Causal Discovery for Time Series : Based on Continuous Optimization

Sammanfattning: Causal discovery is an important field of study that seeks to understand the underlying relationships between variables in a system. The goal of causal discovery is to discover the causal relationships from observational data and determine the direction of influence between variables. This information is crucial for making informed decisions and predictions about the behavior of complex systems. This thesis investigates the application of continuous optimization-based causal discovery methods for time series data that exhibit temporal dependencies. The research focuses on finding the optimal method for discovering causal relationships in real-world data, which can include nonlinear associations. Additionally, this thesis evaluated and compared three causal discovery methods, namely NTS-NOTEARS (a neural network-based approach), DYNOTEARS (optimization-based approaches), and the newly developed LTS-NOTEARS (optimization-based approaches). After a thorough examination, NTS-NOTEARS was determined to be the optimal method due to its impressive performance and the potential for further uncertainty analysis. The NTS-NOTEARS method was subjected to extensive testing using various data sets and showed high accuracy, robustness to changes in sample size and number of nodes, and reliability in terms of uncertainty. In conclusion, this thesis provides a comprehensive analysis of the application of continuous optimization-based causal discovery methods for time series data. The research focuses on finding the optimal method for discovering causal relationships in real-world data and introduces a novel measure for analyzing model uncertainty in neural network-based methods. The thesis also presents a novel adaptation of established causal discovery methods to examine delayed causation and generate Structural Vector Auto-regressive (SVAR) models. After extensive testing and evaluation, the NTS-NOTEARS method was determined to be the preferred method, due to its high accuracy, robustness, and reliability.