Understanding causal relations in dynamic systems is essential in epidemiology. While causal inference methods have been extensively studied, they often rely on fully specified causal graphs, which may not always be available in complex dynamic systems. Partially specified causal graphs, and in particular summary causal graphs (SCGs), provide a simplified representation of causal relations between time series when working spacio-temporal data, omitting temporal information and focusing on causal structures between clusters of of temporal variables. Unlike fully specified causal graphs, SCGs can contain cycles, which complicate their analysis and interpretation. In addition, their cluster-based nature introduces new challenges concerning the types of queries of interest: macro queries, which involve relationships between clusters represented as vertices in the graph, and micro queries, which pertain to relationships between variables that are not directly visible through the vertices of the graph. In this paper, we first clearly distinguish between macro conditional independencies and micro conditional independencies and between macro total effects and micro total effects. Then, we demonstrate the soundness and completeness of the d-separation to identify macro conditional independencies in SCGs. Furthermore, we establish that the do-calculus is sound and complete for identifying macro total effects in SCGs. Finally, we give a graphical characterization for the non-identifiability of macro total effects in SCGs.

The do-calculus is a sound and complete tool for identifying causal effects in acyclic directed mixed graphs (ADMGs) induced by structural causal models (SCMs). However, in many real-world applications, especially in high-dimensional settings, constructing a fully specified ADMG is often infeasible. This limitation has led to growing interest in partially specified causal representations, particularly through cluster-directed mixed graphs (C-DMGs), which group variables into clusters and offer a more abstract yet practical view of causal dependencies. While these representations can include cycles, recent work has shown that the do-calculus remains sound and complete for identifying macro-level causal effects in C-DMGs over ADMGs under the assumption that all clusters sizes are greater than 1. Nevertheless, real-world systems often exhibit cyclic causal dynamics at the structural level. To account for this, input-output structural causal models (ioSCMs) have been introduced as a generalization of SCMs that allow for cycles. ioSCMs induce another type of graph structure known as a directed mixed graph (DMG). Analogous to the ADMG setting, one can define C-DMGs over DMGs as high-level representations of causal relations among clusters of variables. In this paper, we prove that, unlike in the ADMG setting, the do-calculus is unconditionally sound and complete for identifying macro causal effects in C-DMGs over DMGs. Furthermore, we show that the graphical criteria for non-identifiability of macro causal effects previously established C-DMGs over ADMGs naturally extends to a subset of C-DMGs over DMGs.

Dynamic structural causal models (SCMs) are a powerful framework for reasoning in dynamic systems about direct effects which measure how a change in one variable affects another variable while holding all other variables constant. The causal relations in a dynamic structural causal model can be qualitatively represented with an acyclic full-time causal graph. Assuming linearity and no hidden confounding and given the full-time causal graph, the direct causal effect is always identifiable. However, in many application such a graph is not available for various reasons but nevertheless experts have access to the summary causal graph of the full-time causal graph which represents causal relations between time series while omitting temporal information and allowing cycles. This paper presents a complete identifiability result which characterizes all cases for which the direct effect is graphically identifiable from a summary causal graph and gives two sound finite adjustment sets that can be used to estimate the direct effect whenever it is identifiable.

This paper introduces a new structural causal model tailored for representing threshold-based IT systems and presents a new algorithm designed to rapidly detect root causes of anomalies in such systems. When root causes are not causally related, the method is proven to be correct; while an extension is proposed based on the intervention of an agent to relax this assumption. Our algorithm and its agent-based extension leverage causal discovery from offline data and engage in subgraph traversal when encountering new anomalies in online data. Our extensive experiments demonstrate the superior performance of our methods, even when applied to data generated from alternative structural causal models or real IT monitoring data.

We study the problem of identifiability of the total effect of an intervention from observational time series only given an abstraction of the causal graph of the system. Specifically, we consider two types of abstractions: the extended summary causal graph which conflates all lagged causal relations but distinguishes between lagged and instantaneous relations; and the summary causal graph which does not give any indication about the lag between causal relations. We show that the total effect is always identifiable in extended summary causal graphs and we provide necessary and sufficient graphical conditions for identifiability in summary causal graphs. Furthermore, we provide adjustment sets allowing to estimate the total effect whenever it is identifiable.

This paper presents an approach for identifying the root causes of collective anomalies given observational time series and an acyclic summary causal graph which depicts an abstraction of causal relations present in a dynamic system at its normal regime. The paper first shows how the problem of root cause identification can be divided into many independent subproblems by grouping related anomalies using d-separation. Further, it shows how, under this setting, some root causes can be found directly from the graph and from the time of appearance of anomalies. Finally, it shows, how the rest of the root causes can be found by comparing direct effects in the normal and in the anomalous regime. To this end, an adjustment set for identifying direct effects is introduced. Extensive experiments conducted on both simulated and real-world datasets demonstrate the effectiveness of the proposed method.

We introduce in this survey the major concepts, models, and algorithms proposed so far to infer causal relations from observational time series, a task usually referred to as causal discovery in time series. To do so, after a description of the underlying concepts and modelling assumptions, we present different methods according to the family of approaches they belong to: Granger causality, constraint-based approaches, noise-based approaches, score-based approaches, logic-based approaches, topology-based approaches, and difference-based approaches. We then evaluate several representative methods to illustrate the behaviour of different families of approaches. This illustration is conducted on both artificial and real datasets, with different characteristics. The main conclusions one can draw from this survey is that causal discovery in times series is an active research field in which new methods (in every family of approaches) are regularly proposed, and that no family or method stands out in all situations. Indeed, they all rely on assumptions that may or may not be appropriate for a particular dataset.

This study addresses the problem of learning an extended summary causal graph from time series. The algorithms we propose fit within the well-known constraint-based framework for causal discovery and make use of information-theoretic measures to determine (in)dependencies between time series. We first introduce generalizations of the causation entropy measure to any lagged or instantaneous relations, prior to using this measure to construct extended summary causal graphs by adapting two well-known algorithms, namely PC and FCI. The behaviour of our method is illustrated through several experiments.

We introduce in this survey the major concepts, models, and algorithms proposed so far to infer causal relations from observational time series, a task usually referred to as causal discovery in time series. To do so, after a description of the underlying concepts and modelling assumptions, we present different methods according to the family of approaches they belong to: Granger causality, constraint-based approaches, noise-based approaches, score-based approaches, logic-based approaches, topology-based approaches, and difference-based approaches. We then evaluate several representative methods to illustrate the behaviour of different families of approaches. This illustration is conducted on both artificial and real datasets, with different characteristics. The main conclusions one can draw from this survey is that causal discovery in times series is an active research field in which new methods (in every family of approaches) are regularly proposed, and that no family or method stands out in all situations. Indeed, they all rely on assumptions that may or may not be appropriate for a particular dataset.