Deep Fuzzy Cognitive Maps for Interpretable Multivariate Time Series Prediction

The fuzzy cognitive map (FCM) is a powerful model for system state prediction and interpretable knowledge representation. Recent years have witnessed the tremendous efforts devoted to enhancing the basic FCM, such as introducing temporal factors, uncertainty or fuzzy rules to improve interpretation, and introducing fuzzy neural networks or wavelets to improve time series prediction. But how to achieve high-precision yet interpretable prediction in cross-domain real-life applications remains a great challenge. In this article, we propose a novel FCM extension called deep FCM (DFCM) for multivariate time series forecasting, in order to take both the advantage of FCM in interpretation and the advantage of deep neural networks in prediction. Specifically, to improve the predictive power, DFCM leverages a fully connected neural network to model connections (relationships) among concepts in a system, and a recurrent neural network to model unknown exogenous factors that have influences on system dynamics. Moreover, to foster model interpretability encumbered by the embedded deep structures, a partial derivative-based approach is proposed to measure the connection strengths between concepts in DFCM. An alternate function gradient descent algorithm is then proposed for parameter inference. The effectiveness of DFCM is validated over four publicly available datasets with the presence of seven baselines. DFCM indeed provides an important clue to building interpretable predictors for real-life applications.