Identifying the root causes of outliers is a fundamental problem in causal inference and anomaly detection. Traditional approaches based on heuristics or counterfactual reasoning often struggle under uncertainty and high-dimensional dependencies. We introduce SIREN, a novel and scalable method that attributes the root causes of outliers by estimating the score functions of the data likelihood. Attribution is computed via integrated gradients that accumulate score contributions along paths from the outlier toward the normal data distribution. Our method satisfies three of the four classic Shapley value axioms-dummy, efficiency, and linearity-as well as an asymmetry axiom derived from the underlying causal structure. Unlike prior work, SIREN operates directly on the score function, enabling tractable and uncertainty-aware root cause attribution in nonlinear, high-dimensional, and heteroscedastic causal models. Extensive experiments on synthetic random graphs and real-world cloud service and supply chain datasets show that SIREN outperforms state-of-the-art baselines in both attribution accuracy and computational efficiency.

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 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.

Designing new physical products and processes requires enormous experimentation. The scientific simulators play a fundamental role for such design tasks. To design a new product with certain target characteristics, a search is performed in the design space by trying out a large number of design combinations through simulators before reaching to the target characteristics. However, searching for the target design using simulators is generally expensive and becomes prohibitive when the target is either revised or only partially specified. To address this problem, we use a machine learning model to predict the design in single step using the target product specifications as input. We overcome two technical challenges: the first caused due to one-to-many mapping when learning the inverse problem and the second caused due to a user specifying the target specifications only partially. We unify a conditional variational auto-encoder model (to address the partial target specification) with mixture density networks (to address the one-to-many mapping) and train an end-to-end model to predict the optimum design.