Constraint-based causal discovery is widely used for learning causal structures, but heavy reliance on conditional independence (CI) testing makes it computationally expensive in high-dimensional settings. To mitigate this limitation, many divide-and-conquer frameworks have been proposed, but most assume causal sufficiency, i.e., no latent variables. In this paper, we show that divide-and-conquer strategies can be theoretically generalized beyond causal sufficiency to settings with latent variables. Specifically, we propose a recursive decomposition framework, termed DiCoLa, that enables divide-and-conquer causal discovery in the presence of latent variables. It recursively decomposes the global learning task into smaller subproblems and integrates their solutions through a principled reconstruction step to recover the global structure. We theoretically establish the soundness and completeness of the proposed framework. Extensive experiments on synthetic data demonstrate that our approach significantly improves computational efficiency across a range of causal discovery algorithms, while experiments on a real-world dataset further illustrate its practical effectiveness.

Neural Information Processing Systems http://nips.cc/

Inferring causal structure poses a combinatorial search problem that typically involves evaluating structures with a score or independence test. The resulting search is costly, and designing suitable scores or tests that capture prior knowledge is difficult. In this work, we propose to amortize causal structure learning. Rather than searching over structures, we train a variational inference model to directly predict the causal structure from observational or interventional data. This allows our inference model to acquire domain-specific inductive biases for causal discovery solely from data generated by a simulator, bypassing both the hand-engineering of suitable score functions and the search over graphs. The architecture of our inference model emulates permutation invariances that are crucial for statistical efficiency in structure learning, which facilitates generalization to significantly larger problem instances than seen during training. On synthetic data and semisynthetic gene expression data, our models exhibit robust generalization capabilities when subject to substantial distribution shifts and significantly outperform existing algorithms, especially in the challenging genomics domain. Our code and models are publicly available at: https://github.com/larslorch/avici

Causal structure learning is a key problem in many domains. Causal structures can be learnt by performing experiments on the system of interest. We address the largely unexplored problem of designing a batch of experiments that each simultaneously intervene on multiple variables. While potentially more informative than the commonly considered single-variable interventions, selecting such interventions is algorithmically much more challenging, due to the doubly-exponential combinatorial search space over sets of composite interventions. In this paper, we develop efficient algorithms for optimizing different objective functions quantifying the informativeness of a budget-constrained batch of experiments. By establishing novel submodularity properties of these objectives, we provide approximation guarantees for our algorithms. Our algorithms empirically perform superior to both random interventions and algorithms that only select single-variable interventions.

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.

Inferring causal structure poses a combinatorial search problem that typically involves evaluating structures with a score or independence test. The resulting search is costly, and designing suitable scores or tests that capture prior knowledge is difficult. In this work, we propose to amortize causal structure learning. Rather than searching over structures, we train a variational inference model to directly predict the causal structure from observational or interventional data. This allows our inference model to acquire domain-specific inductive biases for causal discovery solely from data generated by a simulator, bypassing both the hand-engineering of suitable score functions and the search over graphs. The architecture of our inference model emulates permutation invariances that are crucial for statistical efficiency in structure learning, which facilitates generalization to significantly larger problem instances than seen during training.

Causal structure learning is a key problem in many domains. Causal structures can be learnt by performing experiments on the system of interest. We address the largely unexplored problem of designing a batch of experiments that each simultaneously intervene on multiple variables. While potentially more informative than the commonly considered single-variable interventions, selecting such interventions is algorithmically much more challenging, due to the doubly-exponential combinatorial search space over sets of composite interventions. In this paper, we develop efficient algorithms for optimizing different objective functions quantifying the informativeness of a budget-constrained batch of experiments.

Causal discovery is becoming a key part in medical AI research. These methods can enhance healthcare by identifying causal links between biomarkers, demographics, treatments and outcomes. They can aid medical professionals in choosing more impactful treatments and strategies. In parallel, Large Language Models (LLMs) have shown great potential in identifying patterns and generating insights from text data. In this paper we investigate applying LLMs to the problem of determining the directionality of edges in causal discovery. Specifically, we test our approach on a deidentified set of Non Small Cell Lung Cancer(NSCLC) patients that have both electronic health record and genomic panel data. Graphs are validated using Bayesian Dirichlet estimators using tabular data. Our result shows that LLMs can accurately predict the directionality of edges in causal graphs, outperforming existing state-of-the-art methods. These findings suggests that LLMs can play a significant role in advancing causal discovery and help us better understand complex systems.

In the context of inferring a Bayesian network structure (directed acyclic graph, DAG for short), we devise a non-reversible continuous time Markov chain, the "Causal Zig-Zag sampler", that targets a probability distribution over classes of observationally equivalent (Markov equivalent) DAGs. The classes are represented as completed partially directed acyclic graphs (CPDAGs). The non-reversible Markov chain relies on the operators used in Chickering's Greedy Equivalence Search (GES) and is endowed with a momentum variable, which improves mixing significantly as we show empirically. The possible target distributions include posterior distributions based on a prior over DAGs and a Markov equivalent likelihood. We offer an efficient implementation wherein we develop new algorithms for listing, counting, uniformly sampling, and applying possible moves of the GES operators, all of which significantly improve upon the state-of-the-art.

In this paper, we introduce a novel causal structure learning algorithm called Endogenous and Exogenous Markov Blankets Intersection (EEMBI), which combines the properties of Bayesian networks and Structural Causal Models (SCM). Exogenous variables are special variables that are applied in SCM. We find that exogenous variables have some special characteristics and these characteristics are still useful under the property of the Bayesian network. EEMBI intersects the Markov blankets of exogenous variables and Markov blankets of endogenous variables, i.e. the original variables, to remove the irrelevant connections and find the true causal structure theoretically. Furthermore, we propose an extended version of EEMBI, namely EEMBI-PC, which integrates the last step of the PC algorithm into EEMBI. This modification enhances the algorithm's performance by leveraging the strengths of both approaches. Plenty of experiments are provided to prove that EEMBI and EEMBI-PC have state-of-the-art performance on both discrete and continuous datasets.