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The discovery of causal mechanisms from time series data is a key problem in fields working with complex systems. Most identifiability results and learning algorithms assume the underlying dynamics to be discrete in time. Comparatively few, in contrast, explicitly define causal associations in infinitesimal intervals of time, independently of the scale of observation and of the regularity of sampling. In this paper, we consider causal discovery in continuous-time for the study of dynamical systems. We prove that for vector fields parameterized in a large class of neural networks, adaptive regularization schemes consistently recover causal graphs in systems of ordinary differential equations (ODEs). Using this insight, we propose a causal discovery algorithm based on penalized Neural ODEs that we show to be applicable to the general setting of irregularly-sampled multivariate time series and to strongly outperform the state of the art.
Counterfactual estimation using synthetic controls is one of the most successful recent methodological developments in causal inference. Despite its popularity, the current description only considers time series aligned across units and synthetic con
Going beyond correlations, the understanding and identification of causal relationships in observational time series, an important subfield of Causal Discovery, poses a major challenge. The lack of access to a well-defined ground truth for real-world
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
Despite having been studied to a great extent, the task of conditional generation of sequences of frames, or videos, remains extremely challenging. It is a common belief that a key step towards solving this task resides in modelling accurately both s
Continuous-time event data are common in applications such as individual behavior data, financial transactions, and medical health records. Modeling such data can be very challenging, in particular for applications with many different types of events