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Many real-world processes are trajectories that may be regarded as continuous-time "functional data". Examples include patients' biomarker concentrations, environmental pollutant levels, and prices of stocks. Corresponding advances in data…

Statistics Theory · Mathematics 2022-11-30 Jinghao Sun , Forrest W. Crawford

Causal discovery problems use a set of observations to deduce causality between variables in the real world, typically to answer questions about biological or physical systems. These observations are often recorded at regular time…

Signal Processing · Electrical Eng. & Systems 2026-02-24 Kurt Butler , Damian Machlanski , Panagiotis Dimitrakopoulos , Sotirios A. Tsaftaris

Modeling hierarchical latent dynamics behind time series data is critical for capturing temporal dependencies across multiple levels of abstraction in real-world tasks. However, existing temporal causal representation learning methods fail…

Machine Learning · Computer Science 2025-10-22 Zijian Li , Minghao Fu , Junxian Huang , Yifan Shen , Ruichu Cai , Yuewen Sun , Guangyi Chen , Kun Zhang

In science, macro level descriptions of the causal interactions within complex, dynamical systems are typically deemed convenient, but ultimately reducible to a complete causal account of the underlying micro constituents. Yet, such a…

Neurons and Cognition · Quantitative Biology 2020-04-02 Larissa Albantakis , Francesco Massari , Maggie Beheler-Amass , Giulio Tononi

Time series data are often affected by various forms of corruption, such as missing values, noise, and outliers, which pose significant challenges for tasks such as forecasting and anomaly detection. To address these issues, inverse…

Machine Learning · Computer Science 2025-10-21 Keivan Faghih Niresi , Zepeng Zhang , Olga Fink

We design a new nonparametric method that allows one to estimate the matrix of integrated kernels of a multivariate Hawkes process. This matrix not only encodes the mutual influences of each nodes of the process, but also disentangles the…

Machine Learning · Statistics 2017-05-31 Massil Achab , Emmanuel Bacry , Stéphane Gaïffas , Iacopo Mastromatteo , Jean-Francois Muzy

Multivariate time series (MTS) classification is foundational to pervasive computing and financial analysis, yet existing multi-scale paradigms are often constrained by suboptimal representation fidelity. We identify two critical…

Machine Learning · Computer Science 2026-05-22 Fan Zhang , Yating Cui , Hua Wang

Granger causal inference is a contentious but widespread method used in fields ranging from economics to neuroscience. The original definition addresses the notion of causality in time series by establishing functional dependence…

Methodology · Statistics 2023-09-19 Noah D. Gade , Jordan Rodu

Several interpretability methods for convolutional network-based classifiers exist. Most of these methods focus on extracting saliency maps for a given sample, providing a local explanation that highlights the main regions for the…

Machine Learning · Computer Science 2025-06-17 Alejandro Kuratomi , Zed Lee , Guilherme Dinis Chaliane Junior , Tony Lindgren , Diego García Pérez

Causal discovery with time series data remains a challenging yet increasingly important task across many scientific domains. Convergent cross mapping (CCM) and related methods have been proposed to study time series that are generated by…

Machine Learning · Computer Science 2025-06-25 Kurt Butler , Daniel Waxman , Petar M. Djurić

It is commonplace to encounter heterogeneous or nonstationary data, of which the underlying generating process changes across domains or over time. Such a distribution shift feature presents both challenges and opportunities for causal…

Machine Learning · Computer Science 2020-06-26 Biwei Huang , Kun Zhang , Jiji Zhang , Joseph Ramsey , Ruben Sanchez-Romero , Clark Glymour , Bernhard Schölkopf

Learning the causes of time-series data is a fundamental task in many applications, spanning from finance to earth sciences or bio-medical applications. Common approaches for this task are based on vector auto-regression, and they do not…

Machine Learning · Computer Science 2025-09-30 Emmanouil Angelis , Francesco Quinzan , Ashkan Soleymani , Patrick Jaillet , Stefan Bauer

We are sometimes forced to use the Interrupted Time Series (ITS) design as an identification strategy for potential policy change, such as when we only have a single treated unit and no comparable controls. For example, with recent county-…

Methodology · Statistics 2020-02-17 Luke Miratrix

The growing availability and importance of time series data across various domains, including environmental science, epidemiology, and economics, has led to an increasing need for time-series causal discovery methods that can identify the…

Machine Learning · Computer Science 2024-04-03 Omar Faruque , Sahara Ali , Xue Zheng , Jianwu Wang

We present a new method for linear and nonlinear, lagged and contemporaneous constraint-based causal discovery from observational time series in the presence of latent confounders. We show that existing causal discovery methods such as FCI…

Methodology · Statistics 2021-02-03 Andreas Gerhardus , Jakob Runge

While dynamic graph neural networks have shown promise in various applications, explaining their predictions on continuous-time dynamic graphs (CTDGs) is difficult. This paper investigates a new research task: self-interpretable GNNs for…

Machine Learning · Computer Science 2024-05-30 Lanting Fang , Yulian Yang , Kai Wang , Shanshan Feng , Kaiyu Feng , Jie Gui , Shuliang Wang , Yew-Soon Ong

Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic,…

Machine Learning · Computer Science 2025-10-13 Benjamin Herdeanu , Juan Nathaniel , Carla Roesch , Jatan Buch , Gregor Ramien , Johannes Haux , Pierre Gentine

Inference of causality in time series has been principally based on the prediction paradigm. Nonetheless, the predictive causality approach may overlook the simultaneous and reciprocal nature of causal interactions observed in real world…

Data Analysis, Statistics and Probability · Physics 2018-10-24 Albert C. Yang , Norden E. Huang , Chung-Kang Peng

We present a sound and complete algorithm for recovering causal graphs from observed, non-interventional data, in the possible presence of latent confounders and selection bias. We rely on the causal Markov and faithfulness assumptions and…

Artificial Intelligence · Computer Science 2020-12-25 Raanan Y. Rohekar , Yaniv Gurwicz , Shami Nisimov , Gal Novik

Coupled dynamical systems are frequently observed in nature, but often not well understood in terms of their causal structure without additional domain knowledge about the system. Especially when analyzing observational time series data of…

Machine Learning · Statistics 2021-10-26 Will Glad , Thomas Woolf