Connecting Machine Learning to Causal Structure Learning with the Jacobian Matrix

Abstract

In this thesis, a novel approach is proposed to connect machine learning to causal structure learning with the Jacobian matrix of neural networks w.r.t. input variables. Causal learning distinguishing causes and effects is the way human understanding and modeling the world. In the machine learning era, it also ensures that the model is more interpretable and sufficiently robust. Due to the enormous cost of the traditional intervention and randomized experimental methods, studies of causal learning have focused on passive observational data which can generally be divided into static data and time-series data. For different data types and different levels of causal modeling, different machine learning techniques are applied to do causal modeling and the causal structure can be read out by the Jacobian matrix. We focus on three aspects in this thesis. Firstly, a novel framework of neural networks to causal structure learning on static data under structural causal models assumptions is proposed and the results of various experiments show our method has achieved state-of-the-art performance. Secondly, we extend static data causal modeling to the highest level as the physical system which is usually in terms of ordinary differential equations. Lastly, our Jacobianbased causal modeling framework is applied to time series data with the ORE-RNN technique and the results show that the success of temporal causal structure learning in time series cases.