Probabilistic Missing Value Imputation for Mixed Categorical and Ordered Data

Many real-world datasets contain missing entries and mixed data types including categorical and ordered (e.g. continuous and ordinal) variables. Imputing the missing entries is necessary, since many data analysis pipelines require complete data, but this is challenging especially for mixed data. This paper proposes a probabilistic imputation method using an extended Gaussian copula model that supports both single and multiple imputation. This method models mixed categorical and ordered data using a latent Gaussian distribution. The unordered characteristics of categorical variables is explicitly modeled using the argmax operator. This model makes no assumptions on the data marginals nor does it require any hyperparameter. Experimental results on synthetic and real datasets show that imputation with the extended Gaussian copula outperforms the current state-of-the-art for both categorical and ordered variables in mixed data. Preprint. Under review.