Collaborative Imputation for Multivariate Time Series with Convergence Guarantee

Missing values often occur in multivariate time series, affecting data analysis and applications. Existing studies typically use complete data to train imputation models, which are then used to fill missing values. However, in practice, missing values could appear in various cells. Such varieties unfortunately prevent imputation models performing, even making fillings unavailable without the convergence guarantee, i.e., lacking the ensurance of obtaining the optimal solution when the iteration tends to infinite. The reasons are that (1) the imputed values of multiple cells could affect each other towards the conformance to models, and (2) dependencies obtained from complete data may not be accurate enough to impute many unobserved values, which poses a tougher challenge of the convergence. In this work, we study the collaborative imputation with the convergence guarantee. By “collaborative”, we mean (1) all the missing cells can be collaboratively imputed with the guaranteed conformance to models, and (2) the imputation models are collaboratively optimized according to fillings as well. Our major technical highlights include 1) introducing the statistically explainable collaborative imputation via likelihood maximization, 2) designing a collaborative imputation algorithm for multiple missing cells and extending it into a parallel version equivalently, 3) improving the algorithm by both imputation values and models collaboratively optimized with the convergence guarantee in parallel, 4) designing the streaming imputation and adaptive parameter determination strategies. Experiments on real incomplete datasets demonstrate the superiority of our methods against twelve baselines, in both imputation accuracy and downstream applications.