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1. 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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2. Causal Markov Blanket Representation Learning for Out-of-distribution Generalization

   Yin, Naiyu; Wang, Hanjing; Gao, Tia; Dhurandhar, Amit; Ji, Qiang (December 2023, NeurIPS Workshop: Causal Representation Learning, 2023)

   The pursuit of generalizable representations in the realm of machine learning and computer vision is a dynamic field of research. Typically, current methods aim to secure invariant representations by either harnessing domain expertise or leveraging data from multiple domains. In this paper, we introduce a novel approach that involves acquiring Causal Markov Blanket (CMB) representations to improve prediction performance in the face of distribution shifts. Causal Markov Blanket representations comprise the direct causes and effects of the target variable, rendering them invariant across diverse domains. To elaborate, our approach commences with the introduction of a novel structural causal model (SCM) equipped with latent representations, designed to capture the underlying causal mechanisms governing the data generation process. Subsequently, we propose a CMB representation learning framework that derives representations conforming to the proposed SCM. In comparison to state-of-the-art domain generalization methods, our approach exhibits robustness and adaptability under distribution shifts 

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3. Effective Causal Discovery under Identifiable Heteroscedastic Noise Model

   https://doi.org/10.1609/aaai.v38i15.29586  

   Yin, Naiyu; Gao, Tian; Yu, Yue; Ji, Qiang (March 2024, Proceedings of the AAAI Conference on Artificial Intelligence)

   Capturing the underlying structural causal relations represented by Directed Acyclic Graphs (DAGs) has been a fundamental task in various AI disciplines. Causal DAG learning via the continuous optimization framework has recently achieved promising performance in terms of accuracy and efficiency. However, most methods make strong assumptions of homoscedastic noise, i.e., exogenous noises have equal variances across variables, observations, or even both. The noises in real data usually violate both assumptions due to the biases introduced by different data collection processes. To address the heteroscedastic noise issue, we introduce relaxed implementable sufficient conditions and prove the identifiability of a general class of SEM subject to those conditions. Based on the identifiable general SEM, we propose a novel formulation for DAG learning which accounts for the noise variance variation across variables and observations. We then propose an effective two-phase iterative DAG learning algorithm to address the increasing optimization difficulties and learn a causal DAG from data with heteroscedastic variables noise under varying variance. We show significant empirical gains of the proposed approaches over state-of-the-art methods on both synthetic data and real data. 

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4. Towards Characterizing Domain Counterfactuals for Invertible Latent Causal Models

   Zhou, Zeyu; Bai, Ruqi; Kulinski, Sean; Kocaoglu, Murat; Inouye, David I (May 2024, International Conference on Learning Representations)

   Answering counterfactual queries has important applications such as explainability, robustness, and fairness but is challenging when the causal variables are unobserved and the observations are non-linear mixtures of these latent variables, such as pixels in images. One approach is to recover the latent Structural Causal Model (SCM), which may be infeasible in practice due to requiring strong assumptions, e.g., linearity of the causal mechanisms or perfect atomic interventions. Meanwhile, more practical ML-based approaches using naive domain translation models to generate counterfactual samples lack theoretical grounding and may construct invalid counterfactuals. In this work, we strive to strike a balance between practicality and theoretical guarantees by analyzing a specific type of causal query called domain counterfactuals, which hypothesizes what a sample would have looked like if it had been generated in a different domain (or environment). We show that recovering the latent SCM is unnecessary for estimating domain counterfactuals, thereby sidestepping some of the theoretic challenges. By assuming invertibility and sparsity of intervention, we prove domain counterfactual estimation error can be bounded by a data fit term and intervention sparsity term. Building upon our theoretical results, we develop a theoretically grounded practical algorithm that simplifies the modeling process to generative model estimation under autoregressive and shared parameter constraints that enforce intervention sparsity. Finally, we show an improvement in counterfactual estimation over baseline methods through extensive simulated and image-based experiments. 

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5. Identification of Nonlinear Latent Hierarchical Models

   Kong Lingjing, Huang Biwei (July 2023, arXivorg)

   Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be highly challenging, especially when observed variables are generated by causally related latent variables and the relationships are nonlinear. In this work, we investigate the identification problem for nonlinear latent hierarchical causal models in which observed variables are generated by a set of causally related latent variables, and some latent variables may not have observed children. We show that the identifiability of both causal structure and latent variables can be achieved under mild assumptions: on causal structures, we allow for the existence of multiple paths between any pair of variables in the graph, which relaxes latent tree assumptions in prior work; on structural functions, we do not make parametric assumptions, thus permitting general nonlinearity and multi-dimensional continuous variables. Specifically, we first develop a basic identification criterion in the form of novel identifiability guarantees for an elementary latent variable model. Leveraging this criterion, we show that both causal structures and latent variables of the hierarchical model can be identified asymptotically by explicitly constructing an estimation procedure. To the best of our knowledge, our work is the first to establish identifiability guarantees for both causal structures and latent variables in nonlinear latent hierarchical models. 

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