Modern large scale datasets are often plagued with missing entries. For tabular data with missing values, a flurry of imputation algorithms solve for a complete matrix which minimizes some penalized reconstruction error. However, almost none of them can estimate the uncertainty of its imputations. This paper proposes a probabilistic and scalable framework for missing value imputation with quantified uncertainty.

Current domain adaptation methods under missingness shift are restricted to Missing At Random (MAR) missingness mechanisms. However, in many real-world examples, the MAR assumption may be too restrictive. When covariates are Missing Not At Random (MNAR) in both source and target data, the common covariate shift solutions, including importance weighting, are not directly applicable. We show that under reasonable assumptions, the problem of MNAR missingness shift can be reduced to an imputation problem. This allows us to leverage recent methodological developments in both the traditional statistics and machine/deep-learning literature for MNAR imputation to develop a novel domain adaptation procedure for MNAR missingness shift. We further show that our proposed procedure can be extended to handle simultaneous MNAR missingness and covariate shifts. We apply our procedure to Electronic Health Record (EHR) data from two hospitals in south and northeast regions of the US. In this setting we expect different hospital networks and regions to serve different populations and to have different procedures, practices, and software for inputting and recording data, causing simultaneous missingness and covariate shifts.

A significant challenge in time-series (TS) modeling is the presence of missing values in real-world TS datasets. Traditional two-stage frameworks, involving imputation followed by modeling, suffer from two key drawbacks: (1) the propagation of imputation errors into subsequent TS modeling, (2) the trade-offs between imputation efficacy and imputation complexity. While one-stage approaches attempt to address these limitations, they often struggle with scalability or fully leveraging partially observed features. To this end, we propose a novel imputation-free approach for handling missing values in time series termed Missing Feature-aware Time Series Modeling (MissTSM) with two main innovations. First, we develop a novel embedding scheme that treats every combination of time-step and feature (or channel) as a distinct token. Second, we introduce a novel Missing Feature-Aware Attention (MFAA) Layer to learn latent representations at every time-step based on partially observed features. We evaluate the effectiveness of MissTSM in handling missing values over multiple benchmark datasets.

We pose transductive classification as a matrix completion problem. By assuming the underlying matrix has a low rank, our formulation is able to handle three problems simultaneously: i) multi-label learning, where each item has more than one label, ii) transduction, where most of these labels are unspecified, and iii) missing data, where a large number of features are missing. We obtained satisfactory results on several real-world tasks, suggesting that the low rank assumption may not be as restrictive as it seems. Our method allows for different loss functions to apply on the feature and label entries of the matrix. The resulting nuclear norm minimization problem is solved with a modified fixed-point continuation method that is guaranteed to find the global optimum.

We pose transductive classification as a matrix completion problem. By assuming the underlying matrix has a low rank, our formulation is able to handle three problems simultaneously: i) multi-label learning, where each item has more than one label, ii) transduction, where most of these labels are unspecified, and iii) missing data, where a large number of features are missing. We obtained satisfactory results on several real-world tasks, suggesting that the low rank assumption may not be as restrictive as it seems. Our method allows for different loss functions to apply on the feature and label entries of the matrix. The resulting nuclear norm minimization problem is solved with a modified fixed-point continuation method that is guaranteed to find the global optimum.