Missing data presents a widespread challenge in real-world data collection. In this paper, our goal is to impute missing entries while accurately reflecting the uncertainty associated with them. We introduce U-VAE, a method that employs a non-parametric distributional learning strategy to parameterize the likelihood of missing values. To address the infeasibility of directly estimating the underlying conditional distributions due to data incompleteness, we incorporate stochastic re-masking and un-masking techniques during training. Specifically, we replace the conventional reconstruction loss with the continuous ranked probability score (CRPS), a strictly proper scoring rule, and theoretically demonstrate that the discrepancy between the underlying conditional distribution and our imputer is upper-bounded. We evaluate the performance of U-VAE on 11 real-world datasets, showing its effectiveness in both single and multiple imputations, while also enhancing post-imputation performance and supporting valid statistical inference.

In this paper, our goal is to generate synthetic data for heterogeneous (mixed-type) tabular datasets with high machine learning utility (MLu). Since the MLu performance depends on accurately approximating the conditional distributions, we focus on devising a synthetic data generation method based on conditional distribution estimation. We introduce MaCoDE by redefining the consecutive multi-class classification task of Masked Language Modeling (MLM) as histogram-based non-parametric conditional density estimation. Our approach enables the estimation of conditional densities across arbitrary combinations of target and conditional variables. We bridge the theoretical gap between distributional learning and MLM by demonstrating that minimizing the orderless multi-class classification loss leads to minimizing the total variation distance between conditional distributions. To validate our proposed model, we evaluate its performance in synthetic data generation across 10 real-world datasets, demonstrating its ability to adjust data privacy levels easily without re-training. Additionally, since masked input tokens in MLM are analogous to missing data, we further assess its effectiveness in handling training datasets with missing values, including multiple imputations of the missing entries.