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1. Entropic Inequality Constraints from e-separation Relations in Directed Acyclic Graphs with Hidden Variables

   Noam Finkelstein; Beata Zjawin; Elie Wolfe; Ilya Shpitser; Robert W. Spekkens (July 2021, Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence)

   de Campos, Cassio and (Ed.)

   Directed acyclic graphs (DAGs) with hidden variables are often used to characterize causal relations between variables in a system. When some variables are unobserved, DAGs imply a notoriously complicated set of constraints on the distribution of observed variables. In this work, we present entropic inequality constraints that are implied by e- separation relations in hidden variable DAGs with discrete observed variables. The constraints can intuitively be understood to follow from the fact that the capacity of variables along a causal path- way to convey information is restricted by their entropy; e.g. at the extreme case, a variable with entropy 0 can convey no information. We show how these constraints can be used to learn about the true causal model from an observed data distribution. In addition, we propose a measure of causal influence called the minimal mediary entropy, and demonstrate that it can augment traditional measures such as the average causal effect. 

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2. Causal lifting and link prediction

   https://doi.org/10.1098/rspa.2023.0121  

   Cotta, Leonardo; Bevilacqua, Beatrice; Ahmed, Nesreen; Ribeiro, Bruno (August 2023, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences)

   Existing causal models for link prediction assume an underlying set of inherent node factors—an innate characteristic defined at the node’s birth—that governs the causal evolution of links in the graph. In some causal tasks, however, link formation ispath-dependent: the outcome of link interventions depends on existing links. Unfortunately, these existing causal methods are not designed for path-dependent link formation, as the cascading functional dependencies between links (arising frompath dependence) are either unidentifiable or require an impractical number of control variables. To overcome this, we develop the first causal model capable of dealing with path dependencies in link prediction. In this work, we introduce the concept of causal lifting, an invariance in causal models of independent interest that, on graphs, allows the identification of causal link prediction queries using limited interventional data. Further, we show how structural pairwise embeddings exhibit lower bias and correctly represent the task’s causal structure, as opposed to existing node embeddings, e.g. graph neural network node embeddings and matrix factorization. Finally, we validate our theoretical findings on three scenarios for causal link prediction tasks: knowledge base completion, covariance matrix estimation and consumer-product recommendations. 

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3. iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Models

   Chen, Tianyu; Bello, Kevin; Aragam, Bryon; Ravikumar, Pradeep (December 2023, Neural Information Processing Systems (NeurIPS), 2023)

   Structural causal models (SCMs) are widely used in various disciplines to repre- sent causal relationships among variables in complex systems. Unfortunately, the underlying causal structure is often unknown, and estimating it from data remains a challenging task. In many situations, however, the end goal is to localize the changes (shifts) in the causal mechanisms between related datasets instead of learn- ing the full causal structure of the individual datasets. Some applications include root cause analysis, analyzing gene regulatory network structure changes between healthy and cancerous individuals, or explaining distribution shifts. This paper focuses on identifying the causal mechanism shifts in two or more related datasets over the same set of variables—without estimating the entire DAG structure of each SCM. Prior work under this setting assumed linear models with Gaussian noises; instead, in this work we assume that each SCM belongs to the more general class of nonlinear additive noise models (ANMs). A key technical contribution of this work is to show that the Jacobian of the score function for the mixture distribution allows for the identification of shifts under general non-parametric functional mechanisms. Once the shifted variables are identified, we leverage recent work to estimate the structural differences, if any, for the shifted variables. Experiments on synthetic and real-world data are provided to showcase the applicability of this approach. Code implementing the proposed method is open-source and publicly available at https://github.com/kevinsbello/iSCAN. 

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4. Transition to Limit-Cycle Oscillation in Fluid-Structure Interactions: Mutual Correlations and Causal Dependencies

   https://doi.org/10.2514/1.J062082  

   Bagchi, Sombuddha; Unni, Vishnu R.; Saha, Abhishek (April 2023, AIAA Journal)

   We investigate the dynamic characteristics corresponding to the structural fluctuations of a cantilever suspended in a turbulent flow. To investigate the intricate dynamics of the flow–structure interaction, first, we explore the ability of network analysis to identify the different dynamic states and probe the viability of using quantifiers of network topology as precursors for the onset of limit-cycle oscillations. By increasing the Reynolds number, we observe that the structural oscillations, measured using a strain gauge, transition from low-amplitude chaotic oscillations to large-amplitude periodic oscillations associated with limit-cycle oscillations. We characterize the dynamic states of the system by constructing the weighted correlation network from the time series of strain and identifying the network properties that have the potential to be used as precursors for the onset of limit-cycle oscillations. Furthermore, we use Pearson correlation to illustrate the evolution of mutual statistical influence between the structural oscillations and the flowfield. We use this information and the Granger causality to identify the causal dependence between the structural oscillations and velocity fluctuations. By identifying the causal variable during each regime, we illustrate the directional dependence through a cause–effect relationship in this flow–structure interaction as it transitions to limit-cycle oscillations. 

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5. Learning nonparametric latent causal graphs with unknown interventions

   Jiang, Yibo; Aragam, Bryon (September 2024, Advances in Neural Information Processing Systems 36 (NeurIPS 2023) Main Conference Track)

   We establish conditions under which latent causal graphs are nonparametrically identifiable and can be reconstructed from unknown interventions in the latent space. Our primary focus is the identification of the latent structure in a measurement model, i.e. causal graphical models where dependence between observed variables is insignificant compared to dependence between latent representations, without making parametric assumptions such as linearity or Gaussianity. Moreover, we do not assume the number of hidden variables is known, and we show that at most one unknown intervention per hidden variable is needed. This extends a recent line of work on learning causal representations from observations and interventions. The proofs are constructive and introduce two new graphical concepts -- imaginary subsets and isolated edges -- that may be useful in their own right. As a matter of independent interest, the proofs also involve a novel characterization of the limits of edge orientations within the equivalence class of DAGs induced by unknown interventions. Experiments confirm that the latent graph can be recovered from data using our theoretical results. These are the first results to characterize the conditions under which causal representations are identifiable without making any parametric assumptions in a general setting with unknown interventions and without faithfulness. 

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