Various probabilistic time series forecasting models have sprung up and shown remarkably good performance. However, the choice of model highly relies on the characteristics of the input time series and the fixed distribution that the model is based on. Due to the fact that the probability distributions cannot be averaged over different models straightforwardly, the current time series model ensemble methods cannot be directly applied to improve the robustness and accuracy of forecasting. To address this issue, we propose pTSE, a multi-model distribution ensemble method for probabilistic forecasting based on Hidden Markov Model (HMM). pTSE only takes off-the-shelf outputs from member models without requiring further information about each model. Besides, we provide a complete theoretical analysis of pTSE to prove that the empirical distribution of time series subject to an HMM will converge to the stationary distribution almost surely. Experiments on benchmarks show the superiority of pTSE overall member models and competitive ensemble methods.

Recent work on Natural Language Interfaces to Databases (NLIDB) has attracted considerable attention. NLIDB allow users to search databases using natural language instead of SQL-like query languages. While saving the users from having to learn query languages, multi-turn interaction with NLIDB usually involves multiple queries where contextual information is vital to understand the users' query intents. In this paper, we address a typical contextual understanding problem, termed as follow-up query analysis. In spite of its ubiquity, follow-up query analysis has not been well studied due to two primary obstacles: the multifarious nature of follow-up query scenarios and the lack of high-quality datasets. Our work summarizes typical follow-up query scenarios and provides a new FollowUp dataset with $1000$ query triples on 120 tables. Moreover, we propose a novel approach FANDA, which takes into account the structures of queries and employs a ranking model with weakly supervised max-margin learning. The experimental results on FollowUp demonstrate the superiority of FANDA over multiple baselines across multiple metrics.