Optimized Linear Imputation

TL;DR

This paper introduces a new linear imputation method formulated as an optimization problem with guaranteed convergence, outperforming IRMI and other methods in handling missing data in high-dimensional datasets.

Contribution

The paper presents a convergent, optimization-based linear imputation method that improves upon IRMI's iterative approach for missing data imputation.

Findings

Method guarantees convergence to a local minimum.

Performance is superior to IRMI in non-converging cases.

Results are comparable to IRMI when IRMI converges.

Abstract

Often in real-world datasets, especially in high dimensional data, some feature values are missing. Since most data analysis and statistical methods do not handle gracefully missing values, the first step in the analysis requires the imputation of missing values. Indeed, there has been a long standing interest in methods for the imputation of missing values as a pre-processing step. One recent and effective approach, the IRMI stepwise regression imputation method, uses a linear regression model for each real-valued feature on the basis of all other features in the dataset. However, the proposed iterative formulation lacks convergence guarantee. Here we propose a closely related method, stated as a single optimization problem and a block coordinate-descent solution which is guaranteed to converge to a local minimum. Experiments show results on both synthetic and benchmark datasets, which are comparable to the results of the IRMI method whenever it converges. However, while in the set of experiments described here IRMI often does not converge, the performance of our methods is shown to be markedly superior in comparison with other methods.