Title: Top-K Structure Search with Solution Path
Primary area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
Keywords: Structure learning, Bayesian networks, Top-K solutions, Solution path, Model uncertainty

Abstract: Structure learning algorithms often output a single estimated graph without offering alternative candidates or a way to capture model uncertainty. This is limiting in finite-sample settings with weak signals or noise, where multiple structures can explain the data equally well. In this work, we propose Top-K Structure Search with Solution Path, an algorithm that systematically tracks the evolution of edge weights across a range of values of the $\ell_1$ sparsity regularization parameter $\lambda$. By scoring candidate structures with the Bayesian Information Criterion (BIC), our method ranks and returns the Top-K most plausible structures. Unlike traditional approaches that yield a single solution, our framework provides a ranked set of candidates, enabling better uncertainty assessment. Experiments on synthetic and real-world datasets demonstrate the effectiveness of our approach in capturing structural variability. This highlights the advantage of leveraging solution paths for structure learning, especially in scenarios where committing to a single graph is unreliable. Our framework offers a complementary perspective on structure learning by considering multiple candidate solutions, thereby mitigating the practical instability of solely relying on a single result.

TL;DR: We introduce a Top-K structure learning algorithm that tracks edge evolution along the L1-regularization path, returning multiple high-scoring candidate graphs to better capture structural uncertainty in noisy or finite-sample settings.