Synthesized human trajectories are instrumental for a large number of applications. However, existing trajectory synthesizing models are limited in either modeling variable-length trajectories with continuous temporal distribution or incorporating multi-dimensional context information. In this paper, we propose a novel probabilistic model based on the variational temporal point process to synthesize human trajectories. This model combines the classical temporal point process with the novel neural variational inference framework, leading to its strong ability to model human trajectories with continuous temporal distribution, variable length, and multi-dimensional context information. Extensive experimental results on two real-world trajectory datasets show that our proposed model can synthesize trajectories most similar to real-world human trajectories compared with four representative baseline algorithms in terms of a number of usability metrics, demonstrating its effectiveness.

As an asset pricing model in economics and finance, factor model has been widely used in quantitative investment. Towards building more effective factor models, recent years have witnessed the paradigm shift from linear models to more flexible nonlinear data-driven machine learning models. However, due to low signal-to-noise ratio of the financial data, it is quite challenging to learn effective factor models. In this paper, we propose a novel factor model, FactorVAE, as a probabilistic model with inherent randomness for noise modeling. Essentially, our model integrates the dynamic factor model (DFM) with the variational autoencoder (VAE) in machine learning, and we propose a prior-posterior learning method based on VAE, which can effectively guide the learning of model by approximating an optimal posterior factor model with future information. Particularly, considering that risk modeling is important for the noisy stock data, FactorVAE can estimate the variances from the distribution over the latent space of VAE, in addition to predicting returns. The experiments on the real stock market data demonstrate the effectiveness of FactorVAE, which outperforms various baseline methods.