Discovery of causal relationships from observational data is an important problem in many areas. Several recent results have established the identifiability of causal DAGs with non-Gaussian and/or nonlinear structural equation models (SEMs). In this paper, we focus on nonlinear SEMs defined by non-invertible functions, which exist in many data domains, and propose a novel test for non-invertible bivariate causal models. We further develop a method to incorporate this test in structure learning of DAGs that contain both linear and nonlinear causal relations. By extensive numerical comparisons, we show that our algorithms outperform existing DAG learning methods in identifying causal graphical structures. We illustrate the practical application of our method in learning causal networks for combinatorial binding of transcription factors from ChIP-Seq data.
University College London（伦敦大学学院）；Carnegie Mellon University（卡内基梅隆大学）；University of Helsinki（赫尔辛基大学）
We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied especially in the bivariate setting, the majority of current methods assume a linear causal relationship, and the few methods which consider non-linear dependencies usually make the assumption of additive noise. Here, we propose a framework through which we can perform causal discovery in the presence of general non-linear relationships. The proposed method is based on recent progress in non-linear independent compon…
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…
Spotify（声田）；University College London（伦敦大学学院）；Babylon Health（巴比伦健康）
The discovery of causal relationships is a fundamental problem in science and medicine. In recent years, many elegant approaches to discovering causal relationships between two variables from observational data have been proposed. However, most of these deal only with purely directed causal relationships and cannot detect latent common causes. Here, we devise a general heuristic which takes a causal discovery algorithm that can only distinguish purely directed causal relations and modifies it to also detect latent common causes. We apply our method to two directed causal discovery algorithms, …
Discovering causal relationships between different variables from time series data has been a long-standing challenge for many domains such as climate science, finance, and healthcare. Given the complexity of real-world relationships and the nature of observations in discrete time, causal discovery methods need to consider non-linear relations between variables, instantaneous effects and history-dependent noise (the change of noise distribution due to past actions). However, previous works do not offer a solution addressing all these problems together. In this paper, we propose a novel causal …
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,…
Causal discovery estimates the underlying physical process that generates the observed data: does X cause Y or does Y cause X? Current methodologies use structural conditions to turn the causal query into a statistical query, when only observational data is available. But what if these statistical queries are sensitive to causal invariants? This study investigates one such invariant: the causal relationship between X and Y is invariant to the marginal distributions of X and Y. We propose an algorithm that uses a non-parametric estimator that is robust to changes in the marginal distributions. …
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）
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 …
Our goal is to recover time-delayed latent causal variables and identify their relations from measured temporal data. Estimating causally-related latent variables from observations is particularly challenging as the latent variables are not uniquely recoverable in the most general case. In this work, we consider both a nonparametric, nonstationary setting and a parametric setting for the latent processes and propose two provable conditions under which temporally causal latent processes can be identified from their nonlinear mixtures. We propose LEAP, a theoretically-grounded framework that ext…
Digital University Kerala (IIITMK)（喀拉拉数字大学（印度信息技术与管理学院喀拉拉邦分院））
In recent years, causal modelling has been used widely to improve generalization and to provide interpretability in machine learning models. To determine cause-effect relationships in the absence of a randomized trial, we can model causal systems with counterfactuals and interventions given enough domain knowledge. However, there are several cases where domain knowledge is almost absent and the only recourse is using a statistical method to estimate causal relationships. While there have been several works done in estimating causal relationships in unstructured data, we are yet to find a well-…
RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Shiga University（滋贺大学）
Causal discovery from data affected by unobserved variables is an important but difficult problem to solve. The effects that unobserved variables have on the relationships between observed variables are more complex in nonlinear cases than in linear cases. In this study, we focus on causal additive models in the presence of unobserved variables. Causal additive models exhibit structural equations that are additive in the variables and error terms. We take into account the presence of not only unobserved common causes but also unobserved intermediate variables. Our theoretical results show that…
IE University（IE大学）；Universitat de València（瓦伦西亚大学）
Causal discovery algorithms aim at untangling complex causal relationships from data. Here, we study causal discovery and inference methods based on staged tree models, which can represent complex and asymmetric causal relationships between categorical variables. We provide a first graphical representation of the equivalence class of a staged tree, by looking only at a specific subset of its underlying independences. We further define a new pre-metric, inspired by the widely used structural intervention distance, to quantify the closeness between two staged trees in terms of their correspondin…
Massachusetts Institute of Technology（麻省理工学院）；Scripps Institution of Oceanography（斯克里普斯海洋研究所）；Paul Scherrer Institute（保罗·谢勒研究所）；University of California San Diego（加利福尼亚大学圣迭戈分校）
Causal Discovery methods aim to identify a DAG structure that represents causal relationships from observational data. In this article, we stress that it is important to test such methods for robustness in practical settings. As our main example, we analyze the NOTEARS method, for which we demonstrate a lack of scale-invariance. We show that NOTEARS is a method that aims to identify a parsimonious DAG from the data that explains the residual variance. We conclude that NOTEARS is not suitable for identifying truly causal relationships from the data.
Centre for Speckled Computing（散斑计算中心）；University of Edinburgh（爱丁堡大学）
According to the Lancet report on the global burden of disease published in October 2020, air pollution is among the five highest risk factors for global health, reducing life expectancy on average by 20 months. This paper describes a data-driven method for establishing causal relationships within and between two multivariate time series data streams derived from wearable sensors: personal exposure to airborne particulate matter of aerodynamic sizes less than 2.5um (PM2.5) gathered from the Airspeck monitor worn on the person and continuous respiratory rate (breaths per minute) measured by the…
Estimation of causal effects is fundamental in situations were the underlying system will be subject to active interventions. Part of building a causal inference engine is defining how variables relate to each other, that is, defining the functional relationship between variables given conditional dependencies. In this paper, we deviate from the common assumption of linear relationships in causal models by making use of neural autoregressive density estimators and use them to estimate causal effects within the Pearl's do-calculus framework. Using synthetic data, we show that the approach can r…
Progress in probabilistic generative models has accelerated, developing richer models with neural architectures, implicit densities, and with scalable algorithms for their Bayesian inference. However, there has been limited progress in models that capture causal relationships, for example, how individual genetic factors cause major human diseases. In this work, we focus on two challenges in particular: How do we build richer causal models, which can capture highly nonlinear relationships and interactions between multiple causes? How do we adjust for latent confounders, which are variables infl…
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…
Most causal discovery algorithms find causal structure among a set of observed variables. Learning the causal structure among latent variables remains an important open problem, particularly when using high-dimensional data. In this paper, we address a problem for which it is known that inputs cause outputs, and these causal relationships are encoded by a causal network among a set of an unknown number of latent variables. We developed a deep learning model, which we call a redundant input neural network (RINN), with a modified architecture and a regularized objective function to find causal r…
Causal structure discovery in complex dynamical systems is an important challenge for many scientific domains. Although data from (interventional) experiments is usually limited, large amounts of observational time series data sets are usually available. Current methods that learn causal structure from time series often assume linear relationships. Hence, they may fail in realistic settings that contain nonlinear relations between the variables. We propose Neural Additive Vector Autoregression (NAVAR) models, a neural approach to causal structure learning that can discover nonlinear relationsh…
Indian Institute of Technology Hyderabad（印度理工学院海得拉巴分校）；Microsoft Research（微软研究院）
A trained neural network can be interpreted as a structural causal model (SCM) that provides the effect of changing input variables on the model's output. However, if training data contains both causal and correlational relationships, a model that optimizes prediction accuracy may not necessarily learn the true causal relationships between input and output variables. On the other hand, expert users often have prior knowledge of the causal relationship between certain input variables and output from domain knowledge. Therefore, we propose a regularization method that aligns the learned causal e…
University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）
Conventional temporal causal discovery (CD) methods suffer from high dimensionality, fail to identify lagged causal relationships, and often ignore dynamics in relations. In this study, we present a novel constraint-based CD approach for autocorrelated and non-stationary time series data (eCDANs) capable of detecting lagged and contemporaneous causal relationships along with temporal changes. eCDANs addresses high dimensionality by optimizing the conditioning sets while conducting conditional independence (CI) tests and identifies the changes in causal relations by introducing a surrogate vari…
KTH Royal Institute of Technology（瑞典皇家理工学院）；Carnegie Mellon University（卡内基梅隆大学）；Karolinska Institute（卡罗林斯卡学院）
Applying machine learning in the health care domain has shown promising results in recent years. Interpretable outputs from learning algorithms are desirable for decision making by health care personnel. In this work, we explore the possibility of utilizing causal relationships to refine diagnostic prediction. We focus on the task of diagnostic prediction using discomfort drawings, and explore two ways to employ causal identification to improve the diagnostic results. Firstly, we use causal identification to infer the causal relationships among diagnostic labels which, by itself, provides inte…
This paper presents a new open source Python framework for causal discovery from observational data and domain background knowledge, aimed at causal graph and causal mechanism modeling. The 'cdt' package implements the end-to-end approach, recovering the direct dependencies (the skeleton of the causal graph) and the causal relationships between variables. It includes algorithms from the 'Bnlearn' and 'Pcalg' packages, together with algorithms for pairwise causal discovery such as ANM. 'cdt' is available under the MIT License at https://github.com/Diviyan-Kalainathan/CausalDiscoveryToolbox.
Identifying the causal structure of systems with multiple dynamic elements is critical to several scientific disciplines. The conventional approach is to conduct statistical tests of causality, for example with Granger Causality, between observed signals that are selected a priori. Here it is posited that, in many systems, the causal relations are embedded in a latent space that is expressed in the observed data as a linear mixture. A technique for blindly identifying the latent sources is presented: the observations are projected into pairs of components -- driving and driven -- to maximize t…
German Center for Neurodegenerative Diseases (DZNE)（德国神经退行性疾病中心（DZNE））
We consider learning ancestral causal relationships in high dimensions. Our approach is driven by a supervised learning perspective, with discrete indicators of causal relationships treated as labels to be learned from available data. We focus on the setting in which some causal (ancestral) relationships are known (via background knowledge or experimental data) and put forward a general approach that scales to large problems. This is motivated by problems in human biology which are characterized by high dimensionality and potentially many latent variables. We present a case study involving int…
Rethinking Causal Relationships Learning in Graph Neural Networks
Science and Technology on Integrated Information System Laboratory, Institute of Software Chinese Academy of Sciences（中国科学院软件研究所综合信息系统技术国家级重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；State Key Laboratory of Intelligent Game（智能博弈国家重点实验室）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）
On the Relationship Between Explanation and Prediction: A Causal View
MPI for Intelligent Systems（马克斯·普朗克智能系统研究所）；ETH Zurich（苏黎世联邦理工学院）；Google Research（谷歌研究院）；CISPA-Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）
Latent variables may lead to spurious relationships that can be misinterpreted as causal relationships. In Bayesian Networks (BNs), this challenge is known as learning under causal insufficiency. Structure learning algorithms that assume causal insufficiency tend to reconstruct the ancestral graph of a BN, where bi-directed edges represent confounding and directed edges represent direct or ancestral relationships. This paper describes a hybrid structure learning algorithm, called CCHM, which combines the constraint-based part of cFCI with hill-climbing score-based learning. The score-based pro…
Hefei University of Technology（合肥工业大学）；University of South Australia（南澳大学）；Mininglamp Academy of Sciences, Mininglamp Technology（明略科技明略科学院）
Feature selection is a crucial preprocessing step in data analytics and machine learning. Classical feature selection algorithms select features based on the correlations between predictive features and the class variable and do not attempt to capture causal relationships between them. It has been shown that the knowledge about the causal relationships between features and the class variable has potential benefits for building interpretable and robust prediction models, since causal relationships imply the underlying mechanism of a system. Consequently, causality-based feature selection has gr…
Gene regulatory networks play a crucial role in controlling an organism's biological processes, which is why there is significant interest in developing computational methods that are able to extract their structure from high-throughput genetic data. Many of these computational methods are designed to infer individual regulatory relationships among genes from data on gene expression. We propose a novel efficient Bayesian method for discovering local causal relationships among triplets of (normally distributed) variables. In our approach, we score covariance structures for each triplet in one g…
BMW Group（宝马集团）；TU Dortmund University（多特蒙德工业大学）；Research Center Trustworthy Data Science and Security（可信数据科学与安全研究中心）
Many production processes are characterized by numerous and complex cause-and-effect relationships. Since they are only partially known they pose a challenge to effective process control. In this work we present how Structural Equation Models can be used for deriving cause-and-effect relationships from the combination of prior knowledge and process data in the manufacturing domain. Compared to existing applications, we do not assume linear relationships leading to more informative results.
In this paper, we propose a mixture of probabilistic partial canonical correlation analysis (MPPCCA) that extracts the Causal Patterns from two multivariate time series. Causal patterns refer to the signal patterns within interactions of two elements having multiple types of mutually causal relationships, rather than a mixture of simultaneous correlations or the absence of presence of a causal relationship between the elements. In multivariate statistics, partial canonical correlation analysis (PCCA) evaluates the correlation between two multivariates after subtracting the effect of the third …
Information Technologies Institute, Centre of Research and Technology Hellas（希腊研究与技术中心信息技术研究所）
Multivariate time series forecasting is of great importance to many scientific disciplines and industrial sectors. The evolution of a multivariate time series depends on the dynamics of its variables and the connectivity network of causal interrelationships among them. Most of the existing time series models do not account for the causal effects among the system's variables and even if they do they rely just on determining the between-variables causality network. Knowing the structure of such a complex network and even more specifically knowing the exact lagged variables that contribute to the…
We study optimal covariate balance for causal inferences from observational data when rich covariates and complex relationships necessitate flexible modeling with neural networks. Standard approaches such as propensity weighting and matching/balancing fail in such settings due to miscalibrated propensity nets and inappropriate covariate representations, respectively. We propose a new method based on adversarial training of a weighting and a discriminator network that effectively addresses this methodological gap. This is demonstrated through new theoretical characterizations of the method as w…
This paper frames causal structure estimation as a machine learning task. The idea is to treat indicators of causal relationships between variables as `labels' and to exploit available data on the variables of interest to provide features for the labelling task. Background scientific knowledge or any available interventional data provide labels on some causal relationships and the remainder are treated as unlabelled. To illustrate the key ideas, we develop a distance-based approach (based on bivariate histograms) within a manifold regularization framework. We present empirical results on three…
