Imputation Meets Clustering: Exploiting Latent Subgroup Structure for Missing Data Recovery

Real-world datasets often contain multiple latent subgroups with distinct statistical distributions. Standard imputation methods typically treat data as a monolithic entity, leading to "global" estimates that blur subgroup boundaries and fail to capture instance-level fidelity. This paper addresses the challenge of performing accurate imputation when the underlying population heterogeneity is unknown and the data is incomplete.

The authors propose Cluster-Aware Generative Imputation (CAGI), which reformulates the problem as a co-optimization task. CAGI follows a "Partition-Guide-Restore" strategy:

1. Partition: A missing-tolerant clustering module assigns samples to subgroups even when data is incomplete, using a specialized distance metric that computes partial distances based only on co-observed features.
2. Guide: The cluster assignments act as conditioning signals for a Generative Adversarial Network (GAN), narrowing the generative search space to subgroup-specific manifolds.
3. Restore: An iterative feedback loop alternates between updating the generator and refining cluster assignments. To ensure stability, the model uses a multi-level objective that combines instance-level reconstruction (MSE), adversarial training, and distribution-level regularization (Sinkhorn divergence) to prevent distributional fragmentation.

By explicitly modeling latent subgroup structure, CAGI avoids the "averaging" effect common in traditional imputation, where imputed values are plausible on average but incorrect for specific subgroups. This is particularly critical in fields like clinical diagnostics or customer segmentation, where preserving the integrity of distinct subgroups is essential for downstream analysis. The iterative nature of the framework allows the model to self-correct, progressively improving both the quality of the imputed values and the accuracy of the discovered subgroup structure.