Structural Causal Models

We study identifiability in continuous-time linear stationary stochastic differential equations with a known causal structure. Unlike existing approaches, we relax the assumption of a known diffusion matrix, thereby respecting the model's intrinsic scale invariance. Therefore, rather than recovering drift coefficients themselves, we introduce edge-sign identifiability: for a given causal structure, we ask whether the sign of a given drift entry is uniquely determined across all observational covariance matrices induced by parametrisations compatible with that structure. This leads to a trichotomy of edge-sign identifiability: identifiable, non-identifiable, and partially identifiable. This trichotomy introduces the new notion of partial identifiability to the literature, which we show is a genuine category in our setting. Under a notion of faithfulness, we derive criteria to identify membership of each category for general graphs. Applying our criteria to specific causal structures, both analogous to classical causal settings (e.g., instrumental variables) and novel cyclic settings, we determine their edge-sign identifiability and, in some cases, obtain explicit expressions for the sign of a target edge in terms of the observational covariance matrix.

Which internal mechanisms of a neural network can be replaced while preserving the computation it performs? Structured pruning asks for smaller deployable networks; causal abstraction asks for high-level models that commute with interventions. We introduce causal mechanism reduction (CMR), a framework that treats a trained network as a deterministic structural causal model and replaces selected internal variables by constants or affine functions of retained variables. These replacements compile exactly into smaller dense networks by bias and weight folding, and induce reduced causal models testable with interchange interventions. We derive a unified second-order replacement-risk objective whose special cases recover mean replacement, variance-based pruning (VBP), logit-distortion scoring, and affine neuron merging, together with a margin-based certificate linking logit distortion to interchange-intervention agreement. The framework also exposes a basic invariance requirement: functionally identical ReLU networks should induce the same reduction. Under exact positive-scaling reparameterizations, VBP's kept set collapses to chance-level overlap while the logit-distortion score is exactly invariant. Empirically, CMR variants are competitive with VBP under matched fine-tuning of DeiT-Tiny on ImageNet-100; the clearer separation appears in the invariance and interchange tests, where the logit-distortion score preserves kept sets and consistently improves distributional fidelity. CMR thus gives pruning, compilation, and causal-abstraction verification a common object to optimize and verify.

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 and yields encouraging results on simulated data and real data from biology and cloud computing.

Fair machine learning seeks to identify and mitigate biases in predictions against unfavorable populations characterized by demographic attributes, such as race and gender. Recent research has extended fairness to graph data, such as social networks, but many studies neglect the causal relationships among data instances. This paper addresses a prevalent challenge in many fair machine learning research, which typically assumes independent and identically distributed (IID) data, from the causal perspective. Specifically, this work targets the circumstance where nodes with different neighborhood structures follow different causal mechanisms, violating the invariance assumptions required for classical structural causal models and do-calculus. We base our research on the Network Structural Causal Model (NSCM) framework and develop a Message Passing Variational Autoencoder for Causal Inference (MPVA) to compute interventional distributions for causally fair node classification. We establish theoretical soundness under two conditions: Decomposability and Graph Independence. These conditions formalize when causal mechanism heterogeneity can be overcome by constructing a structural representation that restores invariance and facilitates the computation of interventional distributions using do-calculus in non-IID settings. Empirical evaluations on semi-synthetic and real-world datasets demonstrate that MPVA outperforms conventional methods by effectively approximating interventional distributions and mitigating bias. Our findings demonstrate the potential of causality-based fairness in complex ML applications and motivate future work on relaxing the classic assumptions in algorithmic fairness.

Causal discovery is a difficult problem that typically relies on strong assumptions on the data-generating model, such as non-Gaussianity. In practice, many modern applications provide multiple related views of the same system, which has rarely been considered for causal discovery. Here, we leverage this multi-view structure to achieve causal discovery with weak assumptions. We propose a multi-view linear Structural Equation Model (SEM) that extends the well-known framework of non-Gaussian disturbances by alternatively leveraging correlation over views. We prove the identifiability of the model for acyclic SEMs. Subsequently, we propose several multi-view causal discovery algorithms, inspired by single-view algorithms (DirectLiNGAM, PairwiseLiNGAM, and ICA-LiNGAM). The new methods are validated through simulations and applications on neuroimaging data, where they enable the estimation of causal graphs between brain regions.

We study the problem of restricting a Markov equivalence class of maximal ancestral graphs (MAGs) to only those MAGs that contain certain edge marks, which we refer to as expert or orientation knowledge. Such a restriction of the Markov equivalence class can be uniquely represented by a restricted essential ancestral graph. Our contributions are several-fold. First, we prove certain properties for the entire Markov equivalence class including a conjecture from Ali et al. (2009). Second, we present several new sound graphical orientation rules for adding orientation knowledge to an essential ancestral graph. We also show that some orientation rules of Zhang (2008b) are not needed for restricting the Markov equivalence class with orientation knowledge. Third, we provide an algorithm for including this orientation knowledge and show that in certain settings the output of our algorithm is a restricted essential ancestral graph. Finally, outside of the specified settings, we provide an algorithm for checking whether a graph is a restricted essential graph and discuss its runtime. This work can be seen as a generalization of Meek (1995) to settings which allow for latent confounding.

Continuous-Time Dynamic Graphs (CTDGs) enable fine-grained modeling of evolving relational systems. However, most existing CTDG representation learning methods are tailored to in-distribution settings and exhibit limited robustness under out-of-distribution (OOD) shifts. Although recent causal approaches learn invariant representations via interventions, they are primarily designed for static or discrete-time graphs and become computationally prohibitive for CTDGs due to the combinatorial explosion of structural and temporal variations. To address these challenges, we propose CIR, a framework grounded in a novel structural causal model termed the ICCM. To avoid exhaustive interventions, we leverage the Normalized Weighted Geometric Mean (NWGM) to efficiently approximate interventional predictions. We further instantiate ICCM within a practical deep learning architecture that jointly captures invariant structural and temporal patterns through dedicated subgraph extractors, and maintains an environment memory bank to model distributional shifts across evolving contexts. Extensive experiments demonstrate that CIR consistently outperforms existing methods under diverse OOD scenarios.