Learning DAGs from Data with Few Root Causes
This work addresses DAG learning for data with sparse root causes, which is incremental as it builds on existing linear SEM frameworks.
The paper tackles the problem of learning directed acyclic graphs (DAGs) from data by introducing a model with few root causes and noise, proving identifiability and showing that the true DAG minimizes the L0-norm of root causes. It demonstrates superior performance compared to prior methods in this setting.
We present a novel perspective and algorithm for learning directed acyclic graphs (DAGs) from data generated by a linear structural equation model (SEM). First, we show that a linear SEM can be viewed as a linear transform that, in prior work, computes the data from a dense input vector of random valued root causes (as we will call them) associated with the nodes. Instead, we consider the case of (approximately) few root causes and also introduce noise in the measurement of the data. Intuitively, this means that the DAG data is produced by few data-generating events whose effect percolates through the DAG. We prove identifiability in this new setting and show that the true DAG is the global minimizer of the $L^0$-norm of the vector of root causes. For data with few root causes, with and without noise, we show superior performance compared to prior DAG learning methods.