An End-to-End Time Series Model for Simultaneous Imputation and Forecast

Learning the complex structure of multivariate time series has been one of the major interests across many application domains, including economics, transportation, manufacturing [Fortuin et al., 2020, Wu et al., 2021, Li et al., 2019, Zhou et al., 2021]. While there has been much progress in the data-driven learning and processing complex time series, it still remains as a challenging topic, in particular, when the data is corrupted [Cao et al., 2018, Kreindler and Lumsden, 2006, Yoon et al., 2018, Du et al., 2022]. In this paper, we consider the forecasting task which aims to make prediction of future values using historical data that may contain missing values. In addition, for many industrial problems, the time series features can be in two categories: auxiliary features (X) that provide information about the state of a system and target variables (Y) that depends on the auxiliary features and may convey valuable information. For example, in the operation of a chemical reactor, the auxiliary features include temperature, pressure and concentration of chemicals observed through a sensor network, while the target variable may include the quality of the material and throughput. We are interested in the time series problem where the data set consists of X and Y. In general, X is more readily available, as it is obtained from a sensor network, while Y may be temporally sparse since it may be expensive or difficult to collect the data. This so-called soft sensor problem has been of interest in many industrial applications [Shardt et al., 2015, Yuan et al., 2021].