Time series graphical models have recently received considerable attention for characterizing (conditional) dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned blockwise dependence, with distinct patterns within and across blocks. In this paper, we introduce a new class of time series Gaussian chain graph models that represent contemporaneous and lagged causal relations via directed edges across blocks, while capturing within-block conditional dependencies through undirected edges. In the frequency domain, this formulation induces a cross-frequency shared group sparse plus group low-rank decomposition of the inverse spectral density matrices, which we exploit to establish identifiability of the time series chain graph structure. Building on this, we then propose a three-stage learning procedure for estimating the undirected and directed edge sets, which involves optimizing a regularized Whittle likelihood with a group lasso penalty to encourage group sparsity and a novel tensor-unfolding nuclear norm penalty to enforce group low-rank structure. We investigate the asymptotic properties of the proposed method, ensuring its consistency for exact recovery of the chain graph structure. The superior empirical performance of the proposed method is demonstrated through both extensive simulation studies and an application to U.S. macroeconomic data that highlights key monetary policy transmission mechanisms.

Neural Information Processing Systems http://nips.cc/

Maximal Ancestral Graphs (MAGs) provide an abstract representation of Directed Acyclic Graphs (DAGs) with latent (selection) variables. These graphical objects encode information about ancestral relations and d-separations of the DAGs they represent. This abstract representation has been used amongst others to prove the soundness and completeness of the FCI algorithm for causal discovery, and to derive a do-calculus for its output. One significant inherent limitation of MAGs is that they rule out the possibility of cyclic causal relationships. In this work, we address that limitation. We introduce and study a class of graphical objects that we coin ''$σ$-Maximal Ancestral Graphs'' (''$σ$-MAGs''). We show how these graphs provide an abstract representation of (possibly cyclic) Directed Graphs (DGs) with latent (selection) variables, analogously to how MAGs represent DAGs. We study the properties of these objects and provide a characterization of their Markov equivalence classes.

Deep learning offers a promising avenue for automating many recognition tasks in fields such as medicine and forensics. However, the "black box" nature of these models hinders their adoption in high-stakes applications where trust and accountability are required. For 3D shape recognition tasks in particular, this paper introduces the Class Node Graph Attention Network (CGAT) architecture to address this need. Applied to 3D meshes of third molars derived from CBCT images, for Demirjian stage allocation, CGAT utilizes graph attention convolutions and an inherent attention mechanism, visualized via attention rollout, to explain its decision-making process. We evaluated the local mean curvature and distance to centroid node features, both individually and in combination, as well as model depth, finding that models incorporating directed edges to a global CLS node produced more intuitive attention maps, while also yielding desirable classification performance. We analyzed the attention-based explanations of the models, and their predictive performances to propose optimal settings for the CGAT. The combination of local mean curvature and distance to centroid as node features yielded a slight performance increase with a 0.76 weighted F1 score, and more comprehensive attention visualizations. The CGAT architecture's ability to generate human-understandable attention maps can enhance trust and facilitate expert validation of model decisions. While demonstrated on dental data, CGAT is broadly applicable to graph-based classification and regression tasks, promoting wider adoption of transparent and competitive deep learning models in high-stakes environments.

(Theorem 1). A.1 Graphical representation Theorem 1. V ertex X is removable in a MAG M over the variables V, if and only if 1. for any Y 2 Adj ( X) and Z 2 Ch ( X) [ N ( X) \{ Y }, Y and Z are adjacent, and 2. Let H denote the induced subgraph of M over V \{ X } . Since X is removable in M, by definition of removability, ( Y? M, Lemma 6 implies that u is not m-connecting relative to W in H . (: Lemma 6 implies that u is not m-connecting relative to W in M . This contradiction proves that X cannot have a descendant in { Y,Z }[ W, which implies that X blocks u in M .

Not every causal relation between variables is equal, and this can be leveraged for the task of causal discovery. Recent research shows that pairs of variables with particular type assignments induce a preference on the causal direction of other pairs of variables with the same type. Although useful, this assignment of a specific type to a variable can be tricky in practice. We propose a tag-based causal discovery approach where multiple tags are assigned to each variable in a causal graph. Existing causal discovery approaches are first applied to direct some edges, which are then used to determine edge relations between tags. Then, these edge relations are used to direct the undirected edges. Doing so improves upon purely type-based relations, where the assumption of type consistency lacks robustness and flexibility due to being restricted to single types for each variable. Our experimental evaluations show that this boosts causal discovery and that these high-level tag relations fit common knowledge.

Recent advances have established the identifiability of a directed acyclic graph (DAG) under additive noise models (ANMs), spurring the development of various causal discovery methods. However, most existing methods make restrictive model assumptions, rely heavily on general independence tests, or require substantial computational time. To address these limitations, we propose a sequential procedure to orient undirected edges in a completed partial DAG (CPDAG), representing an equivalence class of DAGs, by leveraging the pairwise additive noise model (PANM) to identify their causal directions. We prove that this procedure can recover the true causal DAG assuming a restricted ANM. Building on this result, we develop a novel constraint-based algorithm for learning causal DAGs under nonlinear ANMs. Given an estimated CPDAG, we develop a ranking procedure that sorts undirected edges by their adherence to the PANM, which defines an evaluation order of the edges. To determine the edge direction, we devise a statistical test that compares the log-likelihood values, evaluated with respect to the competing directions, of a sub-graph comprising just the candidate nodes and their identified parents in the partial DAG. We further establish the structural learning consistency of our algorithm in the large-sample limit. Extensive experiments on synthetic and real-world datasets demonstrate that our method is computationally efficient, robust to model misspecification, and consistently outperforms many existing nonlinear DAG learning methods.

Unmanned Aerial Vehicles (UAVs), also known as drones, have gained popularity in various fields such as agriculture, emergency response, and search and rescue operations. UAV networks are susceptible to several security threats, such as wormhole, jamming, spoofing, and false data injection. Time Delay Attack (TDA) is a unique attack in which malicious UAVs intentionally delay packet forwarding, posing significant threats, especially in time-sensitive applications. It is challenging to distinguish malicious delay from benign network delay due to the dynamic nature of UAV networks, intermittent wireless connectivity, or the Store-Carry-Forward (SCF) mechanism during multi-hop communication. Some existing works propose machine learning-based centralized approaches to detect TDA, which are computationally intensive and have large message overheads. This paper proposes a novel approach DATAMUt, where the temporal dynamics of the network are represented by a weighted time-window graph (TWiG), and then two deterministic polynomial-time algorithms are presented to detect TDA when UAVs have global and local network knowledge. Simulation studies show that the proposed algorithms have reduced message overhead by a factor of five and twelve in global and local knowledge, respectively, compared to existing approaches. Additionally, our approaches achieve approximately 860 and 1050 times less execution time in global and local knowledge, respectively, outperforming the existing methods.

Large language models (LLMs) have demonstrated remarkable capabilities across various domains, especially in text processing and generative tasks. Recent advancements in the reasoning capabilities of state-of-the-art LLMs, such as OpenAI-o1, have significantly broadened their applicability, particularly in complex problem-solving and logical inference. However, most existing LLMs struggle with notable limitations in handling graph combinatorial optimization (GCO) problems. To bridge this gap, we formally define the Optimal Thoughts Design (OTD) problem, including its state and action thought space. We then introduce a novel framework, GraphThought, designed to generate high-quality thought datasets for GCO problems. Leveraging these datasets, we fine-tune the Llama-3-8B-Instruct model to develop Llama-GT. Notably, despite its compact 8B-parameter architecture, Llama-GT matches the performance of state-of-the-art LLMs on the GraphArena benchmark. Experimental results show that our approach outperforms both proprietary and open-source models, even rivaling specialized models like o1-mini. This work sets a new state-of-the-art benchmark while challenging the prevailing notion that model scale is the primary driver of reasoning capability.