The aim in many sciences is to understand the mechanisms that underlie the observed distribution of variables, starting from a set of initial hypotheses. Causal discovery allows us to infer mechanisms as sets of cause and effect relationships in a generalized way -- without necessarily tailoring to a specific domain. Causal discovery algorithms search over a structured hypothesis space, defined by the set of directed acyclic graphs, to find the graph that best explains the data. For high-dimensional problems, however, this search becomes intractable and scalable algorithms for causal discovery are needed to bridge the gap. In this paper, we define a novel causal graph partition that allows for divide-and-conquer causal discovery with theoretical guarantees. We leverage the idea of a superstructure -- a set of learned or existing candidate hypotheses -- to partition the search space. We prove under certain assumptions that learning with a causal graph partition always yields the Markov Equivalence Class of the true causal graph. We show our algorithm achieves comparable accuracy and a faster time to solution for biologically-tuned synthetic networks and networks up to ${10^4}$ variables. This makes our method applicable to gene regulatory network inference and other domains with high-dimensional structured hypothesis spaces.
Sorbonne Université（索邦大学）；Inserm（法国国家健康与医学研究院）；Sorbonne Public Health Institute（索邦公共卫生研究所）；Equipe PEPITES（PEPITES团队）；Assistance Publique - Hôpitaux de Paris（巴黎公立协助医院）；Hôpital Pitié Salpêtrière（皮蒂埃-萨尔佩特里耶尔医院）；Département de Santé Publique（公共卫生系）；Centre de Pharmacoépidémiologie (Cephepi)（药物流行病学中心）；APHP（巴黎公立协助医院）；Hôpital Saint-Antoine（圣安东医院）；Inria（法国国家计算机科学与控制研究院）；CNRS（法国国家科学研究中心）；Paris Brain Institute（巴黎脑研究所）
In this paper we study the problems of estimating heterogeneity in causal effects in experimental or observational studies and conducting inference about the magnitude of the differences in treatment effects across subsets of the population. In applications, our method provides a data-driven approach to determine which subpopulations have large or small treatment effects and to test hypotheses about the differences in these effects. For experiments, our method allows researchers to identify heterogeneity in treatment effects that was not specified in a pre-analysis plan, without concern about …
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）
Machine learning approaches commonly rely on the assumption of independent and identically distributed (i.i.d.) data. In reality, however, this assumption is almost always violated due to distribution shifts between environments. Although valuable learning signals can be provided by heterogeneous data from changing distributions, it is also known that learning under arbitrary (adversarial) changes is impossible. Causality provides a useful framework for modeling distribution shifts, since causal models encode both observational and interventional distributions. In this work, we explore the spa…
We interpret the predictions of any black-box structured input-structured output model around a specific input-output pair. Our method returns an "explanation" consisting of groups of input-output tokens that are causally related. These dependencies are inferred by querying the black-box model with perturbed inputs, generating a graph over tokens from the responses, and solving a partitioning problem to select the most relevant components. We focus the general approach on sequence-to-sequence problems, adopting a variational autoencoder to yield meaningful input perturbations. We test our meth…
We study the problem of learning to choose from m discrete treatment options (e.g., news item or medical drug) the one with best causal effect for a particular instance (e.g., user or patient) where the training data consists of passive observations of covariates, treatment, and the outcome of the treatment. The standard approach to this problem is regress and compare: split the training data by treatment, fit a regression model in each split, and, for a new instance, predict all m outcomes and pick the best. By reformulating the problem as a single learning task rather than m separate ones, w…
The regression discontinuity (RD) design is a popular approach to causal inference in non-randomized studies. This is because it can be used to identify and estimate causal effects under mild conditions. Specifically, for each subject, the RD design assigns a treatment or non-treatment, depending on whether or not an observed value of an assignment variable exceeds a fixed and known cutoff value. In this paper, we propose a Bayesian nonparametric regression modeling approach to RD designs, which exploits a local randomization feature. In this approach, the assignment variable is treated as a c…
Many outcomes of interest in the social and health sciences, as well as in modern applications in computational social science and experimentation on social media platforms, are ordinal and do not have a meaningful scale. Causal analyses that leverage this type of data, termed ordinal non-numeric, require careful treatment, as much of the classical potential outcomes literature is concerned with estimation and hypothesis testing for outcomes whose relative magnitudes are well defined. Here, we propose a class of finite population causal estimands that depend on conditional distributions of the…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
We propose a kernel method to identify finite mixtures of nonparametric product distributions. It is based on a Hilbert space embedding of the joint distribution. The rank of the constructed tensor is equal to the number of mixture components. We present an algorithm to recover the components by partitioning the data points into clusters such that the variables are jointly conditionally independent given the cluster. This method can be used to identify finite confounders.
The internal validity of observational study is often subject to debate. In this study, we define the counterfactuals as the unobserved sample and intend to quantify its relationship with the null hypothesis statistical testing (NHST). We propose the probability of a causal inference is robust for internal validity, i.e., the PIV, as a robustness index of causal inference. Formally, the PIV is the probability of rejecting the null hypothesis again based on both the observed sample and the counterfactuals, provided the same null hypothesis has already been rejected based on the observed sample.…
Rensselaer Polytechnic Institute（伦斯勒理工学院）；Northeast Normal University（东北师范大学）
Causal discovery is to learn cause-effect relationships among variables given observational data and is important for many applications. Existing causal discovery methods assume data sufficiency, which may not be the case in many real world datasets. As a result, many existing causal discovery methods can fail under limited data. In this work, we propose Bayesian-augmented frequentist independence tests to improve the performance of constraint-based causal discovery methods under insufficient data: 1) We firstly introduce a Bayesian method to estimate mutual information (MI), based on which we…
Single-subject health data are becoming increasingly available thanks to advances in self-tracking technology (e.g., wearable devices, mobile apps, sensors, implants). Many users and health caregivers seek to use such observational time series data to recommend changing health practices in order to achieve desired health outcomes. However, there are few available causal inference approaches that are flexible enough to analyze such idiographic data. We develop a recently introduced causal-analysis framework based on n-of-1 randomized trials, and implement a flexible random-forests g-formula app…
Mila, Université de Montreal（蒙特利尔大学Mila研究所）；SAIT AI Lab, Montreal（蒙特利尔SAIT人工智能实验室）
Consider a collection of datasets generated by unknown interventions on an unknown structural causal model $G$. Recently, Bengio et al. (2020) conjectured that among all candidate models, $G$ is the fastest to adapt from one dataset to another, along with promising experiments. Indeed, intuitively $G$ has less mechanisms to adapt, but this justification is incomplete. Our contribution is a more thorough analysis of this hypothesis. We investigate the adaptation speed of cause-effect SCMs. Using convergence rates from stochastic optimization, we justify that a relevant proxy for adaptation spee…
The University of Chicago（芝加哥大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
Motivated by the rising abundance of observational data with continuous treatments, we investigate the problem of estimating the average dose-response curve (ADRF). Available parametric methods are limited in their model space, and previous attempts in leveraging neural network to enhance model expressiveness relied on partitioning continuous treatment into blocks and using separate heads for each block; this however produces in practice discontinuous ADRFs. Therefore, the question of how to adapt the structure and training of neural network to estimate ADRFs remains open. This paper makes two…
External validity is often questionable in empirical research, especially in randomized experiments due to the trade-off between internal validity and external validity. To quantify the robustness of external validity, one must first conceptualize the gap between a sample that is fully representative of the target population (i.e., the ideal sample) and the observed sample. Drawing on Frank & Min (2007) and Frank et al. (2013), I define such gap as the unobserved sample and intend to quantify its relationship with the null hypothesis statistical testing (NHST) in this study. The probability of…
We consider a causal effect that is confounded by an unobserved variable, but with observed proxy variables of the confounder. We show that, with at least two independent proxy variables satisfying a certain rank condition, the causal effect is nonparametrically identified, even if the measurement error mechanism, i.e., the conditional distribution of the proxies given the con- founder, may not be identified. Our result generalizes the identification strategy of Kuroki & Pearl (2014) that rests on identification of the measurement error mechanism. When only one proxy for the confounder is avai…
The origin of adversarial examples is still inexplicable in research fields, and it arouses arguments from various viewpoints, albeit comprehensive investigations. In this paper, we propose a way of delving into the unexpected vulnerability in adversarially trained networks from a causal perspective, namely adversarial instrumental variable (IV) regression. By deploying it, we estimate the causal relation of adversarial prediction under an unbiased environment dissociated from unknown confounders. Our approach aims to demystify inherent causal features on adversarial examples by leveraging a z…
Unquantified sources of uncertainty in observational causal analyses can break the integrity of the results. One would never want another analyst to repeat a calculation with the same dataset, using a seemingly identical procedure, only to find a different conclusion. However, as we show in this work, there is a typical source of uncertainty that is essentially never considered in observational causal studies: the choice of match assignment for matched groups, that is, which unit is matched to which other unit before a hypothesis test is conducted. The choice of match assignment is anything bu…
Centre d’Analyse et de Mathématique Sociales（社会分析与数学中心）；EHESS（高等社会科学研究院）；Centre de Mathématiques Appliquées（应用数学中心）；École Polytechnique（巴黎综合理工学院）；Inria XPOP（法国国家信息与自动化研究所XPOP团队）；Google Research（谷歌研究院）
Inferring causal effects of a treatment, intervention or policy from observational data is central to many applications. However, state-of-the-art methods for causal inference seldom consider the possibility that covariates have missing values, which is ubiquitous in many real-world analyses. Missing data greatly complicate causal inference procedures as they require an adapted unconfoundedness hypothesis which can be difficult to justify in practice. We circumvent this issue by considering latent confounders whose distribution is learned through variational autoencoders adapted to missing val…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Radboud University（拉德堡德大学）
We consider the problem of function estimation in the case where an underlying causal model can be inferred. This has implications for popular scenarios such as covariate shift, concept drift, transfer learning and semi-supervised learning. We argue that causal knowledge may facilitate some approaches for a given problem, and rule out others. In particular, we formulate a hypothesis for when semi-supervised learning can help, and corroborate it with empirical results.
Interference exists when a unit's outcome depends on another unit's treatment assignment. For example, intensive policing on one street could have a spillover effect on neighboring streets. Classical randomization tests typically break down in this setting because many null hypotheses of interest are no longer sharp under interference. A promising alternative is to instead construct a conditional randomization test on a subset of units and assignments for which a given null hypothesis is sharp. Finding these subsets is challenging, however, and existing methods are limited to special cases or …
Under the potential outcomes framework, causal effects are defined as comparisons between potential outcomes under treatment and control. To infer causal effects from randomized experiments, Neyman proposed to test the null hypothesis of zero average causal effect (Neyman's null), and Fisher proposed to test the null hypothesis of zero individual causal effect (Fisher's null). Although the subtle difference between Neyman's null and Fisher's null has caused lots of controversies and confusions for both theoretical and practical statisticians, a careful comparison between the two approaches has…
A framework for causal inference from two-level factorial designs is proposed. The framework utilizes the concept of potential outcomes that lies at the center stage of causal inference and extends Neyman's repeated sampling approach for estimation of causal effects and randomization tests based on Fisher's sharp null hypothesis to the case of 2-level factorial experiments. The framework allows for statistical inference from a finite population, permits definition and estimation of estimands other than "average factorial effects" and leads to more flexible inference procedures than those based…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Conditional independence testing is an important problem, especially in Bayesian network learning and causal discovery. Due to the curse of dimensionality, testing for conditional independence of continuous variables is particularly challenging. We propose a Kernel-based Conditional Independence test (KCI-test), by constructing an appropriate test statistic and deriving its asymptotic distribution under the null hypothesis of conditional independence. The proposed method is computationally efficient and easy to implement. Experimental results show that it outperforms other methods, especially …
Information Geometric Causal Inference (IGCI) is a new approach to distinguish between cause and effect for two variables. It is based on an independence assumption between input distribution and causal mechanism that can be phrased in terms of orthogonality in information space. We describe two intuitive reinterpretations of this approach that makes IGCI more accessible to a broader audience. Moreover, we show that the described independence is related to the hypothesis that unsupervised learning and semi-supervised learning only works for predicting the cause from the effect and not vice ver…
Universitas Islam Indonesia（印度尼西亚伊斯兰大学）；Radboud University Nijmegen（奈梅亨拉德堡德大学）；Radboud University Medical Centre（拉德堡德大学医学中心）
Causal modeling has long been an attractive topic for many researchers and in recent decades there has seen a surge in theoretical development and discovery algorithms. Generally discovery algorithms can be divided into two approaches: constraint-based and score-based. The constraint-based approach is able to detect common causes of the observed variables but the use of independence tests makes it less reliable. The score-based approach produces a result that is easier to interpret as it also measures the reliability of the inferred causal relationships, but it is unable to detect common confo…
ISI Foundation（ISI基金会）；UniCredit（裕信银行）；New York University（纽约大学）；Stanford University（斯坦福大学）
Mastering the dynamics of social influence requires separating, in a database of information propagation traces, the genuine causal processes from temporal correlation, i.e., homophily and other spurious causes. However, most studies to characterize social influence, and, in general, most data-science analyses focus on correlations, statistical independence, or conditional independence. Only recently, there has been a resurgence of interest in "causal data science", e.g., grounded on causality theories. In this paper we adopt a principled causal approach to the analysis of social influence fro…
The case-crossover design (Maclure, 1991) is widely used in epidemiology and other fields to study causal effects of transient treatments on acute outcomes. However, its validity and causal interpretation have only been justified under informal conditions. Here, we place the design in a formal counterfactual framework for the first time. Doing so helps to clarify its assumptions and interpretation. In particular, when the treatment effect is non-null, we identify a previously unnoticed bias arising from common causes of the outcome at different person-times. We analytically characterize the di…
In many data scientific problems, we are interested in inferring causal relationships in the data generating mechanism. Here, we consider the following real-world question: how has the Colombian conflict influenced tropical forest loss? There is evidence for both enhancing and reducing impacts. Answering such questions requires the use of causal models. In this work, we propose a class of causal models for spatio-temporal stochastic processes. It allows us to formally define and quantify the causal effect of a vector of covariates $X$ on a real-valued response $Y$, even if the causal backgroun…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Max Planck Institute for Biological Cybernetics（马克斯·普朗克生物控制论研究所）
The postulate of independence of cause and mechanism (ICM) has recently led to several new causal discovery algorithms. The interpretation of independence and the way it is utilized, however, varies across these methods. Our aim in this paper is to propose a group theoretic framework for ICM to unify and generalize these approaches. In our setting, the cause-mechanism relationship is assessed by comparing it against a null hypothesis through the application of random generic group transformations. We show that the group theoretic view provides a very general tool to study the structure of data…
In many scientific studies, it is of interest to determine whether an exposure has a causal effect on an outcome. In observational studies, this is a challenging task due to the presence of confounding variables that affect both the exposure and the outcome. Many methods have been developed to test for the presence of a causal effect when all such confounding variables are observed and when the exposure of interest is discrete. In this article, we propose a class of nonparametric tests of the null hypothesis that there is no average causal effect of an arbitrary univariate exposure on an outco…
