Recovering Markov boundary-the minimal set of variables that maximizes predictive performance for a response variable-is crucial in many applications. While recent advances improve upon traditional constraint-based techniques by scoring local causal structures, they still rely on nonparametric estimators and heuristic searches, lacking theoretical guarantees for reliability. This paper investigates a framework for efficient Markov boundary discovery by integrating conditional entropy from information theory as a scoring criterion. We design a novel masked autoregressive network to capture complex dependencies. A parallelizable greedy search strategy in polynomial time is proposed, supported by analytical evidence. We also discuss how initializing a graph with learned Markov boundaries accelerates the convergence of causal discovery. Comprehensive evaluations on real-world and synthetic datasets demonstrate the scalability and superior performance of our method in both Markov boundary discovery and causal discovery tasks.

Distinguishing the cause and effect from bivariate observational data is the foundational problem that finds applications in many scientific disciplines. One solution to this problem is assuming that cause and effect are generated from a structural causal model, enabling identification of the causal direction after estimating the model in each direction. The heteroscedastic noise model is a type of structural causal model where the cause can contribute to both the mean and variance of the noise. Current methods for estimating heteroscedas-tic noise models choose the Gaussian likelihood as the optimization objective which can be suboptimal and unstable when the data has a non-Gaussian distribution. To address this limitation, we propose a novel approach to estimating this model with Student's t-distribution, which is known for its robustness in accounting for sampling variability with smaller sample sizes and extreme values without significantly altering the overall distribution shape. This adaptability is beneficial for capturing the parameters of the noise distribution in het-eroscedastic noise models. Our empirical evaluations demonstrate that our estimators are more robust and achieve better overall performance across synthetic and real benchmarks.

Abstract Detecting conditional independencies plays a key role in several statistical and machine learning tasks, especially in causal discovery algorithms, yet it remains a highly challenging problem due to dimensionality and complex relationships presented in data. In this study, we introduce LCIT (Latent representation-based Conditional Independence Test)—a novel method for conditional independence testing based on representation learning. Our main contribution involves a hypothesis testing framework in which to test for the independence between X and Y given Z, we first learn to infer the latent representations of target variables X and Y that contain no information about the conditioning variable Z. The latent variables are then investigated for any significant remaining dependencies, which can be performed using a conventional correlation test. Moreover, LCIT can also handle discrete and mixed-type data in general by converting discrete variables into the continuous domain via variational dequantization. The empirical evaluations show that LCIT outperforms several state-of-the-art baselines consistently under different evaluation metrics, and is able to adapt really well to both nonlinear, high-dimensional, and mixed data settings on a diverse collection of synthetic and real data sets.

Abstract Distributional estimates in Bayesian approaches in structure learning have advantages compared to the ones performing point estimates when handling epistemic uncertainty. Differentiable methods for Bayesian structure learning have been developed to enhance the scalability of the inference process and are achieving optimistic outcomes. However, in the differentiable continuous setting, constraining the acyclicity of learned graphs emerges as another challenge. Various works utilize post-hoc penalization scores to impose this constraint which cannot assure acyclicity. The topological ordering of the variables is one type of prior knowledge that contains valuable information about the acyclicity of a directed graph. In this work, we propose a framework to guarantee the acyclicity of inferred graphs by integrating the information from the topological ordering into the inference process. Our integration framework does not interfere with the differentiable inference process while being able to strictly assure the acyclicity of learned graphs and reduce the inference complexity. Our extensive empirical experiments on both synthetic and real data have demonstrated the effectiveness of our approach with preferable results compared to related Bayesian approaches.

Score-based approaches in the structure learning task are thriving because of their scalability. Continuous relaxation has been the key reason for this advancement. Despite achieving promising outcomes, most of these methods are still struggling to ensure that the graphs generated from the latent space are acyclic by minimizing a defined score. There has also been another trend of permutation-based approaches, which concern the search for the topological ordering of the variables in the directed acyclic graph in order to limit the search space of the graph. In this study, we propose an alternative approach for strictly constraining the acyclicty of the graphs with an integration of the knowledge from the topological orderings. Our approach can reduce inference complexity while ensuring the structures of the generated graphs to be acyclic. Our empirical experiments with simulated and real-world data show that our approach can outperform related Bayesian score-based approaches.

Out-of-distribution (OOD) generalisation aims to build a model that can generalise well on an unseen target domain using knowledge from multiple source domains. To this end, the model should seek the causal dependence between inputs and labels, which may be determined by the semantics of inputs and remain invariant across domains. However, statistical or non-causal methods often cannot capture this dependence and perform poorly due to not considering spurious correlations learnt from model training via unobserved confounders. A well-known existing causal inference method like back-door adjustment cannot be applied to remove spurious correlations as it requires the observation of confounders. In this paper, we propose a novel method that effectively deals with hidden confounders by successfully implementing front-door adjustment (FA). FA requires the choice of a mediator, which we regard as the semantic information of images that helps access the causal mechanism without the need for observing confounders. Further, we propose to estimate the combination of the mediator with other observed images in the front-door formula via style transfer algorithms. Our use of style transfer to estimate FA is novel and sensible for OOD generalisation, which we justify by extensive experimental results on widely used benchmark datasets.

Detecting conditional independencies plays a key role in several statistical and machine learning tasks, especially in causal discovery algorithms, yet it remains a highly challenging problem due to dimensionality and complex relationships presented in data. In this study, we introduce LCIT (Latent representation based Conditional Independence Test) -a novel method for conditional independence testing based on representation learning. Our main contribution involves a hypothesis testing framework in which to test for the independence between X and Y given Z, we first learn to infer the latent representations of target variables X and Y that contain no information about the conditioning variable Z. The latent variables are then investigated for any significant remaining dependencies, which can be performed using a conventional correlation test. The empirical evaluations show that LCIT outperforms several state-of-the-art baselines consistently under different evaluation metrics, and is able to adapt really well to both non-linear and high-dimensional settings on a diverse collection of synthetic and real data sets.

This study investigates antecedents to and outcomes of two stress reactions, telework distress (detrimental stress), and telework eustress (beneficial stress) using a model derived from an integration of the transactional model of stress with the job-demands and resources model. The model includes a person antecedent (resilience), and three environment antecedents (work-family conflict, work overload, and autonomy). These factors should influence experienced distress and eustress, which, in turn, affect telework outcomes (telework satisfaction, exhaustion, perceived performance, and perceived productivity. The model is evaluated using a sample of 329 Chinese teleworkers. This study findings indicate that resilience, work-family conflict, and work overload affect experienced distress, while resilience and autonomy affect experienced eustress. Experienced distress influenced satisfaction, exhaustion, and perceived performance; eustress had effects on all four outcomes. Interestingly, resilience had the largest total effect sizes on telework outcomes.