Causal discovery from observational data is a fundamental problem. A large number of algorithms have been proposed over the years for that purpose, but they usually handle the data of a single type, either continuous or discrete variables only. Recently, a few causal structure discovery algorithms have been developed for mixed data types, and received many applications. In this paper, we propose a structural equation model for mixed data types, which allows the causal mechanisms to be nonlinear and can consequently model many read-world situations. We prove that the causal structure is identifiable from the data distribution generated by the model under certain conditions. Moreover, we propose a maximum likelihood estimator and develop an efficient order search algorithm benefiting from a novel method of order space cutting, which can handle several hundred variables. We adopt automatic relevance determination kernel-based variable selection after order learning to recover the causal structure. Experiments on synthetic datasets demonstrate the accuracy and scalability of our approach. Especially, we apply our method to publicly available causal-effect pairs and show its superiority in the causal direction identification of mixed causal pairs. In addition, we show that our method can sensibly recover causal relationships on a publicly available real dataset and a private real-world dataset.

Prescriptive pricing is one of the most advanced pricing techniques, which derives the optimal price strategy to maximize the future profit/revenue by carrying out a two-stage process, demand modeling and price optimization.Demand modeling tries to reveal price-demand laws by discovering causal relationships among demands, prices, and objective factors, which is the foundation of price optimization.Existing methods either use regression or causal learning for uncovering the price-demand relations, but suffer from pain points in either accuracy/efficiency or mixed data type processing, while all of these are actual requirements in practical pricing scenarios.This paper proposes a novel demand modeling technique for practical usage.Speaking concretely, we propose a new locally consistent information criterion named MIC,and derive MIC-based inference algorithms for an accurate recovery of causal structure on mixed factor space.Experiments on simulate/real datasets show the superiority of our new approach in both price-demand law recovery and demand forecasting, as well as show promising performance in supporting optimal pricing.