Rumor detection on social media remains a challenging task due to the complex propagation dynamics and the limited interpretability of existing models. While recent neural architectures capture content and structural features, they often fail to reveal the underlying causal mechanisms of misinformation spread. We propose CausalMamba, a novel framework that integrates Mamba-based sequence modeling, graph convolutional networks (GCNs), and differentiable causal discovery via NOTEARS. CausalMamba learns joint representations of temporal tweet sequences and reply structures, while uncovering latent causal graphs to identify influential nodes within each propagation chain. Experiments on the Twitter15 dataset show that our model achieves competitive classification performance compared to strong baselines, and uniquely enables counterfactual intervention analysis. Qualitative results demonstrate that removing top-ranked causal nodes significantly alters graph connectivity, offering interpretable insights into rumor dynamics. Our framework provides a unified approach for rumor classification and influence analysis, paving the way for more explainable and actionable misinformation detection systems.

We examine the number of controlled experiments required to discover a causal graph. Hauser and Buhlmann showed that the number of experiments required is logarithmic in the cardinality of maximum undirected clique in the essential graph. Their lower bounds, however, assume that the experiment designer cannot use randomization in selecting the experiments. We show that significant improvements are possible with the aid of randomization - in an adversarial (worst-case) setting, the designer can then recover the causal graph using at most O(log log n) experiments in expectation. This bound cannot be improved; we show it is tight for some causal graphs.

We examine the number of controlled experiments required to discover a causal graph. Hauser and Buhlmann showed that the number of experiments required is logarithmic in the cardinality of maximum undirected clique in the essential graph. Their lower bounds, however, assume that the experiment designer cannot use randomization in selecting the experiments. We show that significant improvements are possible with the aid of randomization – in an adversarial (worst-case) setting, the designer can then recover the causal graph using at most O(log log n) experiments in expectation. This bound cannot be improved; we show it is tight for some causal graphs.

Causal Graph Discovery (CGD) is the process of estimating the underlying probabilistic graphical model that represents joint distribution of features of a dataset. CGD-algorithms are broadly classified into two categories: (i) Constraint-based algorithms (outcome depends on conditional independence (CI) tests), (ii) Score-based algorithms (outcome depends on optimized score-function). Since, sensitive features of observational data is prone to privacy-leakage, Differential Privacy (DP) has been adopted to ensure user privacy in CGD. Adding same amount of noise in this sequential-natured estimation process affects the predictive performance of the algorithms. As initial CI tests in constraint-based algorithms and later iterations of the optimization process of score-based algorithms are crucial, they need to be more accurate, less noisy. Based on this key observation, we present CURATE (CaUsal gRaph AdapTivE privacy), a DP-CGD framework with adaptive privacy budgeting. In contrast to existing DP-CGD algorithms with uniform privacy budgeting across all iterations, CURATE allows adaptive privacy budgeting by minimizing error probability (for constraint-based), maximizing iterations of the optimization problem (for score-based) while keeping the cumulative leakage bounded. To validate our framework, we present a comprehensive set of experiments on several datasets and show that CURATE achieves higher utility compared to existing DP-CGD algorithms with less privacy-leakage.

We present a generalized linear structural causal model, coupled with a novel data-adaptive linear regularization, to recover causal directed acyclic graphs (DAGs) from time series. By leveraging a recently developed stochastic monotone Variational Inequality (VI) formulation, we cast the causal discovery problem as a general convex optimization. Furthermore, we develop a non-asymptotic recovery guarantee and quantifiable uncertainty by solving a linear program to establish confidence intervals for a wide range of non-linear monotone link functions. We validate our theoretical results and show the competitive performance of our method via extensive numerical experiments. Most importantly, we demonstrate the effectiveness of our approach in recovering highly interpretable causal DAGs over Sepsis Associated Derangements (SADs) while achieving comparable prediction performance to powerful ``black-box'' models such as XGBoost. Thus, the future adoption of our proposed method to conduct continuous surveillance of high-risk patients by clinicians is much more likely.

Causal Discovery methods aim to identify a DAG structure that represents causal relationships from observational data. In this article, we stress that it is important to test such methods for robustness in practical settings. As our main example, we analyze the NOTEARS method, for which we demonstrate a lack of scale-invariance. We show that NOTEARS is a method that aims to identify a parsimonious DAG from the data that explains the residual variance. We conclude that NOTEARS is not suitable for identifying truly causal relationships from the data.

We examine the number of controlled experiments required to discover a causal graph. Hauser and Buhlmann showed that the number of experiments required is logarithmic in the cardinality of maximum undirected clique in the essential graph. Their lower bounds, however, assume that the experiment designer cannot use randomization in selecting the experiments. We show that significant improvements are possible with the aid of randomization – in an adversarial (worst-case) setting, the designer can then recover the causal graph using at most O(log log n) experiments in expectation. This bound cannot be improved; we show it is tight for some causal graphs. We then show that in a non-adversarial (average-case) setting, even larger improvements are possible: if the causal graph is chosen uniformly at random under a Erdös-Rényi model then the expected number of experiments to discover the causal graph is constant.