Causal Discovery with Fewer Conditional Independence Tests
This addresses a fundamental bottleneck in causal inference for science and data analysis, offering a more scalable approach, though it is incremental as it builds on existing constraint-based methods.
The paper tackles the problem of causal discovery algorithms requiring an exponential number of conditional independence tests by showing that a coarser representation of the causal graph can be learned with a polynomial number of tests, leading to the first efficient algorithm for recovering the true causal graph in identifiable cases.
Many questions in science center around the fundamental problem of understanding causal relationships. However, most constraint-based causal discovery algorithms, including the well-celebrated PC algorithm, often incur an exponential number of conditional independence (CI) tests, posing limitations in various applications. Addressing this, our work focuses on characterizing what can be learned about the underlying causal graph with a reduced number of CI tests. We show that it is possible to a learn a coarser representation of the hidden causal graph with a polynomial number of tests. This coarser representation, named Causal Consistent Partition Graph (CCPG), comprises of a partition of the vertices and a directed graph defined over its components. CCPG satisfies consistency of orientations and additional constraints which favor finer partitions. Furthermore, it reduces to the underlying causal graph when the causal graph is identifiable. As a consequence, our results offer the first efficient algorithm for recovering the true causal graph with a polynomial number of tests, in special cases where the causal graph is fully identifiable through observational data and potentially additional interventions.