pTSE: A Multi-model Ensemble Method for Probabilistic Time Series Forecasting

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.

Hierarchical Capsule Prediction Network for Marketing Campaigns Effect

Marketing campaigns are a set of strategic activities that can promote a business's goal. The effect prediction for marketing campaigns in a real industrial scenario is very complex and challenging due to the fact that prior knowledge is often learned from observation data, without any intervention for the marketing campaign. Furthermore, each subject is always under the interference of several marketing campaigns simultaneously. Therefore, we cannot easily parse and evaluate the effect of a single marketing campaign. To the best of our knowledge, there are currently no effective methodologies to solve such a problem, i.e., modeling an individual-level prediction task based on a hierarchical structure with multiple intertwined events. In this paper, we provide an in-depth analysis of the underlying parse tree-like structure involved in the effect prediction task and we further establish a Hierarchical Capsule Prediction Network (HapNet) for predicting the effects of marketing campaigns. Extensive results based on both the synthetic data and real data demonstrate the superiority of our model over the state-of-the-art methods and show remarkable practicability in real industrial applications.