [DPER: Efficient Parameter Estimation for Randomly Missing Data](https://mlsanity.com/paper/2106.05190/) (2021)
- [Directly Handling Missing Data in Linear Discriminant Analysis for Enhancing Classification Accuracy and Interpretability](https://mlsanity.com/paper/2407.00710/) (2024)
- [DPERC: Direct Parameter Estimation for Mixed Data](https://mlsanity.com/paper/2501.10540/) (2025)

## Abstract (arXiv)

We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the PCA model. Using a simulation study and real data sets, the method is compared to two classical approaches: multiple imputation based on joint modelling and on fully conditional modelling. Contrary to the others, the proposed method can be easily used on data sets where the number of individuals is less than the number of variables and when the variables are highly correlated. In addition, it provides unbiased point estimates of quantities of interest, such as an expectation, a regression coefficient or a correlation coefficient, with a smaller mean squared error. Furthermore, the widths of the confidence intervals built for the quantities of interest are often smaller whilst ensuring a valid coverage.