CFMI: Flow Matching for Missing Data Imputation (2506.09258v1)

Abstract: We introduce conditional flow matching for imputation (CFMI), a new general-purpose method to impute missing data. The method combines continuous normalising flows, flow-matching, and shared conditional modelling to deal with intractabilities of traditional multiple imputation. Our comparison with nine classical and state-of-the-art imputation methods on 24 small to moderate-dimensional tabular data sets shows that CFMI matches or outperforms both traditional and modern techniques across a wide range of metrics. Applying the method to zero-shot imputation of time-series data, we find that it matches the accuracy of a related diffusion-based method while outperforming it in terms of computational efficiency. Overall, CFMI performs at least as well as traditional methods on lower-dimensional data while remaining scalable to high-dimensional settings, matching or exceeding the performance of other deep learning-based approaches, making it a go-to imputation method for a wide range of data types and dimensionalities.

• The paper introduces CFMI, a method that uses conditional CNFs and flow matching to improve missing data imputation.
• It employs a flow matching training objective to minimize the L2 distance between predicted and true conditional vector fields.
• CFMI demonstrates scalability and robust performance across synthetic, tabular, and time-series datasets, outperforming traditional methods.

Conditional Flow Matching for Missing Data Imputation: An Expert Overview

The academic paper titled "CFMI: Flow Matching for Missing Data Imputation" introduces Conditional Flow Matching for Imputation (CFMI), a novel technique aimed at addressing the pervasive issue of missing data in statistical analyses. This method is engineered to function effectively with both low- and high-dimensional datasets, exhibiting versatility across various data types such as tabular and time-series data. Building on the contemporary advances in continuous normalising flows (CNFs) and flow-matching techniques, CFMI provides a compelling alternative to existing imputation methodologies.

Technical Foundation

The core of CFMI's methodological framework rests on conditional normalising flows trained via flow matching. This approach synergizes continuous normalising flows, shared conditional modelling, and flow-matching techniques to mitigate the computational and analytical complexities typical of traditional multiple imputation strategies. Unlike standard joint modelling, which often struggles with computational efficiency in handling incomplete data, CFMI simplifies the task by modelling conditional distributions directly, thus leveraging a shared model architecture adept at capturing all possible missing-data patterns.

Methodological Contributions

1. Conditional Modelling: CFMI employs conditional CNFs, expanding the flow-matching paradigm to impute missing data effectively. By leveraging zero-padded inputs and shared conditional models, CFMI elegantly bypasses the need to model each missingness pattern separately, a typical bottleneck in high-dimensional data settings.
2. Flow Matching Training Objective: The model utilizes a training objective that minimizes the L2 distance between the predicted vector field and the true conditional vector field. This approach, which draws from independent coupling schemes in flow-matching literature, ensures that learned conditional distributions are comprehensive and performance-optimised for imputation tasks.
3. Scalable Imputation: By ensuring that their model is capable of handling high-dimensional input efficiently, CFMI facilitates scalable imputation. The use of Euler integration with the trained vector-field model underscores the method's computational efficiency.

Empirical Evaluation

CFMI's evaluation traverses synthetic datasets, 24 UCI tabular datasets, and time-series datasets like PhysioNet and PM2.5. Those experimental results consistently highlight CFMI's robustness:

• Synthetic Datasets: CFMI demonstrated its ability to unerringly approximate conditional distributions in synthetic settings, showcasing flexible imputation performance that accurately reflects ground truth distributions.
• UCI Datasets: Across 24 small- to moderate-dimensional tabular datasets, CFMI outperformed both traditional methods like missForest and modern methods like HyperImpute and CSDI, especially as the fraction of missing data increased. It effectively maintained performance across varying levels of missingness, underscoring its utility as a scalable imputation method.
• Time-Series Datasets: In zero-shot imputation settings involving time-series data, CFMI rivaled the performance of state-of-the-art diffusion-based methods while boasting superior training efficiency.

Future Implications and Developments

The implications of such an imputation method are profound. In practical terms, CFMI caters to settings where datasets are heterogeneous in nature or where dimensional scaling poses an inherent challenge. In theoretical contexts, it paves the way for further exploration into the applications of flow-matching within imputation tasks, particularly in domains requiring real-time data analysis. A logical progression for future research could investigate the incorporation of CFMI in the development of foundation models aiming to integrate multi-modal and cross-disciplinary datasets, particularly in fields like healthcare where incomplete data are prevalent owing to privacy concerns or logistical constraints.

CFMI represents an advancement in the field of data imputation, harnessing recent advancements in the neural flow models to render a technique both versatile and efficient. Its ability to maintain robust performance across diverse dataset types and dimensional scales positions it not only as a highly adaptive method but also as a benchmark framework that could steer future developments in imputation methodologies.