Optimal structure learning and conditional independence testing
A new research paper establishes a fundamental link between optimal structure learning and optimal conditional independence testing. The study demonstrates that the minimax optimal rate for structure learning is determined by the minimax rate for conditional independence testing. This connection is achieved through a general reduction between the two problems for poly-forests and is illustrated with examples from Bernoulli, Gaussian, and nonparametric models. The findings suggest that a modified PC algorithm can achieve optimal performance in these settings, offering a unified framework for analyzing the statistical complexity of structure learning. AI