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1. Identification of Linear Non-{G}aussian Latent Hierarchical Structure

   Xie, Feng; Huang, Biwei; Chen, Zhengming; He, Yangbo; Geng, Zhi; Zhang, Kun (July 2022, Proceedings of Machine Learning Research)

   Chaudhuri, Kamalika; Jegelka, Stefanie; Song, Le; Szepesvari, Csaba; Niu, Gang; Sabato, Sivan (Ed.)

   Traditional causal discovery methods mainly focus on estimating causal relations among measured variables, but in many real-world problems, such as questionnaire-based psychometric studies, measured variables are generated by latent variables that are causally related. Accordingly, this paper investigates the problem of discovering the hidden causal variables and estimating the causal structure, including both the causal relations among latent variables and those between latent and measured variables. We relax the frequently-used measurement assumption and allow the children of latent variables to be latent as well, and hence deal with a specific type of latent hierarchical causal structure. In particular, we define a minimal latent hierarchical structure and show that for linear non-Gaussian models with the minimal latent hierarchical structure, the whole structure is identifiable from only the measured variables. Moreover, we develop a principled method to identify the structure by testing for Generalized Independent Noise (GIN) conditions in specific ways. Experimental results on both synthetic and real-world data show the effectiveness of the proposed approach. 

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2. Testability of Instrumental Variables in Linear Non-Gaussian Acyclic Causal Models

   https://doi.org/10.3390/e24040512  

   Xie, Feng; He, Yangbo; Geng, Zhi; Chen, Zhengming; Hou, Ru; Zhang, Kun (April 2022, Entropy)

   This paper investigates the problem of selecting instrumental variables relative to a target causal influence X→Y from observational data generated by linear non-Gaussian acyclic causal models in the presence of unmeasured confounders. We propose a necessary condition for detecting variables that cannot serve as instrumental variables. Unlike many existing conditions for continuous variables, i.e., that at least two or more valid instrumental variables are present in the system, our condition is designed with a single instrumental variable. We then characterize the graphical implications of our condition in linear non-Gaussian acyclic causal models. Given that the existing graphical criteria for the instrument validity are not directly testable given observational data, we further show whether and how such graphical criteria can be checked by exploiting our condition. Finally, we develop a method to select the set of candidate instrumental variables given observational data. Experimental results on both synthetic and real-world data show the effectiveness of the proposed method. 

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3. Aitia: Efficient Secure Computation of Bivariate Causal Discovery

   Nguyen, T S; Wang, L; Kornaropoulos, E M; Trieu, N (October 2024, CCS)

   Researchers across various fields seek to understand causal relationships but often find controlled experiments impractical. To address this, statistical tools for causal discovery from naturally observed data have become crucial. Non-linear regression models, such as Gaussian process regression, are commonly used in causal inference but have limitations due to high costs when adapted for secure computation. Support vector regression (SVR) offers an alternative but remains costly in an Multi-party computation context due to conditional branches and support vector updates. In this paper, we propose Aitia, the first two-party secure computation protocol for bivariate causal discovery. The protocol is based on optimized multi-party computation design choices and is secure in the semi-honest setting. At the core of our approach is BSGD-SVR, a new non-linear regression algorithm designed for MPC applications, achieving both high accuracy and low computation and communication costs. Specifically, we reduce the training complexity of the non-linear regression model from approximately from O (𝑁^3) to O (𝑁^2) where 𝑁 is the number of training samples. We implement Aitia using CrypTen and assess its performance across various datasets. Empirical evaluations show a significant speedup of 3.6× to 340× compared to the baseline approach. 

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4. Multi-domain Causal Structure Learning in Linear Systems

   AmirEmad Ghassami, Biwei Huang (December 2018, Advances in neural information processing systems)

   We study the problem of causal structure learning in linear systems from observational data given in multiple domains, across which the causal coefficients and/or the distribution of the exogenous noises may vary. The main tool used in our approach is the principle that in a causally sufficient system, the causal modules, as well as their included parameters, change independently across domains. We first introduce our approach for finding causal direction in a system comprising two variables and propose efficient methods for identifying causal direction. Then we generalize our methods to causal structure learning in networks of variables. Most of previous work in structure learning from multi-domain data assume that certain types of invariance are held in causal modules across domains. Our approach unifies the idea in those works and generalizes to the case that there is no such invariance across the domains. Our proposed methods are generally capable of identifying causal direction from fewer than ten domains. When the invariance property holds, two domains are generally sufficient. 

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5. A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery

   Lin, Yingyu; Huang, Yuxing; Liu, Wenqin; Deng, Haoran; Ng, Ignavier; Zhang, Kun; Gong, Mingming; Ma, Yian; Huang, Biwei (April 2025, OpenReview.net)

   Real-world data often violates the equal-variance assumption (homoscedasticity), making it essential to account for heteroscedastic noise in causal discovery. In this work, we explore heteroscedastic symmetric noise models (HSNMs), where the effect Y is modeled as Y = f(X) + σ(X)N, with X as the cause and N as independent noise following a symmetric distribution. We introduce a novel criterion for identifying HSNMs based on the skewness of the score (i.e., the gradient of the log density) of the data distribution. This criterion establishes a computationally tractable measurement that is zero in the causal direction but nonzero in the anticausal direction, enabling the causal direction discovery. We extend this skewness-based criterion to the multivariate setting and propose SkewScore, an algorithm that handles heteroscedastic noise without requiring the extraction of exogenous noise. We also conduct a case study on the robustness of SkewScore in a bivariate model with a latent confounder, providing theoretical insights into its performance. Empirical studies further validate the effectiveness of the proposed method. 

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