Graph topology inference of network processes with co-evolving and interacting time-series is crucial for network studies. Vector autoregressive models (VAR) are popular approaches for topology inference of directed graphs; however, in large networks with short time-series, topology estimation becomes ill-posed. The present paper proposes a novel nonlinearity-preserving topology inference method for directed networks with co-evolving nodal processes that solves the ill-posedness problem. The proposed method, large-scale kernelized Granger causality (lsKGC), uses kernel functions to transform data into a low-dimensional feature space and solves the autoregressive problem in the feature space, then finds the pre-images in the input space to infer the topology. Extensive simulations on synthetic datasets with nonlinear and linear dependencies and known ground-truth demonstrate significant improvement in the Area Under the receiver operating characteristic Curve ( AUC ) of the receiver operating characteristic for network recovery compared to existing methods. Furthermore, tests on real datasets from a functional magnetic resonance imaging (fMRI) study demonstrate 96.3 percent accuracy in diagnosis tasks of schizophrenia patients, which is the highest in the literature with only brain time-series information.
Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University（西安交通大学人工智能与机器人研究所）；RIKEN AIP（理化学研究所人工智能项目）；Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）
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-…
Learning Granger causality for general point processes is a very challenging task. In this paper, we propose an effective method, learning Granger causality, for a special but significant type of point processes --- Hawkes process. We reveal the relationship between Hawkes process's impact function and its Granger causality graph. Specifically, our model represents impact functions using a series of basis functions and recovers the Granger causality graph via group sparsity of the impact functions' coefficients. We propose an effective learning algorithm combining a maximum likelihood estimato…
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Aalborg University（奥尔堡大学）；XaiPient（赛派恩特）；Duke University（杜克大学）
We study the problem of learning Granger causality between event types from asynchronous, interdependent, multi-type event sequences. Existing work suffers from either limited model flexibility or poor model explainability and thus fails to uncover Granger causality across a wide variety of event sequences with diverse event interdependency. To address these weaknesses, we propose CAUSE (Causality from AttribUtions on Sequence of Events), a novel framework for the studied task. The key idea of CAUSE is to first implicitly capture the underlying event interdependency by fitting a neural point p…
Exploring Neural Granger Causality with xLSTMs: Unveiling Temporal Dependencies in Complex Data
Carnegie Mellon University（卡内基梅隆大学）；AI & ML Group, TU Darmstadt（TU达姆施塔特人工智能与机器学习小组）；DFKI；Centre for Cognitive Science, TU Darmstadt（TU达姆施塔特认知科学中心）；TU Eindhoven（埃因霍温理工大学）
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…
Granger causality is a commonly used method for uncovering information flow and dependencies in a time series. Here we introduce JGC (Jacobian Granger Causality), a neural network-based approach to Granger causality using the Jacobian as a measure of variable importance, and propose a thresholding procedure for inferring Granger causal variables using this measure. The resulting approach performs consistently well compared to other approaches in identifying Granger causal variables, the associated time lags, as well as interaction signs. Lastly, through the inclusion of a time variable, we sho…
In this foundational expository article on the application of Causality Analysis in IoT, we establish the basic theory and algorithms for estimating Structural and Granger causality factors from measured multichannel sensor data (vector timeseries). Vector timeseries is modeled as a Structural Vector Autoregressive (SVAR) model; utilizing Kalman Filter and Independent Component Analysis (ICA) methods, Structural and generalized Granger causality factors are estimated. The estimated causal factors are presented as a Fence graph which we call Causal Digital Twin. Practical applications of Causal…
Beijing University of Posts and Telecommunications（北京邮电大学）；Tsinghua University（清华大学）
Granger causality method analyzes the time series causalities without building a complex causality graph. However, the traditional Granger causality method assumes that the causalities lie between time series channels and remain constant, which cannot model the real-world time series data with dynamic causalities along the time series channels. In this paper, we present the dynamic window-level Granger causality method (DWGC) for multi-channel time series data. We build the causality model on the window-level by doing the F-test with the forecasting errors on the sliding windows. We propose th…
We generalize a previously proposed approach for nonlinear Granger causality of time series, based on radial basis function. The proposed model is not constrained to be additive in variables from the two time series and can approximate any function of these variables, still being suitable to evaluate causality. Usefulness of this measure of causality is shown in a physiological example and in the study of the feed-back loop in a model of excitatory and inhibitory neurons.
Granger causality analysis, as one of the most popular time series causality methods, has been widely used in the economics, neuroscience. However, unobserved confounders is a fundamental problem in the observational studies, which is still not solved for the non-linear Granger causality. The application works often deal with this problem in virtue of the proxy variables, who can be treated as a measure of the confounder with noise. But the proxy variables has been proved to be unreliable, because of the bias it may induce. In this paper, we try to "recover" the unobserved confounders for the …
Faculty of Business and Economics, University of Lausanne（洛桑大学商学院）；Department of Statistics, UC Berkeley（伯克利大学统计学系）；Research Institute for Statistics and Information Science, University of Geneva（日内瓦大学统计与信息科学研究所）；Department of Industrial Engineering and Operations Research, Columbia University（哥伦比亚大学工业工程与运筹学系）
National Electronics and Computer Technology Center（国家电子和计算机技术中心）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）
Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of the effect time series is influenced by a combination of other time series with a fixed time delay. However, the assumption of the fixed time delay does not hold in many applications, such as collective behavior, financial markets, and many natural phenomena. To address this issue, we develop variable-lag Granger causality, a generalization of Granger causali…
Introduced more than a half century ago, Granger causality has become a popular tool for analyzing time series data in many application domains, from economics and finance to genomics and neuroscience. Despite this popularity, the validity of this notion for inferring causal relationships among time series has remained the topic of continuous debate. Moreover, while the original definition was general, limitations in computational tools have primarily limited the applications of Granger causality to simple bivariate vector auto-regressive processes or pairwise relationships among a set of vari…
Iowa State University（爱荷华州立大学）；University of Colorado Boulder（科罗拉多大学博尔德分校）；National Renewable Energy Laboratory（国家可再生能源实验室）
Clustering is an unsupervised learning technique that is useful when working with a large volume of unlabeled data. Complex dynamical systems in real life often entail data streaming from a large number of sources. Although it is desirable to use all source variables to form accurate state estimates, it is often impractical due to large computational power requirements, and sufficiently robust algorithms to handle these cases are not common. We propose a hierarchical time series clustering technique based on symbolic dynamic filtering and Granger causality, which serves as a dimensionality red…
Image Processing Laboratory (IPL)（图像处理实验室（IPL））；Universitat de València（瓦伦西亚大学）
Global warming is leading to unprecedented changes in our planet, with great societal, economical and environmental implications, especially with the growing demand of biofuels and food. Assessing the impact of climate on vegetation is of pressing need. We approached the attribution problem with a novel nonlinear Granger causal (GC) methodology and used a large data archive of remote sensing satellite products, environmental and climatic variables spatio-temporally gridded over more than 30 years. We generalize kernel Granger causality by considering the variables cross-relations explicitly in…
National Electronics and Computer Technology Center（国家电子和计算机技术中心）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）；The Ohio State University（俄亥俄州立大学）
Granger causality is a fundamental technique for causal inference in time series data, commonly used in the social and biological sciences. Typical operationalizations of Granger causality make a strong assumption that every time point of the effect time series is influenced by a combination of other time series with a fixed time delay. The assumption of fixed time delay also exists in Transfer Entropy, which is considered to be a non-linear version of Granger causality. However, the assumption of the fixed time delay does not hold in many applications, such as collective behavior, financial m…
IBM Research（IBM研究院）；Istituto Italiano di Tecnologia（意大利理工学院）
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel Hilbert Spaces. We develop a highly scalable and eigendecomposition-free algorithm that orchestrates two inexact solvers for simultaneously learning both the input and output components of separable matrix-valued kernels. As a key application enabled by our framework, we show how high-dimensional…
IBM Research（IBM研究院）；Italian Institute of Technology（意大利理工学院）
We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to be imposed on a dictionary of vector-valued Reproducing Kernel Hilbert Spaces. We develop a highly scalable and eigendecomposition-free algorithm that orchestrates two inexact solvers for simultaneously learning both the input and output components of separable matrix-valued kernels. As a key application enabled by our framework, we show how high-dimensional…
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…
Granger causal modeling is an emerging topic that can uncover Granger causal relationship behind multivariate time series data. In many real-world systems, it is common to encounter a large amount of multivariate time series data collected from different individuals with sharing commonalities. However, there are ongoing concerns regarding Granger causality's applicability in such large scale complex scenarios, presenting both challenges and opportunities for Granger causal structure reconstruction. Existing methods usually train a distinct model for each individual, suffering from inefficiency…
Prediction and Causality of functional MRI and synthetic signal using a Zero-Shot Time-Series Foundation Model
AGH University of Krakow, Poland（克拉科夫AGH大学）；Institut de Neurosciences de la Timone UMR 7289, Aix Marseille Université, CNRS, 13005, Marseille, France（里莫内神经科学研究所）
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…
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Tsinghua-Berkeley Shenzhen Institute（清华-伯克利深圳学院）；Tsinghua Shenzhen International Graduate School（清华大学深圳国际研究生院）；Graduate School, Tsinghua University（清华大学研究生院）
Generating Fine-Grained Causality in Climate Time Series Data for Forecasting and Anomaly Detection
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；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）；Amazon Sustainability Science and Innovation（亚马逊可持续性科学与创新部门）
Emergent Granger Causality in Neural Networks: Can Prediction Alone Reveal Structure?
BESE Division, King Abdullah University of Science and Technology (KAUST)（贝赛分校，卡斯泰技术大学（KAUST））；CEMSE Division, King Abdullah University of Science and Technology (KAUST)（CEMSE分校，卡斯泰技术大学（KAUST））
University of Rochester（罗切斯特大学）；Ludwig Maximilian University（路德维希·马克西米利安大学）
We introduce large-scale Augmented Granger Causality (lsAGC) as a method for connectivity analysis in complex systems. The lsAGC algorithm combines dimension reduction with source time-series augmentation and uses predictive time-series modeling for estimating directed causal relationships among time-series. This method is a multivariate approach, since it is capable of identifying the influence of each time-series on any other time-series in the presence of all other time-series of the underlying dynamic system. We quantitatively evaluate the performance of lsAGC on synthetic directional time…
University of Rochester（罗切斯特大学）；Ludwig Maximilian University（路德维希·马克西米利安大学）
It has been shown in the literature that marijuana use is associated with changes in brain network connectivity. We propose large-scale Extended Granger Causality (lsXGC) and investigate whether it can capture such changes using resting-state fMRI. This method combines dimension reduction with source time-series augmentation and uses predictive time-series modeling for estimating directed causal relationships among fMRI time-series. It is a multivariate approach, since it is capable of identifying the interdependence of time-series in the presence of all other time-series of the underlying dyn…
When a dynamical system can be modeled as a sequence of observations, Granger causality is a powerful approach for detecting predictive interactions between its variables. However, traditional Granger causal inference has limited utility in domains where the dynamics need to be represented as directed acyclic graphs (DAGs) rather than as a linear sequence, such as with cell differentiation trajectories. Here, we present GrID-Net, a framework based on graph neural networks with lagged message passing for Granger causal inference on DAG-structured systems. Our motivating application is the analy…
University of Rochester（罗切斯特大学）；Ludwig Maximilian University（路德维希-马克西米利安大学）
The literature manifests that schizophrenia is associated with alterations in brain network connectivity. We investigate whether large-scale Extended Granger Causality (lsXGC) can capture such alterations using resting-state fMRI data. Our method utilizes dimension reduction combined with the augmentation of source time-series in a predictive time-series model for estimating directed causal relationships among fMRI time-series. The lsXGC is a multivariate approach since it identifies the relationship of the underlying dynamic system in the presence of all other time-series. Here lsXGC serves a…
This paper considers joint learning of multiple sparse Granger graphical models to discover underlying common and differential Granger causality (GC) structures across multiple time series. This can be applied to drawing group-level brain connectivity inferences from a homogeneous group of subjects or discovering network differences among groups of signals collected under heterogeneous conditions. By recognizing that the GC of a single multivariate time series can be characterized by common zeros of vector autoregressive (VAR) lag coefficients, a group sparse prior is included in joint regular…
University of Applied Sciences and Arts of Western Switzerland（瑞士西部应用科学与艺术大学）；University of Geneva（日内瓦大学）
We consider the problem of learning models for forecasting multiple time-series systems together with discovering the leading indicators that serve as good predictors for the system. We model the systems by linear vector autoregressive models (VAR) and link the discovery of leading indicators to inferring sparse graphs of Granger-causality. We propose new problem formulations and develop two new methods to learn such models, gradually increasing the complexity of assumptions and approaches. While the first method assumes common structures across the whole system, our second method uncovers mod…
Nagoya University（名古屋大学）；RIKEN Center for Advanced Intelligence Project（日本理化学研究所先进智能项目）；Doshisha University（同志社大学）；Tokai University（东海大学）；Kyushu University（九州大学）
Extracting the interaction rules of biological agents from movement sequences pose challenges in various domains. Granger causality is a practical framework for analyzing the interactions from observed time-series data; however, this framework ignores the structures and assumptions of the generative process in animal behaviors, which may lead to interpretational problems and sometimes erroneous assessments of causality. In this paper, we propose a new framework for learning Granger causality from multi-animal trajectories via augmented theory-based behavioral models with interpretable data-dri…
A Gradient-based Causal Discovery Framework with Applications to Complex Industrial Processes
School of Artificial Intelligence, Beijing Normal University（北京师范大学人工智能学院）；Advanced Institute of Natural Sciences, Beijing Normal University（北京师范大学自然科学院）
TNPAR: Topological Neural Poisson Auto-Regressive Model for Learning Granger Causal Structure from Event Sequences
Guangdong University of Technology（广东工业大学）；Peng Cheng Laboratory（鹏城实验室）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Huawei（华为）；Shantou University（汕头大学）
