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.

Ensuring privacy in large-scale open datasets is increasingly challenging under regulations such as the General Data Protection Regulation (GDPR). While differential privacy (DP) provides strong theoretical guarantees, it primarily focuses on noise injection during model training, neglecting privacy preservation at the data publishing stage. Existing privacy-preserving data publishing (PPDP) approaches struggle to balance privacy and utility, particularly when data publishers and users are distinct entities. To address this gap, we focus on the graph recovery problem and propose a novel privacy-preserving estimation framework for open graph data, leveraging Gaussian DP (GDP) with a structured noise-injection mechanism. Unlike traditional methods that perturb gradients or model updates, our approach ensures unbiased graph structure recovery while enforcing DP at the data publishing stage. Moreover, we provide theoretical guarantees on estimation accuracy and extend our method to discrete-variable graphs, a setting often overlooked in DP research. Experimental results in graph learning demonstrate robust performance, offering a viable solution for privacy-conscious graph analysis.