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 ordinary differential equation model that can be parameterized to fit measured data using standard numerical optimization techniques. The model makes use of feed forward artificial neural nets to capture nonlinearity, but is a parsimonious and interpretable representation of the network of causal relationships in complex systems. The generated model can easily and rapidly be experimented with and analyzed to determine the origins of behavior using the loops that matter method (Schoenberg et. al 2019). A demonstration of the utility and applicability of the method is given, showing that it produces an accurate, and causally correct model for a three state, non-linear, complex dynamic system of known origin. Generalization to other dynamic systems with other data sources is then discussed.
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-…
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…
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…
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…
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…
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…
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）
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…
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）
Northwestern Polytechnical University（西北工业大学）；Center for Excellence in Molecular Cell Science, Chinese Academy of Sciences（中国科学院分子细胞科学卓越创新中心）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；South China University of Technology（华南理工大学）；Guangdong Institute of Intelligence Science and Technology（广东智能科学技术研究院）；Fudan University（复旦大学）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院）
A recursive Bayesian neural network for constitutive modeling of sands under monotonic and cyclic loading
Department of Civil Engineering（土木工程系）；Indian Institute of Technology Delhi（德里印度理工学院）；Department of Transportation Systems Engineering（交通运输系统工程系）；Technical University of Munich（慕尼黑技术大学）；Department of Applied Mechanics（应用力学系）
Simultaneous EEG-fMRI is a multi-modal neuroimaging technique that provides complementary spatial and temporal resolution. Challenging has been developing principled and interpretable approaches for fusing the modalities, specifically approaches enabling inference of latent source spaces representative of neural activity. In this paper, we address this inference problem within the framework of transcoding -- mapping from a specific encoding (modality) to a decoding (the latent source space) and then encoding the latent source space to the other modality. Specifically, we develop a symmetric me…
A Deep Spatio-Temporal Architecture for Dynamic Effective Connectivity Network Analysis Based on Dynamic Causal Discovery
School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学院）；Department of Biomedical Engineering, Tulane University（杜兰大学生物医学工程系）；Tri-Institutional Center for Translational Research in Neuroimaging and Data Science (TReNDS), Georgia State University, Georgia Institute of Technology, Emory University（佐治亚州立大学、佐治亚理工学院、埃默里大学三方转化神经成像与数据科学中心（TReNDS））；Mind Research Network（心智研究网络）；Institute for Human Neuroscience, Boys Town National Research Hospital（博伊斯镇国家医院人类神经科学研究所）
Discovering and Reasoning of Causality in the Hidden World with Large Language Models
TMLR Group, Hong Kong Baptist University（香港 Baptist 大学 TMLR 组）；Mohamed bin Zayed University of Artificial Intelligence（Mohamed bin Zayed 人工智能大学）；Department of Philosophy, Carnegie Mellon University（哲学系，卡内基梅隆大学）；School of Computer Science, The University of Sydney（悉尼大学计算机科学学院）；School of Mathematics and Statistics, The University of Melbourne（墨尔本大学数学与统计学学院）；The Chinese University of Hong Kong（香港中文大学）
DynGFN: Towards Bayesian Inference of Gene Regulatory Networks with GFlowNets
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；Mila - Quebec AI Institute（Mila-魁北克人工智能研究所）；University Health Network（大学健康网络）；Université de Montréal（蒙特利尔大学）；Valence Labs（Valence实验室）
University of Maryland, College Park（马里兰大学帕克分校）；Indian Institute of Science, Bangalore（班加罗尔印度科学研究所）；Microsoft Research, India（微软研究院（印度））
In this work, we consider the problem of robust parameter estimation from observational data in the context of linear structural equation models (LSEMs). LSEMs are a popular and well-studied class of models for inferring causality in the natural and social sciences. One of the main problems related to LSEMs is to recover the model parameters from the observational data. Under various conditions on LSEMs and the model parameters the prior work provides efficient algorithms to recover the parameters. However, these results are often about generic identifiability. In practice, generic identifiabi…
