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We propose an l1-regularized likelihood method for estimating the inverse covariance matrix in the high-dimensional multivariate normal model in presence of missing data. Our method is based on the assumption that the data are missing at…

Methodology · Statistics 2012-02-28 Nicolas Städler , Peter Bühlmann

Counterfactual learning has become promising for understanding and modeling causality in complex and dynamic systems. This paper presents a novel method for counterfactual learning in the context of multivariate time series analysis and…

Machine Learning · Computer Science 2026-03-03 Gianlucca Zuin , Adriano Veloso

When domain knowledge is limited and experimentation is restricted by ethical, financial, or time constraints, practitioners turn to observational causal discovery methods to recover the causal structure, exploiting the statistical…

Many real-world decision-making tasks require learning causal relationships between a set of variables. Traditional causal discovery methods, however, require that all variables are observed, which is often not feasible in practical…

Methodology · Statistics 2023-06-27 Raj Agrawal , Chandler Squires , Neha Prasad , Caroline Uhler

Many causal systems such as biological processes in cells can only be observed indirectly via measurements, such as gene expression. Causal representation learning -- the task of correctly mapping low-level observations to latent causal…

Machine Learning · Computer Science 2025-10-31 Elliot Layne , Jason Hartford , Sébastien Lachapelle , Mathieu Blanchette , Dhanya Sridhar

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…

Machine Learning · Computer Science 2021-02-11 Yunfei Chu , Xiaowei Wang , Jianxin Ma , Kunyang Jia , Jingren Zhou , Hongxia Yang

Time series data is a collection of chronological observations which is generated by several domains such as medical and financial fields. Over the years, different tasks such as classification, forecasting, and clustering have been…

Machine Learning · Computer Science 2021-02-12 Raha Moraffah , Paras Sheth , Mansooreh Karami , Anchit Bhattacharya , Qianru Wang , Anique Tahir , Adrienne Raglin , Huan Liu

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…

Machine Learning · Computer Science 2020-11-23 Chainarong Amornbunchornvej , Elena Zheleva , Tanya Y. Berger-Wolf

We propose a novel machine learning approach for inferring causal variables of a target variable from observations. Our focus is on directly inferring a set of causal factors without requiring full causal graph reconstruction, which is…

Machine Learning · Computer Science 2025-10-01 Jang-Hyun Kim , Claudia Skok Gibbs , Sangdoo Yun , Hyun Oh Song , Kyunghyun Cho

Time series autoregression (AR) is a classical tool for modeling auto-correlations and periodic structures in real-world systems. We revisit this model from an interpretable machine learning perspective by introducing sparse autoregression…

Machine Learning · Computer Science 2025-07-15 Xinyu Chen , Vassilis Digalakis , Lijun Ding , Dingyi Zhuang , Jinhua Zhao

Bayesian forecasting is developed in multivariate time series analysis for causal inference. Causal evaluation of sequentially observed time series data from control and treated units focuses on the impacts of interventions using…

Methodology · Statistics 2024-06-21 Graham Tierney , Christoph Hellmayr , Greg Barkimer , Kevin Li , Mike West

Causal discovery from data affected by latent confounders is an important and difficult challenge. Causal functional model-based approaches have not been used to present variables whose relationships are affected by latent confounders,…

Machine Learning · Computer Science 2020-11-05 Takashi Nicholas Maeda , Shohei Shimizu

Unmeasured confounding presents a significant challenge in causal inference from observational studies. Classical approaches often rely on collecting proxy variables, such as instrumental variables. However, in applications where the…

Methodology · Statistics 2025-01-16 Xiaochuan Shi , Dehan Kong , Linbo Wang

Causal discovery in time series is increasingly performed using nonlinear machine-learning models, yet the resulting causal relationships are almost always summarized by scalar edge scores. We argue that this practice obscures the true…

Machine Learning · Computer Science 2026-05-29 Valentina V. Kuskova , Dmitry Zaytsev , Michael Coppedge

We investigate the problem of inferring the causal predictors of a response $Y$ from a set of $d$ explanatory variables $(X^1,\dots,X^d)$. Classical ordinary least squares regression includes all predictors that reduce the variance of $Y$.…

Statistics Theory · Mathematics 2018-05-29 Niklas Pfister , Peter Bühlmann , Jonas Peters

Causal inference is a fundamental research topic for discovering the cause-effect relationships in many disciplines. However, not all algorithms are equally well-suited for a given dataset. For instance, some approaches may only be able to…

Machine Learning · Computer Science 2024-03-11 Zhipeng Ma , Marco Kemmerling , Daniel Buschmann , Chrismarie Enslin , Daniel Lütticke , Robert H. Schmitt

We prove that a time series satisfying a (linear) multivariate autoregressive moving average (VARMA) model satisfies the same model assumption in the reversed time direction, too, if all innovations are normally distributed. This…

Statistics Theory · Mathematics 2016-03-03 Stefan Bauer , Bernhard Schölkopf , Jonas Peters

Identifying the topology underlying a set of time series is useful for tasks such as prediction, denoising, and data completion. Vector autoregressive (VAR) model-based topologies capture dependencies among time series and are often…

Signal Processing · Electrical Eng. & Systems 2023-10-30 Bakht Zaman , Luis Miguel Lopez Ramos , Baltasar Beferull-Lozano

We develop new methods to integrate experimental and observational data in causal inference. While randomized controlled trials offer strong internal validity, they are often costly and therefore limited in sample size. Observational data,…

Econometrics · Economics 2025-11-04 Xuelin Yang , Licong Lin , Susan Athey , Michael I. Jordan , Guido W. Imbens

Time series data are found in many areas of healthcare such as medical time series, electronic health records (EHR), measurements of vitals, and wearable devices. Causal discovery, which involves estimating causal relationships from…

Machine Learning · Computer Science 2023-10-18 Muhammad Hasan Ferdous , Uzma Hasan , Md Osman Gani