Detecting switching and intermittent causalities in time series

Incorporation of causality structures to complex network analysis of time-varying behaviour of multivariate time series

This paper presents a new methodology for characterising the evolving behaviour of the time-varying causality between multivariate time series, from the perspective of change in the structure of the causality pattern. We propose that such evolutionary behaviour should be tracked by means of a complex network whose nodes are causality patterns and edges are transitions between those patterns of causality. In our new methodology each edge has a weight that includes the frequency of the given transition and two metrics relating to the gross and net structural change in causality pattern, which we call [Formula: see text] and [Formula: see text]. To characterise aspects of the behaviour within this network, five approaches are presented and motivated. To act as a demonstration of this methodology an application of sample data from the international oil market is presented. This example illustrates how our new methodology is able to extract information about evolving causality behaviour. For example, it reveals non-random time-varying behaviour that favours transitions resulting in predominantly similar causality patterns, and it discovers clustering of similar causality patterns and some transitional behaviour between these clusters. The example illustrates how our new methodology supports the inference that the evolution of causality in the system is related to the addition or removal of a few causality links, primarily keeping a similar causality pattern, and that the evolution is not related to some other measure such as the overall number of causality links.

An Early Stage Researcher's Primer on Systems Medicine Terminology

Background: Systems Medicine is a novel approach to medicine, that is, an interdisciplinary field that considers the human body as a system, composed of multiple parts and of complex relationships at multiple levels, and further integrated into an environment. Exploring Systems Medicine implies understanding and combining concepts coming from diametral different fields, including medicine, biology, statistics, modeling and simulation, and data science. Such heterogeneity leads to semantic issues, which may slow down implementation and fruitful interaction between these highly diverse fields. Methods: In this review, we collect and explain more than100 terms related to Systems Medicine. These include both modeling and data science terms and basic systems medicine terms, along with some synthetic definitions, examples of applications, and lists of relevant references. Results: This glossary aims at being a first aid kit for the Systems Medicine researcher facing an unfamiliar term, where he/she can get a first understanding of them, and, more importantly, examples and references for digging into the topic.

Reconstructing regime-dependent causal relationships from observational time series

Inferring causal relations from observational time series data is a key problem across science and engineering whenever experimental interventions are infeasible or unethical. Increasing data availability over the past few decades has spurred the development of a plethora of causal discovery methods, each addressing particular challenges of this difficult task. In this paper, we focus on an important challenge that is at the core of time series causal discovery: regime-dependent causal relations. Often dynamical systems feature transitions depending on some, often persistent, unobserved background regime, and different regimes may exhibit different causal relations. Here, we assume a persistent and discrete regime variable leading to a finite number of regimes within which we may assume stationary causal relations. To detect regime-dependent causal relations, we combine the conditional independence-based PCMCI method [based on a condition-selection step (PC) followed by the momentary conditional independence (MCI) test] with a regime learning optimization approach. PCMCI allows for causal discovery from high-dimensional and highly correlated time series. Our method, Regime-PCMCI, is evaluated on a number of numerical experiments demonstrating that it can distinguish regimes with different causal directions, time lags, and sign of causal links, as well as changes in the variables' autocorrelation. Furthermore, Regime-PCMCI is employed to observations of El Niño Southern Oscillation and Indian rainfall, demonstrating skill also in real-world datasets.

Uncertainty in Functional Network Representations of Brain Activity of Alcoholic Patients

In spite of the large attention received by brain activity analyses through functional networks, the effects of uncertainty on such representations have mostly been neglected. We here elaborate the hypothesis that such uncertainty is not just a nuisance, but that on the contrary is condition-dependent. We test this hypothesis by analysing a large set of EEG brain recordings corresponding to control subjects and patients suffering from alcoholism, through the reconstruction of the corresponding Maximum Spanning Trees (MSTs), the assessment of their topological differences, and the comparison of two frequentist and Bayesian reconstruction approaches. A machine learning model demonstrates that the Bayesian reconstruction encodes more information than the frequentist one, and that such additional information is related to the uncertainty of the topological structures. We finally show how the Bayesian approach is more effective in the validation of generative models, over and above the frequentist one, by proposing and disproving two models based on additive noise.

Inferring causal relationship in coordinated flight of pigeon flocks

Collective phenomenon of natural animal groups will be attributed to individual intelligence and interagent interactions, where a long-standing challenge is to reveal the causal relationship among individuals. In this study, we propose a causal inference method based on information theory. More precisely, we calculate mutual information by using a data mining algorithm named "k-nearest neighbor" and subsequently induce the transfer entropy to obtain the causality entropy quantifying the causal dependence of one individual on another subject to a condition set consisting of other neighboring ones. Accordingly, we analyze the high-resolution GPS data of three pigeon flocks to extract the hidden interaction mechanism governing the coordinated free flight. The comparison of spatial distribution between causal neighbors and all other remainders validates that no bias exists for the causal inference. We identify the causal relationships to establish the interaction network and observe that the revealed causal relationship follows a local interaction mode. Interestingly, the individuals closer to the mass center and the average velocity direction are more influential than others.

Detecting switching leadership in collective motion

Detecting causal relationships in complex systems from the time series of the individual units is a pressing area of research that has attracted the interest of a broad community. As an open area of study, this entails the development of methodologies to unravel causal relationships that evolve over time, such as switching of leader-follower roles in animal groups. Here, we augment the information theoretic measure of transfer entropy to establish a fitness function suitable for optimal partitioning of time series data to robustly detect leadership switches in collective behavior. The fitness function computes the information outflow from any agent in the group and rewards large sample sizes while normalizing with respect to available information. Our results indicate that for information-rich interactions, leadership switches within a group can be detected over relatively short time durations, with more than 90% accuracy. On a real soccer dataset, instances of leadership counted using the proposed approach are interestingly correlated with ball possession.

Detecting intermittent switching leadership in coupled dynamical systems

Leader-follower relationships are commonly hypothesized as a fundamental mechanism underlying collective behaviour in many biological and physical systems. Understanding the emergence of such behaviour is relevant in science and engineering to control the dynamics of complex systems toward a desired state. In prior works, due in part to the limitations of existing methods for dissecting intermittent causal relationships, leadership is assumed to be consistent in time and space. This assumption has been contradicted by recent progress in the study of animal behaviour. In this work, we leverage information theory and time series analysis to propose a novel and simple method for dissecting changes in causal influence. Our approach computes the cumulative influence function of a given individual on the rest of the group in consecutive time intervals and identify change in the monotonicity of the function as a change in its leadership status. We demonstrate the effectiveness of our approach to dissect potential changes in leadership on self-propelled particles where the emergence of leader-follower relationship can be controlled and on tandem flights of birds recorded in their natural environment. Our method is expected to provide a novel methodological tool to further our understanding of collective behaviour.

Reconstructing complex network for characterizing the time-varying causality evolution behavior of multivariate time series

In order to explore the characteristics of the evolution behavior of the time-varying relationships between multivariate time series, this paper proposes an algorithm to transfer this evolution process to a complex network. We take the causality patterns as nodes and the succeeding sequence relations between patterns as edges. We used four time series as sample data. The results of the analysis reveal some statistical evidences that the causalities between time series is in a dynamic process. It implicates that stationary long-term causalities are not suitable for some special situations. Some short-term causalities that our model recognized can be referenced to the dynamic adjustment of the decisions. The results also show that weighted degree of the nodes obeys power law distribution. This implies that a few types of causality patterns play a major role in the process of the transition and that international crude oil market is statistically significantly not random. The clustering effect appears in the transition process and different clusters have different transition characteristics which provide probability information for predicting the evolution of the causality. The approach presents a potential to analyze multivariate time series and provides important information for investors and decision makers.