Private Data Imputation

TL;DR

This work delivers the first practical private data imputation protocols for horizontally and vertically split data, enabling privacy-preserving collaboration across distributed datasets. It combines radius-based nearest-neighbor search with secure primitives (OPPRF, VOLE-PSI, and circuit-PSI) to privately identify neighbors and compute imputed values, achieving substantial accuracy gains over local imputations. The protocols operate under the semi-honest model, offer controllable leakage through secure variants, and demonstrate practical runtimes on large datasets (e.g., 100,000 records) in high-bandwidth networks. The results indicate meaningful improvements in imputation quality across MCAR/MAR/MNAR scenarios, with fast performance and clear applicability to privacy-preserving analytics in healthcare, finance, and other sectors.

Abstract

Data imputation is an important data preparation task where the data analyst replaces missing or erroneous values to increase the expected accuracy of downstream analyses. The accuracy improvement of data imputation extends to private data analyses across distributed databases. However, existing data imputation methods violate the privacy of the data rendering the privacy protection in the downstream analyses obsolete. We conclude that private data analysis requires private data imputation. In this paper, we present the first optimized protocols for private data imputation. We consider the case of horizontally and vertically split data sets. Our optimization aims to reduce most of the computation to private set intersection (or at least oblivious programmable pseudo-random function) protocols which can be very efficiently computed. We show that private data imputation has -- on average across all evaluated datasets -- an accuracy advantage of 20\% in case of vertically split data and 5\% in case of horizontally split data over imputing data locally. In case of the worst data split we observed that imputing using our method resulted in an increase of up to 32.7 times in the quality of imputation over the vertically split data and 3.4 times in case of horizontally split data. Our protocols are very efficient and run in 2.4 seconds in case of vertically split data and 8.4 seconds in case of horizontally split data for 100,000 records evaluated in the 10 Gbps network setting, performing one data imputation.

Figures (6)

• Figure 1: Ideal functionality for neighbor computation.
• Figure 2: Ideal functionality for imputation value computation.
• Figure 3: RMSE trends for datasets 189, 216, and 287 under MCAR, MAR, and MNAR missingness types. Splitting repetitions in each plot have been ordered by increasing Vertical $k$-NN RMSE. The width of the bands in each plot illustrates 95% confidence intervals.
• Figure 4: Detailed RMSE trends for all evaluated datasets under the MCAR missingness type.
• Figure 5: Detailed RMSE trends for all evaluated datasets under the MAR missingness type.