Recurrent Imputation for Multivariate Time Series with Missing Values

Multivariate time series data are ubiquitous in real-world healthcare systems. It is a common issue that the data contain missing values due to various reasons, such as sensor damage, data corruption, patient dropout. There have been various works on filling the missing values in multivariate time series. Classical imputation methods include KNN-based, Matrix Factorization based, and Expectation-Maximization (EM) based imputation and so on. These methods are developed for general imputation purpose and rarely utilize the temporal relations between observations. Classical statistical time series models such as autoregressive (AR) models and dynamic linear models (DLM) (e.g. [1]) can capture the temporal information, but they are essentially linear and may not be suitable for modern complex large-scale data. ImputeTS [2] employs time dependencies on univariate time series imputation, which ignores feature correlations. Recent works [3, 4] develop the imputation framework that can take advantages of the traditional methods and resolve their drawbacks. Another trend of models is based on recurrent neural network (RNN) [5-10], utilizing RNN to capture temporal dependencies and further considering various aspects of the data characteristics, such as time decay, feature correlation, residual link, and temporal belief gate. In this paper, we propose an RNN-based imputation method for filling the missing values in multivariate time series. RNN is used to capture the temporal information of time series. We use a global RNN and variable-specific RNNs to perform imputation based on historical information, and a fusion gate to combine them. At each timestamp, we use a regression layer to impute the value of a certain variable using other variables, by utilizing the relationship of variables. Bi-directional imputation is adopted to improve the ability of long-term memory and performance of starting timestamps.