Local Fisher Information Enables Sparse Causal Discovery
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Abstract (arXiv)
Sparse causal discovery calls for methods that exploit graph structure without estimating high-dimensional densities. We introduce Fisher Information Completion Search (FiCS), a source-first algorithm for additive noise models that uses one local Fisher score for both ordering and parent selection. Under regularity and nonconstant-parent conditions, we prove that a node's local Fisher information equals the noise Fisher information exactly when the conditioning set contains all parents, provided that it contains no descendants. This Fisher parent completion identifies the parent set as the unique minimal Fisher completion. With a maximum conditioning set size q at least the maximum indegree d, population FiCS queries marginals of at most q+1 variables and recovers the true directed acyclic graph under a positive ordering margin. Bounded conditioning also has a population advantage: reducing q toward d cannot decrease, and can strictly increase, the ordering margin. A growing non-Gaussian family separates local Fisher selection from conditional-variance and leaf-first Fisher ordering. For the regularized kernel Stein estimator, we establish high-dimensional DAG consistency under q1+log(p/q)+log p=o(n), uniform Fisher separation, local approximation, and compatible ridge and parent penalty parameters. Experiments show the strongest gains when n is small relative to p, quantify the effect of the conditioning size, and demonstrate competitive reference-graph recovery on three real-data benchmarks.
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References · 16
- 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 178
- 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 140
- 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 111
- 2018On Causal Discovery with Equal Variance Assumptioncited by 59
- 2015High-dimensional consistency in score-based and hybrid structure learningcited by 46
- 2023Scalable Causal Discovery with Score Matchingcited by 45
- 2023Causal Discovery with Score Matching on Additive Models with Arbitrary Noisecited by 43
- 2025CausalRivers -- Scaling up benchmarking of causal discovery for real-world time-seriescited by 26
- 2020Nonparametric Score Estimatorscited by 23
- 2019Causal discovery in heavy-tailed modelscited by 20
- 2022Optimal estimation of Gaussian DAG modelscited by 17
- 2024Ordering-Based Causal Discovery for Linear and Nonlinear Relationscited by 13
4 more
- 2024Score matching through the roof: linear, nonlinear, and latent variables causal discoverycited by 10
- 2025Unitless Unrestricted Markov-Consistent SCM Generation: Better Benchmark Datasets for Causal Discoverycited by 8
- 2025Causal Discovery via Quantile Partial Effectcited by 4
- 2026Optimization-Free Topological Sort for Causal Discovery via the Schur Complement of Score Jacobianscited by 1
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