Sparsity is a common issue in many trajectory datasets, including human mobility data. This issue frequently brings more difficulty to relevant learning tasks, such as trajectory imputation and prediction. Nowadays, little existing work simultaneously deals with imputation and prediction on human trajectories. This work plans to explore whether the learning process of imputation and prediction could benefit from each other to achieve better outcomes. And the question will be answered by studying the coexistence patterns between missing points and observed ones in incomplete trajectories. More specifically, the proposed model develops an imputation component based on the self-attention mechanism to capture the coexistence patterns between observations and missing points among encoder-decoder layers. Meanwhile, a recurrent unit is integrated to extract the sequential embeddings from newly imputed sequences for predicting the following location. Furthermore, a new implementation called Imputation Cycle is introduced to enable gradual imputation with prediction enhancement at multiple levels, which helps to accelerate the speed of convergence. The experimental results on three different real-world mobility datasets show that the proposed approach has significant advantages over the competitive baselines across both imputation and prediction tasks in terms of accuracy and stability.

Real-world clinical time series data sets exhibit a high prevalence of missing values. Hence, there is an increasing interest in missing data imputation. Traditional statistical approaches impose constraints on the data-generating process and decouple imputation from prediction. Recent works propose recurrent neural network based approaches for missing data imputation and prediction with time series data. However, they generate deterministic outputs and neglect the inherent uncertainty. In this work, we introduce a unified Bayesian recurrent framework for simultaneous imputation and prediction on time series data sets. We evaluate our approach on two real-world mortality prediction tasks using the MIMIC-III and PhysioNet benchmark datasets. We demonstrate significant performance gains over state-of-the-art methods, and provide strategies to use the resulting probability distributions to better assess reliability of the imputations and predictions.