Learning a causal directed acyclic graph from data is a challenging task that involves solving a combinatorial problem for which the solution is not always identifiable. A new line of work reformulates this problem as a continuous constrained optimization one, which is solved via the augmented Lagrangian method. However, most methods based on this idea do not make use of interventional data, which can significantly alleviate identifiability issues. This work constitutes a new step in this direction by proposing a theoretically-grounded method based on neural networks that can leverage interventional data. We illustrate the flexibility of the continuous-constrained framework by taking advantage of expressive neural architectures such as normalizing flows. We show that our approach compares favorably to the state of the art in a variety of settings, including perfect and imperfect interventions for which the targeted nodes may even be unknown.
Arizona State University（亚利桑那州立大学）；Army Research Lab（陆军研究实验室）
We propose a generative Causal Adversarial Network (CAN) for learning and sampling from conditional and interventional distributions. In contrast to the existing CausalGAN which requires the causal graph to be given, our proposed framework learns the causal relations from the data and generates samples accordingly. The proposed CAN comprises a two-fold process namely Label Generation Network (LGN) and Conditional Image Generation Network (CIGN). The LGN is a GAN-based architecture which learns and samples from the causal model over labels. The sampled labels are then fed to CIGN, a conditional…
We explore how observational and interventional causal discovery methods can be combined. A state-of-the-art observational causal discovery algorithm for time series capable of handling latent confounders and contemporaneous effects, called LPCMCI, is extended to profit from casual constraints found through randomized control trials. Numerical results show that, given perfect interventional constraints, the reconstructed structural causal models (SCMs) of the extended LPCMCI allow 84.6% of the time for the optimal prediction of the target variable. The implementation of interventional and obse…
Harvard School of Public Health（哈佛公共卫生学院）；University of Washington（华盛顿大学）
Probabilistic inference in graphical models is the task of computing marginal and conditional densities of interest from a factorized representation of a joint probability distribution. Inference algorithms such as variable elimination and belief propagation take advantage of constraints embedded in this factorization to compute such densities efficiently. In this paper, we propose an algorithm which computes interventional distributions in latent variable causal models represented by acyclic directed mixed graphs(ADMGs). To compute these distributions efficiently, we take advantage of a recur…
Incorporating causal knowledge and mechanisms is essential for refining causal models and improving downstream tasks such as designing new treatments. In this paper, we introduce a novel concept in causal discovery, termed interventional constraints, which differs fundamentally from interventional data. While interventional data require direct perturbations of variables, interventional constraints encode high-level causal knowledge in the form of inequality constraints on causal effects. For instance, in the Sachs dataset (Sachs et al.\ 2005), Akt has been shown to be activated by PIP3, meanin…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Saarland University（萨尔大学）
In this paper, we introduce VACA, a novel class of variational graph autoencoders for causal inference in the absence of hidden confounders, when only observational data and the causal graph are available. Without making any parametric assumptions, VACA mimics the necessary properties of a Structural Causal Model (SCM) to provide a flexible and practical framework for approximating interventions (do-operator) and abduction-action-prediction steps. As a result, and as shown by our empirical results, VACA accurately approximates the interventional and counterfactual distributions on diverse SCMs…
TU Darmstadt（达姆施塔特工业大学）；The University of Texas at Dallas（德克萨斯大学达拉斯分校）；Hessian Center for AI (hessian.AI)（黑森人工智能中心 (hessian.AI)）
While probabilistic models are an important tool for studying causality, doing so suffers from the intractability of inference. As a step towards tractable causal models, we consider the problem of learning interventional distributions using sum-product networks (SPNs) that are over-parameterized by gate functions, e.g., neural networks. Providing an arbitrarily intervened causal graph as input, effectively subsuming Pearl's do-operator, the gate function predicts the parameters of the SPN. The resulting interventional SPNs are motivated and illustrated by a structural causal model themed arou…
Unobserved confounding is one of the main challenges when estimating causal effects. We propose a causal reduction method that, given a causal model, replaces an arbitrary number of possibly high-dimensional latent confounders with a single latent confounder that takes values in the same space as the treatment variable, without changing the observational and interventional distributions the causal model entails. This allows us to estimate the causal effect in a principled way from combined data without relying on the common but often unrealistic assumption that all confounders have been observ…
InfluenceField: A Differentiable Field with Interventionally Identifiable Causal Structure for Multimodal World Modeling
Mathematical Institute, University of Oxford（牛津大学数学研究所）；Department of Computer Science, University of Oxford（牛津大学计算机科学系）；School of Mathematical Sciences, University of Nottingham Ningbo China（宁波诺丁汉大学数学科学学院）
Causal inference is central to many areas of artificial intelligence, including complex reasoning, planning, knowledge-base construction, robotics, explanation, and fairness. An active community of researchers develops and enhances algorithms that learn causal models from data, and this work has produced a series of impressive technical advances. However, evaluation techniques for causal modeling algorithms have remained somewhat primitive, limiting what we can learn from experimental studies of algorithm performance, constraining the types of algorithms and model representations that research…
Causal inference quantifies cause-effect relationships by estimating counterfactual parameters from data. This entails using \emph{identification theory} to establish a link between counterfactual parameters of interest and distributions from which data is available. A line of work characterized non-parametric identification for a wide variety of causal parameters in terms of the \emph{observed data distribution}. More recently, identification results have been extended to settings where experimental data from interventional distributions is also available. In this paper, we use Single World I…
Gatsby Computational Neuroscience Unit, UCL（伦敦大学学院盖茨比计算神经科学单元）；University of Helsinki（赫尔辛基大学）
We posit that autoregressive flow models are well-suited to performing a range of causal inference tasks - ranging from causal discovery to making interventional and counterfactual predictions. In particular, we exploit the fact that autoregressive architectures define an ordering over variables, analogous to a causal ordering, in order to propose a single flow architecture to perform all three aforementioned tasks. We first leverage the fact that flow models estimate normalized log-densities of data to derive a bivariate measure of causal direction based on likelihood ratios. Whilst tradition…
Gatsby Unit, UCL（伦敦大学学院盖茨比单元）；King’s College London（伦敦国王学院）；University of Helsinki（赫尔辛基大学）
Two apparently unrelated fields -- normalizing flows and causality -- have recently received considerable attention in the machine learning community. In this work, we highlight an intrinsic correspondence between a simple family of autoregressive normalizing flows and identifiable causal models. We exploit the fact that autoregressive flow architectures define an ordering over variables, analogous to a causal ordering, to show that they are well-suited to performing a range of causal inference tasks, ranging from causal discovery to making interventional and counterfactual predictions. First,…
Large-Scale Bayesian Causal Discovery with Interventional Data
Department of Computer and Information Science, University of Pennsylvania（计算机与信息科学系，宾夕法尼亚大学）；Genomics and Computational Biology Graduate Group, University of Pennsylvania（基因组与计算生物学研究生组，宾夕法尼亚大学）；Division of Informatics, University of Pennsylvania（信息学 division，宾夕法尼亚大学）；Department of Genetics, University of Pennsylvania（遗传学系，宾夕法尼亚大学）
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Sharif University of Technology（谢里夫理工大学）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
It is known that from purely observational data, a causal DAG is identifiable only up to its Markov equivalence class, and for many ground truth DAGs, the direction of a large portion of the edges will be remained unidentified. The golden standard for learning the causal DAG beyond Markov equivalence is to perform a sequence of interventions in the system and use the data gathered from the interventional distributions. We consider a setup in which given a budget $k$, we design $k$ interventions non-adaptively. We cast the problem of finding the best intervention target set as an optimization p…
Deciphering interventional dynamical causality from non-intervention complex systems
Research Institute of Intelligent Complex Systems & CISOR, Fudan University（智能复杂系统研究所及CISOR，复旦大学）；International Research Center for Neurointelligence, The University of Tokyo Institutes for Advanced Study, The University of Tokyo（神经智能国际研究中心，东京大学先进研究所，东京大学）；School of Pharmacy, Shanghai University of Traditional Chinese Medicine（上海中医药大学药学院）；Institute of AI and Robotics, College of Intelligent Robotics and Advanced Manufacturing, Fudan University（人工智能与机器人研究所，智能机器人与先进制造学院，复旦大学）；Frontiers Science Center for Deep Ocean Multispheres and Earth System, Key Laboratory of Marine Chemistry Theory and Technology, Ministry of Education, Ocean University of China（深海多球体与地球系统前沿科学中心，海洋化学理论与技术重点实验室，教育部，中国海洋大学）；School of Mathematical Sciences and School of AI, Shanghai Jiao Tong University（数学科学学院和人工智能学院，上海交通大学）；Key Laboratory of Systems Health Science of Zhejiang Province, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Chinese Academy of Sciences（浙江省系统健康科学重点实验室，杭州高级研究所，中国科学院大学，中国科学院）
Causal discovery from empirical data is a fundamental problem in many scientific domains. Observational data allows for identifiability only up to Markov equivalence class. In this paper we first propose a polynomial time algorithm for learning the exact correctly-oriented structure of the transitive reduction of any causal Bayesian network with high probability, by using interventional path queries. Each path query takes as input an origin node and a target node, and answers whether there is a directed path from the origin to the target. This is done by intervening on the origin node and obse…
Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning
Imperial College London（伦敦帝国学院）；University of Cambridge（剑桥大学）；University of Toronto（多伦多大学）；Vector Institute（向量研究所）；Alan Turing Institute（艾伦·图灵研究所）；University of Oxford（牛津大学）
The interpretability of prediction mechanisms with respect to the underlying prediction problem is often unclear. While several studies have focused on developing prediction models with meaningful parameters, the causal relationships between the predictors and the actual prediction have not been considered. Here, we connect the underlying causal structure of a data generation process and the causal structure of a prediction mechanism. To achieve this, we propose a framework that identifies the feature with the greatest causal influence on the prediction and estimates the necessary causal inter…
University of Oxford（牛津大学）；Microsoft Research Cambridge（微软研究院剑桥分院）
While causal models are becoming one of the mainstays of machine learning, the problem of uncertainty quantification in causal inference remains challenging. In this paper, we study the causal data fusion problem, where datasets pertaining to multiple causal graphs are combined to estimate the average treatment effect of a target variable. As data arises from multiple sources and can vary in quality and quantity, principled uncertainty quantification becomes essential. To that end, we introduce Bayesian Interventional Mean Processes, a framework which combines ideas from probabilistic integrat…
DeepMind（深度思维）；Mila（米拉（魁北克人工智能研究所））；Polytechnique Montreal（蒙特利尔理工学院）；University of Montreal（蒙特利尔大学）；Google Research（谷歌研究院）
The fundamental challenge in causal induction is to infer the underlying graph structure given observational and/or interventional data. Most existing causal induction algorithms operate by generating candidate graphs and evaluating them using either score-based methods (including continuous optimization) or independence tests. In our work, we instead treat the inference process as a black box and design a neural network architecture that learns the mapping from both observational and interventional data to graph structures via supervised training on synthetic graphs. The learned model general…
Describing the causal relations governing a system is a fundamental task in many scientific fields, ideally addressed by experimental studies. However, obtaining data under intervention scenarios may not always be feasible, while discovering causal relations from purely observational data is notoriously challenging. In certain settings, such as genomics, we may have data from heterogeneous study conditions, with soft (partial) interventions only pertaining to a subset of the study variables, whose effects and targets are possibly unknown. Combining data from experimental and observational stud…
Causal Interventional Prediction System for Robust and Explainable Effect Forecasting
Zhejiang University（浙江大学）；Hangzhou High-Tech Zone (Binjiang) Institute of Blockchain and Data Security（杭州高新区（滨江）区块链与数据安全研究院）；Ant Group（蚂蚁集团）；Nanyang Technological University（南洋理工大学）
PACER: Acyclic Causal Discovery from Large-Scale Interventional Data
Swiss Federal Technology Institute of Lausanne (EPFL), Switzerland（瑞士联邦理工学院洛桑分校）；Cornell University, USA（康奈尔大学）；ETH Zurich, Zurich, Switzerland（苏黎世联邦理工学院）
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Cambridge（剑桥大学）；National University of Singapore（新加坡国立大学）
Modern machine learning approaches excel in static settings where a large amount of i.i.d. training data are available for a given task. In a dynamic environment, though, an intelligent agent needs to be able to transfer knowledge and re-use learned components across domains. It has been argued that this may be possible through causal models, aiming to mirror the modularity of the real world in terms of independent causal mechanisms. However, the true causal structure underlying a given set of data is generally not identifiable, so it is desirable to have means to quantify differences between …
IBM Research（IBM研究院）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；MIT（麻省理工学院）
Directed acyclic graph (DAG) models are popular for capturing causal relationships. From observational and interventional data, a DAG model can only be determined up to its \emph{interventional Markov equivalence class} (I-MEC). We investigate the size of MECs for random DAG models generated by uniformly sampling and ordering an Erdős-Rényi graph. For constant density, we show that the expected $\log$ observational MEC size asymptotically (in the number of vertices) approaches a constant. We characterize I-MEC size in a similar fashion in the above settings with high precision. We show that th…
From observational data alone, a causal DAG is only identifiable up to Markov equivalence. Interventional data generally improves identifiability; however, the gain of an intervention strongly depends on the intervention target, that is, the intervened variables. We present active learning (that is, optimal experimental design) strategies calculating optimal interventions for two different learning goals. The first one is a greedy approach using single-vertex interventions that maximizes the number of edges that can be oriented after each intervention. The second one yields in polynomial time …
University of Oxford（牛津大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；KTH Royal Institute of Technology（瑞典皇家理工学院）
Causal discovery from observational and interventional data is challenging due to limited data and non-identifiability: factors that introduce uncertainty in estimating the underlying structural causal model (SCM). Selecting experiments (interventions) based on the uncertainty arising from both factors can expedite the identification of the SCM. Existing methods in experimental design for causal discovery from limited data either rely on linear assumptions for the SCM or select only the intervention target. This work incorporates recent advances in Bayesian causal discovery into the Bayesian o…
University of Amsterdam（阿姆斯特丹大学）；Qualcomm AI Research（高通人工智能研究院）
Learning the structure of a causal graphical model using both observational and interventional data is a fundamental problem in many scientific fields. A promising direction is continuous optimization for score-based methods, which, however, require constrained optimization to enforce acyclicity or lack convergence guarantees. In this paper, we present ENCO, an efficient structure learning method for directed, acyclic causal graphs leveraging observational and interventional data. ENCO formulates the graph search as an optimization of independent edge likelihoods, with the edge orientation bei…
We consider the problem of estimating causal DAG models from a mix of observational and interventional data, when the intervention targets are partially or completely unknown. This problem is highly relevant for example in genomics, since gene knockout technologies are known to have off-target effects. We characterize the interventional Markov equivalence class of DAGs that can be identified from interventional data with unknown intervention targets. In addition, we propose a provably consistent algorithm for learning the interventional Markov equivalence class from such data. The proposed alg…
Decomposing an exposure effect on an outcome into separate natural indirect effects through multiple mediators requires strict assumptions, such as correctly postulating the causal structure of the mediators, and no unmeasured confounding among the mediators. In contrast, interventional indirect effects for multiple mediators can be identified even when - as often - the mediators either have an unknown causal structure, or share unmeasured common causes, or both. Existing estimation methods for interventional indirect effects require calculating each distinct indirect effect in turn. This can …
The incorporation of causal inference in mediation analysis has led to theoretical and methodological advancements -- effect definitions with causal interpretation, clarification of assumptions required for effect identification, and an expanding array of options for effect estimation. However, the literature on these results is fast-growing and complex, which may be confusing to researchers unfamiliar with causal inference or unfamiliar with mediation. The goal of this paper is to help ease the understanding and adoption of causal mediation analysis. It starts by highlighting a key difference…
