In this work, we formalize the problem of causal inference over graph-based relational time-series data where each node in the graph has one or more time-series associated to it. We propose causal inference models for this problem that leverage both the graph topology and time-series to accurately estimate local causal effects of nodes. Furthermore, the relational time-series causal inference models are able to estimate local effects for individual nodes by exploiting local node-centric temporal dependencies and topological/structural dependencies. We show that simpler causal models that do not consider the graph topology are recovered as special cases of the proposed relational time-series causal inference model. We describe the conditions under which the resulting estimate can be used to estimate a causal effect, and describe how the Durbin-Wu-Hausman test of specification can be used to test for the consistency of the proposed estimator from data. Empirically, we demonstrate the effectiveness of the causal inference models on both synthetic data with known ground-truth and a large-scale observational relational time-series data set collected from Wikipedia.
Purdue University（普渡大学）；Pennsylvania State University（宾夕法尼亚州立大学）
We consider the problem of learning causal relationships from relational data. Existing approaches rely on queries to a relational conditional independence (RCI) oracle to establish and orient causal relations in such a setting. In practice, queries to a RCI oracle have to be replaced by reliable tests for RCI against available data. Relational data present several unique challenges in testing for RCI. We study the conditions under which traditional iid-based conditional independence (CI) tests yield reliable answers to RCI queries against relational data. We show how to conduct CI tests again…
The inference of network topologies from relational data is an important problem in data analysis. Exemplary applications include the reconstruction of social ties from data on human interactions, the inference of gene co-expression networks from DNA microarray data, or the learning of semantic relationships based on co-occurrences of words in documents. Solving these problems requires techniques to infer significant links in noisy relational data. In this short paper, we propose a new statistical modeling framework to address this challenge. It builds on generalized hypergeometric ensembles, …
This study addresses the problem of learning an extended summary causal graph on time series. The algorithms we propose fit within the well-known constraint-based framework for causal discovery and make use of information-theoretic measures to determine (in)dependencies between time series. We first introduce generalizations of the causation entropy measure to any lagged or instantaneous relations, prior to using this measure to construct extended summary causal graphs by adapting two well-known algorithms, namely PC and FCI. The behavior of our methods is illustrated through several experimen…
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. A typical approach consists of a series of conditional independence tests on the covariance structure meant to progressively reduce the space of possible causal models. We propose a novel efficient Bayesian method for discovering the local causal relationships among triplets of (normally distributed) variables. In our approach, we score the patter…
Inferring causal relations from time series measurements is an ill-posed mathematical problem, where typically an infinite number of potential solutions can reproduce the given data. We explore in depth a strategy to disambiguate between possible underlying causal networks by perturbing the network, where the actuations are either targeted or applied at random. The resulting transient dynamics provide the critical information necessary to infer causality. Two methods are shown to provide accurate causal reconstructions: Granger causality (GC) with perturbations, and our proposed perturbation c…
University of Tübingen（图宾根大学）；University of Hohenheim（霍恩海姆大学）
The novel DISTributed Artificial neural Network Architecture (DISTANA) is a generative, recurrent graph convolution neural network. It implements a grid or mesh of locally parameterizable laterally connected network modules. DISTANA is specifically designed to identify the causality behind spatially distributed, non-linear dynamical processes. We show that DISTANA is very well-suited to denoise data streams, given that re-occurring patterns are observed, significantly outperforming alternative approaches, such as temporal convolution networks and ConvLSTMs, on a complex spatial wave propagatio…
Granger causality is a widely-used criterion for analyzing interactions in large-scale networks. As most physical interactions are inherently nonlinear, we consider the problem of inferring the existence of pairwise Granger causality between nonlinearly interacting stochastic processes from their time series measurements. Our proposed approach relies on modeling the embedded nonlinearities in the measurements using a component-wise time series prediction model based on Statistical Recurrent Units (SRUs). We make a case that the network topology of Granger causal relations is directly inferrabl…
Artificial Intelligence Research Laboratory（人工智能研究实验室）；College of Information Sciences and Technology（信息科学与技术学院）；Pennsylvania State University（宾夕法尼亚州立大学）
Maier et al. (2010) introduced the relational causal model (RCM) for representing and inferring causal relationships in relational data. A lifted representation, called abstract ground graph (AGG), plays a central role in reasoning with and learning of RCM. The correctness of the algorithm proposed by Maier et al. (2013a) for learning RCM from data relies on the soundness and completeness of AGG for relational d-separation to reduce the learning of an RCM to learning of an AGG. We revisit the definition of AGG and show that AGG, as defined in Maier et al. (2013b), does not correctly abstract a…
Arizona State University（亚利桑那州立大学）；University of Arkansas at Little Rock（阿肯色大学小石城分校）
Modeling spillover effects from observational data is an important problem in economics, business, and other fields of research. % It helps us infer the causality between two seemingly unrelated set of events. For example, if consumer spending in the United States declines, it has spillover effects on economies that depend on the U.S. as their largest export market. In this paper, we aim to infer the causation that results in spillover effects between pairs of entities (or units), we call this effect as \textit{paired spillover}. To achieve this, we leverage the recent developments in variatio…
Identifying directed interactions between species from time series of their population densities has many uses in ecology. This key statistical task is equivalent to causal time series inference, which connects to the Granger causality (GC) concept: $x$ causes $y$ if $x$ improves the prediction of $y$ in a dynamic model. However, the entangled nature of nonlinear ecological systems has led to question the appropriateness of Granger causality, especially in its classical linear Multivariate AutoRegressive (MAR) model form. Convergent-cross mapping (CCM), a nonparametric method developed for det…
University of Amsterdam（阿姆斯特丹大学）；TNO Intelligent Imaging（荷兰应用科学研究组织智能成像）；New York University（纽约大学）；CIMS（库朗数学科学研究所）；Massachusetts Institute of Technology（麻省理工学院）；CSAIL & IMES（计算机科学与人工智能实验室与医学工程与科学研究所）；University of Toronto（多伦多大学）；CIFAR（加拿大高等研究院）
Learning individual-level causal effects from observational data, such as inferring the most effective medication for a specific patient, is a problem of growing importance for policy makers. The most important aspect of inferring causal effects from observational data is the handling of confounders, factors that affect both an intervention and its outcome. A carefully designed observational study attempts to measure all important confounders. However, even if one does not have direct access to all confounders, there may exist noisy and uncertain measurement of proxies for confounders. We buil…
Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）；Saarland University（萨尔大学）
We consider the problem of inferring the directed, causal graph from observational data, assuming no hidden confounders. We take an information theoretic approach, and make three main contributions. First, we show how through algorithmic information theory we can obtain SCI, a highly robust, effective and computationally efficient test for conditional independence---and show it outperforms the state of the art when applied in constraint-based inference methods such as stable PC. Second, building upon on SCI, we show how to tell apart the parents and children of a given node based on the algori…
To gain insight into complex systems it is a key challenge to infer nonlinear causal directional relations from observational time-series data. Specifically, estimating causal relationships between interacting components in large systems with only short recordings over few temporal observations remains an important, yet unresolved problem. Here, we introduce a large-scale Nonlinear Granger Causality (lsNGC) approach for inferring directional, nonlinear, multivariate causal interactions between system components from short high-dimensional time-series recordings. By modeling interactions with n…
National Institute of Advanced Studies（国家高级研究院）；Indian Institute of Science（印度科学学院）
Causal inference is one of the most fundamental problems across all domains of science. We address the problem of inferring a causal direction from two observed discrete symbolic sequences $X$ and $Y$. We present a framework which relies on lossless compressors for inferring context-free grammars (CFGs) from sequence pairs and quantifies the extent to which the grammar inferred from one sequence compresses the other sequence. We infer $X$ causes $Y$ if the grammar inferred from $X$ better compresses $Y$ than in the other direction. To put this notion to practice, we propose three models that u…
Conventional methods in causal effect inferencetypically rely on specifying a valid set of control variables. When this set is unknown or misspecified, inferences will be erroneous. We propose a method for inferring average causal effects when all potential confounders are observed, but thecontrol variables are unknown. When the data-generating process belongs to the class of acyclical linear structural causal models, we prove that themethod yields asymptotically valid confidence intervals. Our results build upon a smooth characterization of linear directed acyclic graphs. We verify the capabi…
Inferring nonlinear and asymmetric causal relationships between multivariate longitudinal data is a challenging task with wide-ranging application areas including clinical medicine, mathematical biology, economics and environmental research. A number of methods for inferring causal relationships within complex dynamic and stochastic systems have been proposed but there is not a unified consistent definition of causality in this context. We evaluate the performance of ten prominent bivariate causality indices for time series data, across four simulated model systems that have different coupling…
We consider analysis of relational data (a matrix), in which the rows correspond to subjects (e.g., people) and the columns correspond to attributes. The elements of the matrix may be a mix of real and categorical. Each subject and attribute is characterized by a latent binary feature vector, and an inferred matrix maps each row-column pair of binary feature vectors to an observed matrix element. The latent binary features of the rows are modeled via a multivariate Gaussian distribution with low-rank covariance matrix, and the Gaussian random variables are mapped to latent binary features via …
Causal inference from observational data following the restricted structural causal model (SCM) framework hinges largely on the asymmetry between cause and effect from the data generating mechanisms, such as non-Gaussianity or nonlinearity. This methodology can be adapted to stationary time series, yet inferring causal relationships from nonstationary time series remains a challenging task. In this work, we propose a new class of restricted SCM, via a time-varying filter and stationary noise, and exploit the asymmetry from nonstationarity for causal identification in both bivariate and network…
Inferring causal relationships in observational time series data is an important task when interventions cannot be performed. Granger causality is a popular framework to infer potential causal mechanisms between different time series. The original definition of Granger causality is restricted to linear processes and leads to spurious conclusions in the presence of a latent confounder. In this work, we harness the expressive power of recurrent neural networks and propose a deep learning-based approach to model non-linear Granger causality by directly accounting for latent confounders. Our appro…
Structural equation models (SEMs) and vector autoregressive models (VARMs) are two broad families of approaches that have been shown useful in effective brain connectivity studies. While VARMs postulate that a given region of interest in the brain is directionally connected to another one by virtue of time-lagged influences, SEMs assert that causal dependencies arise due to contemporaneous effects, and may even be adopted when nodal measurements are not necessarily multivariate time series. To unify these complementary perspectives, linear structural vector autoregressive models (SVARMs) that …
Exploratory analysis of time series data can yield a better understanding of complex dynamical systems. Granger causality is a practical framework for analysing interactions in sequential data, applied in a wide range of domains. In this paper, we propose a novel framework for inferring multivariate Granger causality under nonlinear dynamics based on an extension of self-explaining neural networks. This framework is more interpretable than other neural-network-based techniques for inferring Granger causality, since in addition to relational inference, it also allows detecting signs of Granger-…
We address the problem of inferring the causal effect of an exposure on an outcome across space, using observational data. The data is possibly subject to unmeasured confounding variables which, in a standard approach, must be adjusted for by estimating a nuisance function. Here we develop a method that eliminates the nuisance function, while mitigating the resulting errors-in-variables. The result is a robust and accurate inference method for spatially varying heterogeneous causal effects. The properties of the method are demonstrated on synthetic as well as real data from Germany and the US.
Inferring the abstract relational and causal structure of the world is a major challenge for reinforcement-learning (RL) agents. For humans, language--particularly in the form of explanations--plays a considerable role in overcoming this challenge. Here, we show that language can play a similar role for deep RL agents in complex environments. While agents typically struggle to acquire relational and causal knowledge, augmenting their experience by training them to predict language descriptions and explanations can overcome these limitations. We show that language can help agents learn challeng…
University College London（伦敦大学学院）；Novartis International AG（诺华国际股份公司）
At the heart of causal structure learning from observational data lies a deceivingly simple question: given two statistically dependent random variables, which one has a causal effect on the other? This is impossible to answer using statistical dependence testing alone and requires that we make additional assumptions. We propose several fast and simple criteria for distinguishing cause and effect in pairs of discrete or continuous random variables. The intuition behind them is that predicting the effect variable using the cause variable should be `simpler' than the reverse -- different notions…
University of Bergen（卑尔根大学）；isee systems inc.（isee系统公司）
This paper presents a new causal network learning algorithm (FSNN, Feedback System Neural Network) based on the construction and analysis of a non-linear system of Ordinary Differential Equations (ODEs). The constructed system provides insight into the mechanisms responsible for generating the past and potential future behavior of dynamic systems. It is also interpretable in terms of real system variables, providing a wholistic, causally accurate, and systemic understanding of the real-life interactions governing observed phenomena. This paper demonstrates the generation of an n-dimensional or…
University of Washington（华盛顿大学）；Duke University（杜克大学）；University of California at Santa Cruz（加州大学圣克鲁兹分校）
Causal inference is at the heart of empirical research in natural and social sciences and is critical for scientific discovery and informed decision making. The gold standard in causal inference is performing randomized controlled trials; unfortunately these are not always feasible due to ethical, legal, or cost constraints. As an alternative, methodologies for causal inference from observational data have been developed in statistical studies and social sciences. However, existing methods critically rely on restrictive assumptions such as the study population consisting of homogeneous element…
Max Planck Institute for Biological Cybernetics（马克斯·普朗克生物控制论研究所）；Vilnius University（维尔纽斯大学）；Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学科学研究所）
We consider two variables that are related to each other by an invertible function. While it has previously been shown that the dependence structure of the noise can provide hints to determine which of the two variables is the cause, we presently show that even in the deterministic (noise-free) case, there are asymmetries that can be exploited for causal inference. Our method is based on the idea that if the function and the probability density of the cause are chosen independently, then the distribution of the effect will, in a certain sense, depend on the function. We provide a theoretical a…
University of Waterloo（滑铁卢大学）；Perimeter Institute for Theoretical Physics（圆周理论物理研究所）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
The problem of using observed correlations to infer causal relations is relevant to a wide variety of scientific disciplines. Yet given correlations between just two classical variables, it is impossible to determine whether they arose from a causal influence of one on the other or a common cause influencing both, unless one can implement a randomized intervention. We here consider the problem of causal inference for quantum variables. We introduce causal tomography, which unifies and generalizes conventional quantum tomography schemes to provide a complete solution to the causal inference pro…
Causal learning is a beneficial approach to analyze the cause and effect relationships among variables in a dataset. A causal graph can be generated from a dataset using a particular causal algorithm, for instance, the PC algorithm or Fast Causal Inference (FCI). Generating a causal graph from a dataset that contains different data types (mixed data) is not trivial. This research offers an easy way to handle the mixed data so that it can be used to learn causal graphs using the existing application of the PC algorithm and FCI. This research proposes using kernel functions and Kernel Alignment …
It is common practice in using regression type models for inferring causal effects, that inferring the correct causal relationship requires extra covariates are included or ``adjusted for''. Without performing this adjustment erroneous causal effects can be inferred. Given this phenomenon it is common practice to include as many covariates as possible, however such advice comes unstuck in the presence of M-bias. M-Bias is a problem in causal inference where the correct estimation of treatment effects requires that certain variables are not adjusted for i.e. are simply neglected from inclusion …
Northeastern University（东北大学）；UC San Diego（加利福尼亚大学圣地亚哥分校）
Inferring interactions from multi-agent trajectories has broad applications in physics, vision and robotics. Neural relational inference (NRI) is a deep generative model that can reason about relations in complex dynamics without supervision. In this paper, we take a careful look at this approach for relational inference in multi-agent trajectories. First, we discover that NRI can be fundamentally limited without sufficient long-term observations. Its ability to accurately infer interactions degrades drastically for short output sequences. Next, we consider a more general setting of relational…
In domains like bioinformatics, information retrieval and social network analysis, one can find learning tasks where the goal consists of inferring a ranking of objects, conditioned on a particular target object. We present a general kernel framework for learning conditional rankings from various types of relational data, where rankings can be conditioned on unseen data objects. We propose efficient algorithms for conditional ranking by optimizing squared regression and ranking loss functions. We show theoretically, that learning with the ranking loss is likely to generalize better than with t…
High-throughput molecular profiling technologies have produced high-dimensional multi-omics data, enabling systematic understanding of living systems at the genome scale. Studying molecular interactions across different data types helps reveal signal transduction mechanisms across different classes of molecules. In this paper, we develop a novel Bayesian representation learning method that infers the relational interactions across multi-omics data types. Our method, Bayesian Relational Learning (BayReL) for multi-omics data integration, takes advantage of a priori known relationships among the…
Georgia Institute of Technology（佐治亚理工学院）；Duke University（杜克大学）
Multivariate Hawkes processes are commonly used to model streaming networked event data in a wide variety of applications. However, it remains a challenge to extract reliable inference from complex datasets with uncertainty quantification. Aiming towards this, we develop a statistical inference framework to learn causal relationships between nodes from networked data, where the underlying directed graph implies Granger causality. We provide uncertainty quantification for the maximum likelihood estimate of the network multivariate Hawkes process by providing a non-asymptotic confidence set. The…
NTT Communication Science Laboratories（NTT通信科学实验室）；NTT Corporation（NTT公司）；The University of Tokyo（东京大学）
The Infinite Relational Model (IRM) is a probabilistic model for relational data clustering that partitions objects into clusters based on observed relationships. This paper presents Averaged CVB (ACVB) solutions for IRM, convergence-guaranteed and practically useful fast Collapsed Variational Bayes (CVB) inferences. We first derive ordinary CVB and CVB0 for IRM based on the lower bound maximization. CVB solutions yield deterministic iterative procedures for inferring IRM given the truncated number of clusters. Our proposal includes CVB0 updates of hyperparameters including the concentration p…
Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）；Saarland University（萨尔大学）
Given data over the joint distribution of two random variables $X$ and $Y$, we consider the problem of inferring the most likely causal direction between $X$ and $Y$. In particular, we consider the general case where both $X$ and $Y$ may be univariate or multivariate, and of the same or mixed data types. We take an information theoretic approach, based on Kolmogorov complexity, from which it follows that first describing the data over cause and then that of effect given cause is shorter than the reverse direction. The ideal score is not computable, but can be approximated through the Minimum D…
Inference of Causal Networks using a Topological Threshold
University of Aveiro（阿威罗大学）；i3N（i3N研究所）；Instituto de Telecomunicações（电信研究所）；Department of Electronics, Telecommunications and Informatics, University of Aveiro（阿威罗大学电子、电信与信息学院）；Department of Physics and i3N, University of Aveiro（阿威罗大学物理与i3N研究所）
Inferring new facts from existing knowledge graphs (KG) with explainable reasoning processes is a significant problem and has received much attention recently. However, few studies have focused on relation types unseen in the original KG, given only one or a few instances for training. To bridge this gap, we propose CogKR for one-shot KG reasoning. The one-shot relational learning problem is tackled through two modules: the summary module summarizes the underlying relationship of the given instances, based on which the reasoning module infers the correct answers. Motivated by the dual process …
