Efficient structure learning with automatic sparsity selection for causal graph processes
This work addresses the challenge of scalable and accurate causal graph learning for researchers and practitioners in fields like finance and network analysis, though it is incremental as it builds on existing LASSO-based methods with improvements in automation and efficiency.
The paper tackles the problem of efficiently learning sparse directed adjacency matrices from time series data in causal graph processes, achieving state-of-the-art performance by automatically selecting the LASSO coefficient using non-parametric error metrics, as demonstrated on simulated stochastic block models and real S&P 500 stock data.
We propose a novel algorithm for efficiently computing a sparse directed adjacency matrix from a group of time series following a causal graph process. Our solution is scalable for both dense and sparse graphs and automatically selects the LASSO coefficient to obtain an appropriate number of edges in the adjacency matrix. Current state-of-the-art approaches rely on sparse-matrix-computation libraries to scale, and either avoid automatic selection of the LASSO penalty coefficient or rely on the prediction mean squared error, which is not directly related to the correct number of edges. Instead, we propose a cyclical coordinate descent algorithm that employs two new non-parametric error metrics to automatically select the LASSO coefficient. We demonstrate state-of-the-art performance of our algorithm on simulated stochastic block models and a real dataset of stocks from the S\&P$500$.