Knowledge Discovery Through Structure Learning in Sequential Gaussian Graphical Models

Abstract

Probabilistic Graphical Models (PGMs) offer a robust yet intuitive framework to deal with uncertainty and complexity and have been effectively applied to diverse problems across multiple domains. While the majority of work has focused on cross-sectional data, there has been a recent increase of interest in developing temporal or sequential extensions to PGMs. In this paper we temporally extend structure learning in Gaussian Graphical Models to facilitate knowledge discovery in multivariate time series. We demonstrate the real world effectiveness of Sequential Gaussian Graphical Models (SEQ-GGMs) by obtaining unique insights into crypto-currency markets. We also propose novel time-domain metrics to analyze SEQ-GGMs. We develop numerical methods to improve computational efficiency and novel graph similarity metrics to evaluate SEQ-GGM prediction accuracy. Our interpolation approach obtains 4x speedup with 80% relative graph similarity accuracy.