Handling Missing Data with Markov Boundary

In machine learning (ML) applications, high-quality data are very important to train a well-performed model that can provide robust predictions and responsible decisions. A common problem in ML applications e.g., healthcare is that the training dataset often consists of samples (or records) with missing values. As a result, the ML model cannot use such samples in its training phase. Handling missing data is thus an important and open research problem. In this paper, we propose a method to predict missing values by considering a causal graphical model framework. Our method exploits the Markov boundary encapsulating all necessary information about the missing variables. By utilizing the information encoded in the Markov boundary, we formulate a predictive function for each feature that has missing values to predict its missing values. Compared to existing methods, our predictive function is trained with only the features involved in the Markov boundary. To demonstrate the effectiveness of our proposed method, we compare its imputation performance with those of state-of-the-art imputation methods via a comprehensive experiment on seven real-world datasets. Our empirical results highlight that our method is significantly better than those of the baselines in terms of the imputation error thanks to its Markov information.