  Multivariate time series (MTS) data, when sampled irregularly and
asynchronously, often present extensive missing values. Conventional
methodologies for MTS analysis tend to rely on temporal embeddings based on
timestamps that necessitate subsequent imputations, yet these imputed values
frequently deviate substantially from their actual counterparts, thereby
compromising prediction accuracy. Furthermore, these methods typically fail to
provide robust initial embeddings for values infrequently observed or even
absent within the training set, posing significant challenges to model
generalizability. In response to these challenges, we propose SCAlable
Numerical Embedding (SCANE), a novel framework that treats each feature value
as an independent token, effectively bypassing the need for imputation. SCANE
regularizes the traits of distinct feature embeddings and enhances
representational learning through a scalable embedding mechanism. Coupling
SCANE with the Transformer Encoder architecture, we develop the Scalable
nUMerical eMbeddIng Transformer (SUMMIT), which is engineered to deliver
precise predictive outputs for MTS characterized by prevalent missing entries.
Our experimental validation, conducted across three disparate electronic health
record (EHR) datasets marked by elevated missing value frequencies, confirms
the superior performance of SUMMIT over contemporary state-of-the-art
approaches addressing similar challenges. These results substantiate the
efficacy of SCANE and SUMMIT, underscoring their potential applicability across
a broad spectrum of MTS data analytical tasks.
