Causal Discovery from Time-Series Data with Short-Term Invariance-Based Convolutional Neural Networks
Faculty of Computing（计算机学院）；Harbin Institute of Technology（哈尔滨工业大学）；The Artificial Intelligence Institute（人工智能研究所）；The Department of Computer Science（计算机科学系）；The University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
Rujia Shen, Boran Wang, Chao Zhao, Yi Guan, Jingchi Jiang
Causal discovery from time-series data aims to capture both intra-slice (contemporaneous) and inter-slice (time-lagged) causality between variables within the temporal chain, which is crucial for various scientific disciplines. Compared to causal discovery from non-time-series data, causal discovery from time-series data necessitates more serialized samples with a larger amount of observed time steps. To address the challenges, we propose a novel gradient-based causal discovery approach STIC, which focuses on \textbf{S}hort-\textbf{T}erm \textbf{I}nvariance using \textbf{C}onvolutional neural networks to uncover the causal relationships from time-series data. Specifically, STIC leverages both the short-term time and mechanism invariance of causality within each window observation, which possesses the property of independence, to enhance sample efficiency. Furthermore, we construct two causal convolution kernels, which correspond to the short-term time and mechanism invariance respectively, to estimate the window causal graph. To demonstrate the necessity of convolutional neural networks for causal discovery from time-series data, we theoretically derive the equivalence between convolution and the underlying generative principle of time-series data under the assumption that the additive noise model is identifiable. Experimental evaluations conducted on both synthetic and FMRI benchmark datasets demonstrate that our STIC outperforms baselines significantly and achieves the state-of-the-art performance, particularly when the datasets contain a limited number of observed time steps. Code is available at \url{https://github.com/HITshenrj/STIC}.
Cause-effect analysis is crucial to understand the underlying mechanism of a system. We propose to exploit model invariance through interventions on the predictors to infer causality in nonlinear multivariate systems of time series. We model nonlinear interactions in time series using DeepAR and then expose the model to different environments using Knockoffs-based interventions to test model invariance. Knockoff samples are pairwise exchangeable, in-distribution and statistically null variables generated without knowing the response. We test model invariance where we show that the distribution…
Reasoning based on causality, instead of association has been considered as a key ingredient towards real machine intelligence. However, it is a challenging task to infer causal relationship/structure among variables. In recent years, an Independent Mechanism (IM) principle was proposed, stating that the mechanism generating the cause and the one mapping the cause to the effect are independent. As the conjecture, it is argued that in the causal direction, the conditional distributions instantiated at different value of the conditioning variable have less variation than the anti-causal directio…
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. …
Imperial College London（帝国理工学院）；IBM Research Europe（IBM欧洲研究院）；Trinity College Dublin（都柏林圣三一学院）；University of Rostock（罗斯托克大学）
Many large-scale applications can be elegantly represented using graph structures. Their scalability, however, is often limited by the domain knowledge required to apply them. To address this problem, we propose a novel Causal Temporal Graph Convolutional Neural Network (CTGCN). Our CTGCN architecture is based on a causal discovery mechanism, and is capable of discovering the underlying causal processes. The major advantages of our approach stem from its ability to overcome computational scalability problems with a divide and conquer technique, and from the greater explainability of prediction…
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…
University of Chicago（芝加哥大学）；Google Research（谷歌研究院）
Real-world classification problems must contend with domain shift, the (potential) mismatch between the domain where a model is deployed and the domain(s) where the training data was gathered. Methods to handle such problems must specify what structure is common between the domains and what varies. A natural assumption is that causal (structural) relationships are invariant in all domains. Then, it is tempting to learn a predictor for label $Y$ that depends only on its causal parents. However, many real-world problems are "anti-causal" in the sense that $Y$ is a cause of the covariates $X$ -- …
Discovering causal models from observational and interventional data is an important first step preceding what-if analysis or counterfactual reasoning. As has been shown before, the direction of pairwise causal relations can, under certain conditions, be inferred from observational data via standard gradient-boosted classifiers (GBC) using carefully engineered statistical features. In this paper we apply deep convolutional neural networks (CNNs) to this problem by plotting attribute pairs as 2-D scatter plots that are fed to the CNN as images. We evaluate our approach on the 'Cause- Effect Pai…
We propose a method for learning linear models whose predictive performance is robust to causal interventions on unobserved variables, when noisy proxies of those variables are available. Our approach takes the form of a regularization term that trades off between in-distribution performance and robustness to interventions. Under the assumption of a linear structural causal model, we show that a single proxy can be used to create estimators that are prediction optimal under interventions of bounded strength. This strength depends on the magnitude of the measurement noise in the proxy, which is…
Cambridge Research Laboratory（剑桥研究实验室）；Toshiba Europe Limited（东芝欧洲有限公司）；University of Cambridge（剑桥大学）
In this paper we present a world model, which learns causal features using the invariance principle. In particular, we use contrastive unsupervised learning to learn the invariant causal features, which enforces invariance across augmentations of irrelevant parts or styles of the observation. The world-model-based reinforcement learning methods independently optimize representation learning and the policy. Thus naive contrastive loss implementation collapses due to a lack of supervisory signals to the representation learning module. We propose an intervention invariant auxiliary task to mitiga…
Xiamen University（厦门大学）；Fudan University（复旦大学）；Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳））；Fujian University of Technology（福建理工大学）
In human-computer interaction, Speech Emotion Recognition (SER) plays an essential role in understanding the user's intent and improving the interactive experience. While similar sentimental speeches own diverse speaker characteristics but share common antecedents and consequences, an essential challenge for SER is how to produce robust and discriminative representations through causality between speech emotions. In this paper, we propose a Gated Multi-scale Temporal Convolutional Network (GM-TCNet) to construct a novel emotional causality representation learning component with a multi-scale r…
GfK SE（GfK公司）；AlgoBalance UG (limited liability)（AlgoBalance有限责任公司）
Inferring the causal direction and causal effect between two discrete random variables X and Y from a finite sample is often a crucial problem and a challenging task. However, if we have access to observational and interventional data, it is possible to solve that task. If X is causing Y, then it does not matter if we observe an effect in Y by observing changes in X or by intervening actively on X. This invariance principle creates a link between observational and interventional distributions in a higher dimensional probability space. We embed distributions that originate from samples of X and…
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.
Causal Graph Learning via Distributional Invariance of Cause-Effect Relationship
The University of Tokyo, Japan（东京大学）；Institute for AI Innovation and Societal Impact (AI4LIFE)（人工智能创新与社会影响研究所）；Hanoi University of Science and Technology（河内科学技术大学）；National Institute of Advanced Industrial Science and Technology (AIST)（国家先进工业科学与技术研究院）；School of Electrical Engineering and Computer Science, Voiland College of Engineering and Architecture, Washington State University, Pullman, Washington, US（电气工程与计算机科学学院，工程与建筑学院，华盛顿州立大学）；RIKEN（日本理化学研究所）
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Coordinated Science Laboratory, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校协调科学实验室）；Carnegie Mellon University（卡内基梅隆大学）
We study causal inference in a multi-environment setting, in which the functional relations for producing the variables from their direct causes remain the same across environments, while the distribution of exogenous noises may vary. We introduce the idea of using the invariance of the functional relations of the variables to their causes across a set of environments. We define a notion of completeness for a causal inference algorithm in this setting and prove the existence of such algorithm by proposing the baseline algorithm. Additionally, we present an alternate algorithm that has signific…
Google Research（谷歌研究院）；University of Chicago（芝加哥大学）
Informally, a 'spurious correlation' is the dependence of a model on some aspect of the input data that an analyst thinks shouldn't matter. In machine learning, these have a know-it-when-you-see-it character; e.g., changing the gender of a sentence's subject changes a sentiment predictor's output. To check for spurious correlations, we can 'stress test' models by perturbing irrelevant parts of input data and seeing if model predictions change. In this paper, we study stress testing using the tools of causal inference. We introduce counterfactual invariance as a formalization of the requirement…
Contextual bandit and reinforcement learning algorithms have been successfully used in various interactive learning systems such as online advertising, recommender systems, and dynamic pricing. However, they have yet to be widely adopted in high-stakes application domains, such as healthcare. One reason may be that existing approaches assume that the underlying mechanisms are static in the sense that they do not change over different environments. In many real-world systems, however, the mechanisms are subject to shifts across environments which may invalidate the static environment assumption…
University of Hong Kong（香港大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Hong Kong University of Science and Technology（香港科技大学）
Domain generalization aims to learn knowledge invariant across different distributions while semantically meaningful for downstream tasks from multiple source domains, to improve the model's generalization ability on unseen target domains. The fundamental objective is to understand the underlying "invariance" behind these observational distributions and such invariance has been shown to have a close connection to causality. While many existing approaches make use of the property that causal features are invariant across domains, we consider the causal invariance of the average causal effect of…
A Causal Convolutional Low-rank Representation Model for Imputation of Water Quality Data
College of Computer and Information Science（计算机与信息科学学院）；Southwest University（西南大学）；School of Environment and Ecology（环境与生态学院）；Chongqing University（重庆大学）；Chongqing Eco-Environment Monitoring Center（重庆生态环境监测中心）
Carnegie Mellon University（卡内基梅隆大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Performance of neural networks can be significantly improved by encoding known invariance for particular tasks. Many image classification tasks, such as those related to cellular imaging, exhibit invariance to rotation. We present a novel scheme using the magnitude response of the 2D-discrete-Fourier transform (2D-DFT) to encode rotational invariance in neural networks, along with a new, efficient convolutional scheme for encoding rotational equivariance throughout convolutional layers. We implemented this scheme for several image classification tasks and demonstrated improved performance, in …
Army Research Laboratory（陆军研究实验室）；School of Computing and Augmented Intelligence, Arizona State University（亚利桑那州立大学计算与增强智能学院）
Machine learning models rely on various assumptions to attain high accuracy. One of the preliminary assumptions of these models is the independent and identical distribution, which suggests that the train and test data are sampled from the same distribution. However, this assumption seldom holds in the real world due to distribution shifts. As a result models that rely on this assumption exhibit poor generalization capabilities. Over the recent years, dedicated efforts have been made to improve the generalization capabilities of these models collectively known as -- \textit{domain generalizati…
Although Convolutional Neural Networks (CNNs) are widely used, their translation invariance (ability to deal with translated inputs) is still subject to some controversy. We explore this question using translation-sensitivity maps to quantify how sensitive a standard CNN is to a translated input. We propose the use of Cosine Similarity as sensitivity metric over Euclidean Distance, and discuss the importance of restricting the dimensionality of either of these metrics when comparing architectures. Our main focus is to investigate the effect of different architectural components of a standard C…
Causal Invariance Learning via Efficient Nonconvex Optimization
Department of Statistics, Rutgers University（罗格斯大学统计系）；Seminar for Statistics, ETH Zürich（苏黎世联邦理工学院统计研究所）；Center for Data Science, Zhejiang University（浙江大学数据科学中心）
Carnegie Mellon University（卡内基梅隆大学）；Microsoft Research（微软研究院）；Southwest Jiaotong University（西南交通大学）；University of Electronic Science and Technology of China（电子科技大学）
Previous work generally believes that improving the spatial invariance of convolutional networks is the key to object counting. However, after verifying several mainstream counting networks, we surprisingly found too strict pixel-level spatial invariance would cause overfit noise in the density map generation. In this paper, we try to use locally connected Gaussian kernels to replace the original convolution filter to estimate the spatial position in the density map. The purpose of this is to allow the feature extraction process to potentially stimulate the density map generation process to ov…
Causal Convolutional Neural Networks as Finite Impulse Response Filters
Future Resilient Systems, Singapore ETH Centre（新加坡未来韧性系统，新加坡ETH中心）；Department of Industrial Systems Engineering and Management（工业系统工程与管理系）；ETHZ；Department of Civil, Environmental and Geomatic Engineering（土木、环境与测绘工程系）
The success of deep convolutional architectures is often attributed in part to their ability to learn multiscale and invariant representations of natural signals. However, a precise study of these properties and how they affect learning guarantees is still missing. In this paper, we consider deep convolutional representations of signals; we study their invariance to translations and to more general groups of transformations, their stability to the action of diffeomorphisms, and their ability to preserve signal information. This analysis is carried by introducing a multilayer kernel based on co…
Recent studies have put into question the commonly assumed shift invariance property of convolutional networks, showing that small shifts in the input can affect the output predictions substantially. In this paper, we analyze the benefits of addressing lack of shift invariance in CNN-based sound event classification. Specifically, we evaluate two pooling methods to improve shift invariance in CNNs, based on low-pass filtering and adaptive sampling of incoming feature maps. These methods are implemented via small architectural modifications inserted into the pooling layers of CNNs. We evaluate …
In this paper we challenge the common assumption that convolutional layers in modern CNNs are translation invariant. We show that CNNs can and will exploit the absolute spatial location by learning filters that respond exclusively to particular absolute locations by exploiting image boundary effects. Because modern CNNs filters have a huge receptive field, these boundary effects operate even far from the image boundary, allowing the network to exploit absolute spatial location all over the image. We give a simple solution to remove spatial location encoding which improves translation invarianc…
How Useful is Causal Invariance for Domain Adaptation in Finite-Sample Settings?
Department of Computer Science, ETH Zurich（苏黎世联邦理工学院计算机科学系）；Causal Artificial Intelligence Lab, Columbia University（哥伦比亚大学因果人工智能实验室）；Department of Statistics, Columbia University（哥伦比亚大学统计系）
The Chinese University of Hong Kong（香港中文大学）；Hong Kong Baptist University（香港浸会大学）；Tencent AI Lab（腾讯人工智能实验室）；The University of Sydney（悉尼大学）
Despite recent success in using the invariance principle for out-of-distribution (OOD) generalization on Euclidean data (e.g., images), studies on graph data are still limited. Different from images, the complex nature of graphs poses unique challenges to adopting the invariance principle. In particular, distribution shifts on graphs can appear in a variety of forms such as attributes and structures, making it difficult to identify the invariance. Moreover, domain or environment partitions, which are often required by OOD methods on Euclidean data, could be highly expensive to obtain for graph…
University of Science and Technology of China（中国科学技术大学）；University of Technology Sydney（悉尼科技大学）
Convolutional Neural Networks (CNNs) have demonstrated state-of-the-art performance on many visual recognition tasks. However, the combination of convolution and pooling operations only shows invariance to small local location changes in meaningful objects in input. Sometimes, such networks are trained using data augmentation to encode this invariance into the parameters, which restricts the capacity of the model to learn the content of these objects. A more efficient use of the parameter budget is to encode rotation or translation invariance into the model architecture, which relieves the mod…
Convolutional neural networks are among the most successful architectures in deep learning with this success at least partially attributable to the efficacy of spatial invariance as an inductive bias. Locally connected layers, which differ from convolutional layers only in their lack of spatial invariance, usually perform poorly in practice. However, these observations still leave open the possibility that some degree of relaxation of spatial invariance may yield a better inductive bias than either convolution or local connectivity. To test this hypothesis, we design a method to relax the spat…
Learning invariant representations from images is one of the hardest challenges facing computer vision. Spatial pooling is widely used to create invariance to spatial shifting, but it is restricted to convolutional models. In this paper, we propose a novel pooling method that can learn soft clustering of features from image sequences. It is trained to improve the temporal coherence of features, while keeping the information loss at minimum. Our method does not use spatial information, so it can be used with non-convolutional models too. Experiments on images extracted from natural videos showe…
University of Lübeck（吕贝克大学）；Robert Bosch GmbH（罗伯特·博世有限公司）
In this contribution, we show how to incorporate prior knowledge to a deep neural network architecture in a principled manner. We enforce feature space invariances using a novel layer based on invariant integration. This allows us to construct a complete feature space invariant to finite transformation groups. We apply our proposed layer to explicitly insert invariance properties for vision-related classification tasks, demonstrate our approach for the case of rotation invariance and report state-of-the-art performance on the Rotated-MNIST dataset. Our method is especially beneficial when trai…
