Human trajectory data, which plays a crucial role in various applications such as crowd management and epidemic prevention, is challenging to obtain due to practical constraints and privacy concerns. In this context, synthetic human trajectory data is generated to simulate as close as possible to real-world human trajectories, often under summary statistics and distributional similarities. However, the complexity of human mobility patterns is oversimplified by these similarities (a.k.a. ``Datasaurus''), resulting in intrinsic biases in both generative model design and benchmarks of the generated trajectories. Against this background, we propose MIRAGE, a huMan-Imitative tRAjectory GenErative model designed as a neural Temporal Point Process integrating an Exploration and Preferential Return model. It imitates the human decision-making process in trajectory generation, rather than fitting any specific statistical distributions as traditional methods do, thus avoiding the Datasaurus issue. Moreover, we also propose a comprehensive task-based evaluation protocol beyond Datasaurus to systematically benchmark trajectory generative models on four typical downstream tasks, integrating multiple techniques and evaluation metrics for each task, to comprehensively assess the ultimate utility of the generated trajectories. We conduct a thorough evaluation of MIRAGE on three real-world user trajectory datasets against a sizeable collection of baselines. Results show that compared to the best baselines, MIRAGE-generated trajectory data not only achieves the best statistical and distributional similarities with 59.0-71.5% improvement, but also yields the best performance in the task-based evaluation with 10.9-33.4% improvement.

Location prediction forecasts a user's location based on historical user mobility traces. To tackle the intrinsic sparsity issue of real-world user mobility traces, spatiotemporal contexts have been shown as significantly useful. Existing solutions mostly incorporate spatiotemporal distances between locations in mobility traces, either by feeding them as additional inputs to Recurrent Neural Networks (RNNs) or by using them to search for informative past hidden states for prediction. However, such distance-based methods fail to capture the time-varying temporal regularities of human mobility, where human mobility is often more regular in the morning than in other periods, for example; this suggests the usefulness of the actual timestamps besides the temporal distances. Against this background, we propose REPLAY, a general RNN architecture learning to capture the time-varying temporal regularities for location prediction. Specifically, REPLAY not only resorts to the spatiotemporal distances in sparse trajectories to search for the informative past hidden states, but also accommodates the time-varying temporal regularities by incorporating smoothed timestamp embeddings using Gaussian weighted averaging with timestamp-specific learnable bandwidths, which can flexibly adapt to the temporal regularities of different strengths across different timestamps. Our extensive evaluation compares REPLAY against a sizable collection of state-of-the-art techniques on two real-world datasets. Results show that REPLAY consistently and significantly outperforms state-of-the-art methods by 7.7\%-10.9\% in the location prediction task, and the bandwidths reveal interesting patterns of the time-varying temporal regularities.