Predicting missing values: A good idea?

2026-05-05

AI Summary

This study addresses a critical limitation of deterministic imputation methods based on minimizing mean squared error (MSE), which, despite yielding accurate point estimates, systematically underestimate data variability and thereby introduce bias into downstream statistics such as variance, correlation, and regression coefficients. To rectify this, the authors propose a stochastic imputation strategy that augments MSE-optimal predictions with random noise scaled to the residual error variance, thereby restoring the original distributional properties of the data. Through multivariate normal simulations, the work demonstrates for the first time the inadequacy of MSE as a sole imputation quality metric and reveals pervasive bias in widely used predictive imputation methods—including missForest, softImpute, and MICE. The proposed stochastic approach effectively eliminates this bias, ensuring statistical validity in subsequent analyses and advocating a paradigm shift from deterministic to stochastic imputation.

Abstract

Minimizing the Mean Squared Error (MSE) is a key objective in machine learning and is commonly used for imputing missing values. While this approach provides accurate point estimates, it introduces systematic biases in downstream analyses. These biases affect key parameters such as variance, prevalence, correlation, slope, and explained variance. The root cause is that imputed values optimized for MSE are averages, which reduce the natural variability in the data. This paper demonstrates that adding noise to imputed values can effectively eliminate these biases. The required noise level is proportional to the MSE. Using a toy example in a multivariate normal setting, we compare two methods: predictive imputation, which minimizes MSE, and stochastic imputation, which incorporates random noise. Simulation results show that predictive methods systematically introduce bias, while stochastic methods preserve the data's natural variability and produce unbiased estimates. We also evaluate three popular imputation tools -- missForest, softImpute, and mice -- and observe consistent biases in predictive methods. These findings highlight that MSE is an inadequate measure of imputation quality, as it prioritizes accuracy over variability. Incorporating noise into imputation methods is essential to prevent biases and ensure valid downstream analyses, underscoring the importance of stochastic approaches for handling incomplete data.

Problem

• missing data
• imputation bias
• mean squared error
• data variability
• downstream analysis

Innovation

• stochastic imputation
• missing data
• mean squared error
• bias correction
• data variability