In the univariate case, we show that by comparing the individual complexities of univariate cause and effect, one can identify the cause and the effect, without considering their interaction at all. In our framework, complexities are captured by the reconstruction error of an autoencoder that operates on the quantiles of the distribution. Comparing the reconstruction errors of the two autoencoders, one for each variable, is shown to perform surprisingly well on the accepted causality directionality benchmarks. Hence, the decision as to which of the two is the cause and which is the effect may not be based on causality but on complexity.
In the multivariate case, where one can ensure that the complexities of the cause and effect are balanced, we propose a new adversarial training method that mimics the disentangled structure of the causal model. We prove that in the multidimensional case, such modeling is likely to fit the data only in the direction of causality. Furthermore, a uniqueness result shows that the learned model is able to identify the underlying causal and residual (noise) components. Our multidimensional method outperforms the literature methods on both synthetic and real world datasets.
Informatics Institute（信息学研究所）；University of Amsterdam（阿姆斯特丹大学）
We address the problem of causal discovery from data, making use of the recently proposed causal modeling framework of modular structural causal models (mSCM) to handle cycles, latent confounders and non-linearities. We introduce σ-connection graphs (σ-CG), a new class of mixed graphs (containing undirected, bidirected and directed edges) with additional structure, and extend the concept of σ-separation, the appropriate generalization of the well-known notion of d-separation in this setting, to apply to σ-CGs. We prove the closedness of σ-separation under marginalisation and conditioning and e…
One major drawback of state-of-the-art artificial intelligence is its lack of explainability. One approach to solve the problem is taking causality into account. Causal mechanisms can be described by structural causal models. In this work, we propose a method for estimating bivariate structural causal models using a combination of normalising flows applied to density estimation and variational Gaussian process regression for post-nonlinear models. It facilitates causal discovery, i.e. distinguishing cause and effect, by either the independence of cause and residual or a likelihood ratio test. …
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）
We consider the problem of learning the functions computing children from parents in a Structural Causal Model once the underlying causal graph has been identified. This is in some sense the second step after causal discovery. Taking a probabilistic approach to estimating these functions, we derive a natural myopic active learning scheme that identifies the intervention which is optimally informative about all of the unknown functions jointly, given previously observed data. We test the derived algorithms on simple examples, to demonstrate that they produce a structured exploration policy that…
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）；Amazon Research（亚马逊研究院）
We introduce an approach to counterfactual inference based on merging information from multiple datasets. We consider a causal reformulation of the statistical marginal problem: given a collection of marginal structural causal models (SCMs) over distinct but overlapping sets of variables, determine the set of joint SCMs that are counterfactually consistent with the marginal ones. We formalise this approach for categorical SCMs using the response function formulation and show that it reduces the space of allowed marginal and joint SCMs. Our work thus highlights a new mode of falsifiability thro…
University of Lübeck（吕贝克大学）；Saarland University（萨尔大学）
Linear structural equation models represent direct causal effects as directed edges and confounding factors as bidirected edges. An open problem is to identify the causal parameters from correlations between the nodes. We investigate models, whose directed component forms a tree, and show that there, besides classical instrumental variables, missing cycles of bidirected edges can be used to identify the model. They can yield systems of quadratic equations that we explicitly solve to obtain one or two solutions for the causal parameters of adjacent directed edges. We show how multiple missing c…
Temporal Latent Variable Structural Causal Model for Causal Discovery under External Interferences
School of Computer Science, Guangdong University of Technology（广东工业大学计算机科学学院）；Peng Cheng Laboratory（鹏城实验室）；Machine Learning Department, Mohamed bin Zayed University of Artificial Intelligence（Mohamed bin Zayed人工智能大学机器学习系）；College of Mathematics and Computer Science, Shantou University（汕头大学数学与计算机科学学院）
We formulate a general framework for building structural causal models (SCMs) with deep learning components. The proposed approach employs normalising flows and variational inference to enable tractable inference of exogenous noise variables - a crucial step for counterfactual inference that is missing from existing deep causal learning methods. Our framework is validated on a synthetic dataset built on MNIST as well as on a real-world medical dataset of brain MRI scans. Our experimental results indicate that we can successfully train deep SCMs that are capable of all three levels of Pearl's l…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Max Planck ETH Center for Learning Systems（马克斯·普朗克-ETH学习系统中心）；University of Cambridge（剑桥大学）；Saarland University（萨尔兰大学）
Recent work has discussed the limitations of counterfactual explanations to recommend actions for algorithmic recourse, and argued for the need of taking causal relationships between features into consideration. Unfortunately, in practice, the true underlying structural causal model is generally unknown. In this work, we first show that it is impossible to guarantee recourse without access to the true structural equations. To address this limitation, we propose two probabilistic approaches to select optimal actions that achieve recourse with high probability given limited causal knowledge (e.g…
Structural causal models (SCMs) are a widespread formalism to deal with causal systems. A recent direction of research has considered the problem of relating formally SCMs at different levels of abstraction, by defining maps between SCMs and imposing a requirement of interventional consistency. This paper offers a review of the solutions proposed so far, focusing on the formal properties of a map between SCMs, and highlighting the different layers (structural, distributional) at which these properties may be enforced. This allows us to distinguish families of abstractions that may or may not b…
Identifying causal relationships for a treatment intervention is a fundamental problem in health sciences. Randomized controlled trials (RCTs) are considered the gold standard for identifying causal relationships. However, recent advancements in the theory of causal inference based on the foundations of structural causal models (SCMs) have allowed the identification of causal relationships from observational data, under certain assumptions. Survival analysis provides standard measures, such as the hazard ratio, to quantify the effects of an intervention. While hazard ratios are widely used in …
Massachusetts Institute of Technology（麻省理工学院）；Microsoft Research（微软研究院）
Recent advances in probabilistic generative modeling have motivated learning Structural Causal Models (SCM) from observational datasets using deep conditional generative models, also known as Deep Structural Causal Models (DSCM). If successful, DSCMs can be utilized for causal estimation tasks, e.g., for answering counterfactual queries. In this work, we warn practitioners about non-identifiability of counterfactual inference from observational data, even in the absence of unobserved confounding and assuming known causal structure. We prove counterfactual identifiability of monotonic generatio…
Multi-View Causal Discovery without Non-Gaussianity: Identifiability and Algorithms
Inria（法国国家信息与自动化技术研究院）；CEA（法国国家科学研究中心）；University of Paris-Saclay（巴黎-萨克勒大学）；University of Carnegie Mellon（卡内基梅隆大学）；Apple（苹果公司）；University of Helsinki（赫尔辛基大学）
Amazon（亚马逊）；Massachusetts Institute of Technology（麻省理工学院）
We extend the definition of the marginal causal effect to the continuous treatment setting and develop a novel characterization of causal bias in the framework of structural causal models. We prove that our derived bias expression is zero if, and only if, the causal effect is identifiable via covariate adjustment. We show that under some restrictions on the structural equations, the causal bias can be estimated efficiently and allows for causal regularization of predictive probabilistic models. We demonstrate the effectiveness of our method for causal bias quantification in various settings wh…
Mila（米拉研究所）；McGill University（麦吉尔大学）；KTH Stockholm（斯德哥尔摩皇家理工学院）；ÉTS Montréal（蒙特利尔高等工程技术学院）；Deepmind（深度思维）；Université de Montréal（蒙特利尔大学）；ÉTS Montreal（蒙特利尔高等工程技术学院）
Causal learning has long concerned itself with the accurate recovery of underlying causal mechanisms. Such causal modelling enables better explanations of out-of-distribution data. Prior works on causal learning assume that the high-level causal variables are given. However, in machine learning tasks, one often operates on low-level data like image pixels or high-dimensional vectors. In such settings, the entire Structural Causal Model (SCM) -- structure, parameters, \textit{and} high-level causal variables -- is unobserved and needs to be learnt from low-level data. We treat this problem as B…
University of Technology Sydney（悉尼科技大学）；Curtin University（科廷大学）
Counterfactual fairness alleviates the discrimination between the model prediction toward an individual in the actual world (observational data) and that in counterfactual world (i.e., what if the individual belongs to other sensitive groups). The existing studies need to pre-define the structural causal model that captures the correlations among variables for counterfactual inference; however, the underlying causal model is usually unknown and difficult to be validated in real-world scenarios. Moreover, the misspecification of the causal model potentially leads to poor performance in model pr…
Georgia Institute of Technology（佐治亚理工学院）；University of Detroit Mercy（底特律梅西大学）；Johns Hopkins University（约翰斯·霍普金斯大学）
Linear structural causal models (SCMs) -- in which each observed variable is generated by a subset of the other observed variables as well as a subset of the exogenous sources -- are pervasive in causal inference and casual discovery. However, for the task of causal discovery, existing work almost exclusively focus on the submodel where each observed variable is associated with a distinct source with non-zero variance. This results in the restriction that no observed variable can deterministically depend on other observed variables or latent confounders. In this paper, we extend the results on…
Causal Discovery in Structural VAR Models Under Equal Noise Variance
Bourns College of Engineering, University of California, Riverside（加州大学河滨分校工程学院）；University of California, San Francisco（加州大学旧金山分校）；Department of Mathematics and Statistics, Boston University（波士顿大学数学与统计学系）
This manuscript contributes a general and practical framework for casting a Markov process model of a system at equilibrium as a structural causal model, and carrying out counterfactual inference. Markov processes mathematically describe the mechanisms in the system, and predict the system's equilibrium behavior upon intervention, but do not support counterfactual inference. In contrast, structural causal models support counterfactual inference, but do not identify the mechanisms. This manuscript leverages the benefits of both approaches. We define the structural causal models in terms of the …
Discovering Mixtures of Structural Causal Models from Time Series Data
Halıcıoğlu Data Science Institute, University of California, San Diego（加利福尼亚大学圣迭戈分校哈利西奥格鲁数据科学学院）；Department of Computer Science and Engineering, University of California, San Diego（加利福尼亚大学圣迭戈分校计算机科学与工程系）
University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）；Northeast Georgia Health System（东北乔治亚医疗系统）；Palos Health（帕洛斯医疗中心）；Penn State University（宾夕法尼亚州立大学）；Purdue University（普渡大学）
Recent advances in causal inference techniques, more specifically, in the theory of structural causal models, provide the framework for identification of causal effects from observational data in the cases where the causal graph is identifiable, i.e., the data generating mechanism can be recovered from the joint distribution. However, no such studies have been done to demonstrate this concept with a clinical example. We present a complete framework to estimate the causal effect from observational data by augmenting expert knowledge in the model development phase and with a practical clinical a…
Massachusetts Institute of Technology（麻省理工学院）；CSAIL（计算机科学与人工智能实验室）
We introduce an off-policy evaluation procedure for highlighting episodes where applying a reinforcement learned (RL) policy is likely to have produced a substantially different outcome than the observed policy. In particular, we introduce a class of structural causal models (SCMs) for generating counterfactual trajectories in finite partially observable Markov Decision Processes (POMDPs). We see this as a useful procedure for off-policy "debugging" in high-risk settings (e.g., healthcare); by decomposing the expected difference in reward between the RL and observed policy into specific episod…
University of Sydney（悉尼大学）；University of Melbourne（墨尔本大学）；Hong Kong Baptist University（香港浸会大学）；RIKEN AIP（理化学研究所先进智能项目中心）；Carnegie Mellon University（卡内基梅隆大学）
Label noise will degenerate the performance of deep learning algorithms because deep neural networks easily overfit label errors. Let X and Y denote the instance and clean label, respectively. When Y is a cause of X, according to which many datasets have been constructed, e.g., SVHN and CIFAR, the distributions of P(X) and P(Y|X) are entangled. This means that the unsupervised instances are helpful to learn the classifier and thus reduce the side effect of label noise. However, it remains elusive on how to exploit the causal information to handle the label noise problem. In this paper, by leve…
TU Darmstadt（达姆施塔特工业大学）；DFKI（德国人工智能研究中心）；Hessian Center for AI (hessian.AI)（黑森人工智能中心）
In explanatory interactive learning (XIL) the user queries the learner, then the learner explains its answer to the user and finally the loop repeats. XIL is attractive for two reasons, (1) the learner becomes better and (2) the user's trust increases. For both reasons to hold, the learner's explanations must be useful to the user and the user must be allowed to ask useful questions. Ideally, both questions and explanations should be grounded in a causal model since they avoid spurious fallacies. Ultimately, we seem to seek a causal variant of XIL. The question part on the user's end we believ…
Informatics Institute, University of Amsterdam（阿姆斯特丹大学信息学研究所）；Empirical Inference, MPI for Intelligent Systems（马克斯·普朗克智能系统研究所经验推断部）；Machine Learning Group, University of Cambridge（剑桥大学机器学习组）；Max Planck ETH Center for Learning Systems（马克斯·普朗克-苏黎世联邦理工学院学习系统中心）
Complex systems can be modelled at various levels of detail. Ideally, causal models of the same system should be consistent with one another in the sense that they agree in their predictions of the effects of interventions. We formalise this notion of consistency in the case of Structural Equation Models (SEMs) by introducing exact transformations between SEMs. This provides a general language to consider, for instance, the different levels of description in the following three scenarios: (a) models with large numbers of variables versus models in which the `irrelevant' or unobservable variabl…
Structural causal models (SCMs), also known as (nonparametric) structural equation models (SEMs), are widely used for causal modeling purposes. In particular, acyclic SCMs, also known as recursive SEMs, form a well-studied subclass of SCMs that generalize causal Bayesian networks to allow for latent confounders. In this paper, we investigate SCMs in a more general setting, allowing for the presence of both latent confounders and cycles. We show that in the presence of cycles, many of the convenient properties of acyclic SCMs do not hold in general: they do not always have a solution; they do n…
Local Causal Discovery for Structural Evidence of Direct Discrimination
Cornell Tech（康奈尔理工学院）；Stevens Institute of Technology（史蒂文斯理工学院）；University of Oxford（牛津大学）；Amazon AWS AI/ML（亚马逊云科技人工智能/机器学习部门）；Weill Cornell Medicine（威尔康奈尔医学院）
Imperial College London（帝国理工学院）；Microsoft Research（微软研究院）
Causal reasoning provides a language to ask important interventional and counterfactual questions beyond purely statistical association. In medical imaging, for example, we may want to study the causal effect of genetic, environmental, or lifestyle factors on the normal and pathological variation of anatomical phenotypes. However, while anatomical shape models of 3D surface meshes, extracted from automated image segmentation, can be reliably constructed, there is a lack of computational tooling to enable causal reasoning about morphological variations. To tackle this problem, we propose deep s…
Precision medicine involves answering counterfactual questions such as "Would this patient respond better to treatment A or treatment B?" These types of questions are causal in nature and require the tools of causal inference to be answered, e.g., with a structural causal model (SCM). In this work, we develop an SCM that models the interaction between demographic information, disease covariates, and magnetic resonance (MR) images of the brain for people with multiple sclerosis. Inference in the SCM generates counterfactual images that show what an MR image of the brain would look like if demog…
Structural Gating and Effect-aligned Lag-resolved Temporal Causal Discovery Framework with Application to Heat-Pollution Extremes
organization= School of Artificial Intelligence , addressline= Guilin University of Electronic Technology , city= Guilin , state= Guangxi , postcode= 541004 , country= China；organization= Department of Electrical Engineering , addressline= University of Chile , city= Santiago , state= Santiago Metropolitan Region , postcode
Beihang University（北京航空航天大学）；Beijing Big Data Centre（北京大数据中心）
As a representative of public transportation, the fundamental issue of managing bike-sharing systems is bike flow prediction. Recent methods overemphasize the spatio-temporal correlations in the data, ignoring the effects of contextual conditions on the transportation system and the inter-regional timevarying causality. In addition, due to the disturbance of incomplete observations in the data, random contextual conditions lead to spurious correlations between data and features, making the prediction of the model ineffective in special scenarios. To overcome this issue, we propose a Spatio-tem…
Wasserstein Distributionally Robust Optimization Through the Lens of Structural Causal Models and Individual Fairness
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Tübingen AI Center（图宾根人工智能中心）；Mila Québec AI Institute（魁北克人工智能研究所）；McGill University（麦吉尔大学）
