Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
High-Dimensional Learning of Linear Causal Networks via Inverse Covariance Estimation
Authors: Po-Ling Loh, Peter Bühlmann
JMLR 2014 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We establish a new framework for statistical estimation of directed acyclic graphs (DAGs) when data are generated from a linear, possibly non-Gaussian structural equation model. Our framework consists of two parts: (1) inferring the moralized graph from the support of the inverse covariance matrix; and (2) selecting the best-scoring graph amongst DAGs that are consistent with the moralized graph. We show that when the error variances are known or estimated to close enough precision, the true DAG is the unique minimizer of the score computed using the reweighted squared ℓ2-loss. Our population-level results have implications for the identifiability of linear SEMs when the error covariances are specified up to a constant multiple. On the statistical side, we establish rigorous conditions for high-dimensional consistency of our two-part algorithm, defined in terms of a gap between the true DAG and the next best candidate. Finally, we demonstrate that dynamic programming may be used to select the optimal DAG in linear time when the treewidth of the moralized graph is bounded. We prove the correctness of our graph estimation algorithm by deriving new results about the theory of linear SEMs. We present a novel result showing that for almost every choice of linear coefficients, the support of the inverse covariance matrix of the joint distribution is identical to the edge structure of the moralized graph. Although a similar relationship between the support of the inverse covariance matrix and the edge structure of an undirected conditional independence graph has long been established for multivariate Gaussian models (Lauritzen, 1996), our core result in Theorem 2 does not exploit Gaussianity, and the proof technique is entirely new. |
| Researcher Affiliation | Academia | Po-Ling Loh EMAIL Department of Statistics The Wharton School 466 Jon M. Huntsman Hall 3730 Walnut Street Philadelphia, PA 19104, USA; Peter Bühlmann EMAIL Seminar für Statistik ETH Zürich Rämistrasse 101, HG G17 8092 Zürich, Switzerland. Both authors are affiliated with universities (The Wharton School, ETH Zurich) as indicated by their institutional names and email domains (.upenn.edu, .ethz.ch). |
| Pseudocode | Yes | Algorithm 1 Framework for DAG estimation 1: Input: Data samples {xi}n i=1 from a linear SEM 2: Obtain estimate bΘ of inverse covariance matrix (e.g., using graphical Lasso) 3: Construct moralized graph c M with edge set defined by supp(bΘ) 4: Compute scores for DAGs that are consistent with c M (e.g., using squared ℓ2-error) 5: Find minimal-scoring b G (using dynamic programming when score is decomposable and c M has bounded treewidth) 6: Output: Estimated DAG b G |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code, nor does it provide links to a code repository or mention code in supplementary materials. |
| Open Datasets | No | The paper discusses theoretical frameworks and algorithms, using generic 'Data samples {xi}n i=1 from a linear SEM' in its algorithm description. It mentions application domains like genetics, epidemiology, and time series analysis but does not provide any specific named datasets, citations to datasets, or links to publicly available data used for empirical evaluation. There is no concrete access information for any dataset. |
| Dataset Splits | No | The paper is theoretical and focuses on algorithm design, proofs, and conditions for statistical consistency, rather than empirical evaluation using specific datasets. Therefore, it does not provide details on training, testing, or validation splits for any dataset. |
| Hardware Specification | No | The paper is theoretical and focuses on statistical methods and algorithms for causal inference. It does not describe any experimental results or the hardware used to perform computations or run simulations. |
| Software Dependencies | No | The paper describes theoretical algorithms and frameworks (e.g., graphical Lasso, dynamic programming) but does not provide specific software names with version numbers or library dependencies required for implementation or reproduction of any empirical results. |
| Experiment Setup | No | The paper presents a theoretical framework and algorithms for learning causal networks. It does not contain any sections detailing an experimental setup, including hyperparameters, training configurations, or system-level settings, as it does not report empirical results. |