Despite the growing availability of large datasets, causal structure learning remains computationally prohibitive at scale. We revisit sparsest-permutation learning for linear structural equation models and show that exact Cholesky factorization is unnecessary for structure recovery. This observation motivates a support-level relaxation that searches for sparse triangular factors over a precision-support screening graph. The relaxed formulation can be efficiently evaluated via masked zero-fill incomplete Cholesky factorization, enabling scalable comparison of candidate orderings. At the population level, we establish soundness for Markov equivalence class (MEC) recovery under no-cancellation and sparsest Markov representation assumptions, as well as robustness to ordering misspecification. Motivated by these guarantees, we introduce SCOPE, a sparse-Cholesky pipeline that provides a scalable implementation of the relaxed formulation. Experiments on synthetic and real datasets demonstrate that SCOPE matches the MEC recovery accuracy of substantially slower baselines, while achieving significantly reduced runtime and scaling to 10k variables.

We propose estimating Gaussian graphical models (GGMs) that are fair with respect to sensitive nodal attributes .

With the rapid development of web services, large amounts of time series data are generated and accumulated across various domains such as finance, healthcare, and online platforms. As such data often co-evolves with multiple variables interacting with each other, estimating the time-varying dependencies between variables (i.e., the dynamic network structure) has become crucial for accurate modeling. However, real-world data is often represented as tensor time series with multiple modes, resulting in large, entangled networks that are hard to interpret and computationally intensive to estimate. In this paper, we propose Kronecker Time-Varying Graphical Lasso (KTVGL), a method designed for modeling tensor time series. Our approach estimates mode-specific dynamic networks in a Kronecker product form, thereby avoiding overly complex entangled structures and producing interpretable modeling results. Moreover, the partitioned network structure prevents the exponential growth of computational time with data dimension. In addition, our method can be extended to stream algorithms, making the computational time independent of the sequence length. Experiments on synthetic data show that the proposed method achieves higher edge estimation accuracy than existing methods while requiring less computation time. To further demonstrate its practical value, we also present a case study using real-world data. Our source code and datasets are available at https://github.com/Higashiguchi-Shingo/KTVGL.

We study the propagation of outliers in cyclic causal graphs with linear structural equations, tracing them back to one or several "root cause" nodes. We show that it is possible to identify a short list of potential root causes provided that the perturbation is sufficiently strong and propagates according to the same structural equations as in the normal mode. This shortlist consists of the true root causes together with those of its parents lying on a cycle with the root cause. Notably, our method does not require prior knowledge of the causal graph.

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. Authors propose a method of estimating a graphical model for continuous data that blends the following three, established ideas: 1) assume the data follows a multivariate Gaussian and estimate using the graphical lasso; 2) do not assume the data follows a multivariate Gaussian and instead use a Gaussian copula, the nonparanormal, to allow arbitrary single variable marginals; or 3) assume a specific tree-structured factorization and model arbitrary bivariate marginals along the tree structure. The proposed method introduces the blossom tree, which is a specific factorization of the model into a collection of densely connected blossom components that are connected by a specific set of tree edges. In particular, each blossom is connected (via a pedicel node) to at most one tree edge. The blossom components are modeled as sparse multivariate Gaussians (or using the non-paranormal copula) and the tree edges are modeled as arbitrary bivariate distributions with single variable marginals that are consistent with the marginal of any blossom pedicel to which they are attached.