We present a unified EM-based framework for imputing a designated target variable$T$in Gaussian causal models under domain shifts. Given fully observed source-domain data and only partially observed target-domain data, our method flexibly handles both covariate and target shifts by exploiting a known Directed Acyclic Graph (DAG) structure to transfer information from observed data to the missing target. Our framework introduces: (i) a population EM operator that characterizes the exact covariance update in the infinite-data regime, (ii) a first-order gradient-EM step that reduces per-iteration cost from$O(p^{3})$to$O(p^{2})$while preserving likelihood ascent, and (iii) a sample-EM routine that adapts to domain shifts by freezing source-invariant parameters and re-estimating only the shifted conditionals. In experiments on a synthetic seven-node Structural Equation Model (SEM), the 64-node MAGIC-IRRI network, and the real single-cell signaling dataset of Sachs et al., our 1st-order EM achieves near-oracle accuracy under severe shifts in the small model, markedly outperforms the classical Kiiveri EM and a fit-on-source Bayesian network baseline in the large model, and demonstrates strong gains on key signaling proteins in real biological data. Because it performs just one EM update and scales linearly with the number of edges, our approach is both computationally efficient and practical for high-dimensional Gaussian causal models.

Modern computer systems are highly configurable, with the total variability space sometimes larger than the number of atoms in the universe. Understanding and reasoning about the performance behavior of highly configurable systems, over a vast and variable space, is challenging. State-of-the-art methods for performance modeling and analyses rely on predictive machine learning models, therefore, they become (i) unreliable in unseen environments (e.g., different hardware, workloads), and (ii) may produce incorrect explanations. To tackle this, we propose a new method, called Unicorn, which (i) captures intricate interactions between configuration options across the software-hardware stack and (ii) describes how such interactions can impact performance variations via causal inference. We evaluated Unicorn on six highly configurable systems, including three on-device machine learning systems, a video encoder, a database management system, and a data analytics pipeline. The experimental results indicate that Unicorn outperforms state-of-the-art performance debugging and optimization methods in finding effective repairs for performance faults and finding configurations with near-optimal performance. Further, unlike the existing methods, the learned causal performance models reliably predict performance for new environments.

This paper provides a graphical characterization of Markov blankets in chaingraphs (CGs) under the Lauritzen-Wermuth-Frydenberg (LWF) interpretation. The characterization is different from the well-known one for Bayesian networks and generalizes it. We provide a novel scalable and sound algorithmfor Markov blanket discovery in LWF CGs and prove that the Grow-Shrink algorithm, the IAMB algorithm, and its variants are still correct for Markov blanket discovery in LWF CGs under the same assumptions as for Bayesian networks. We provide a sound and scalable constraint-based framework for learning the structure of LWF CGs from faithful causally sufficient data and prove its correctness when the Markov blanket discovery algorithms in this paper are used. Our proposed algorithms compare positively/competitively against the state-of-the-art LCD (Learn Chain graphs via Decomposition) algorithm, depending on the algorithm that is used for Markov blanket discovery. Our proposed algorithms make a broad range of inference/learning problems computationallytractable and more reliable because they exploit locality.

This paper deals with chain graphs (CGs) under the Andersson–Madigan–Perlman (AMP) interpretation. We address the problem of finding a minimal separator in an AMP CG, namely, finding a set Z of nodes that separates a given non-adjacent pair of nodes such that no proper subset of Z separates that pair. We analyze several versions of this problem and offer polynomial time algorithms for each. These include finding a minimal separator from a restricted set of nodes, finding a minimal separator for two given disjoint sets, and testing whether a given separator is minimal. To address the problem of learning the structure of AMP CGs from data, we show that the PC-like algorithm is order dependent, in the sense that the output can depend on the order in which the variables are given. We propose several modifications of the PC-like algorithm that remove part or all of this order-dependence. We also extend the decomposition-based approach for learning Bayesian networks (BNs) to learn AMP CGs, which include BNs as a special case, under the faithfulness assumption. We prove the correctness of our extension using the minimal separator results. Using standard benchmarks and synthetically generated models and data in our experiments demonstrate the competitive performance of our decomposition-based method, called LCD-AMP, in comparison with the (modified versions of) PC-like algorithm. The LCD-AMP algorithm usually outperforms the PC-like algorithm, and our modifications of the PC-like algorithm learn structures that are more similar to the underlying ground truth graphs than the original PC-like algorithm, especially in high-dimensional settings. In particular, we empirically show that the results of both algorithms are more accurate and stabler when the sample size is reasonably large and the underlying graph is sparse