Normalized Multivariate Time Series Causality Analysis and Causal Graph Reconstruction

Altered default mode network causal connectivity patterns in autism spectrum disorder revealed by Liang information flow analysis

Autism spectrum disorder (ASD) is a pervasive developmental disorder with severe cognitive impairment in social communication and interaction. Previous studies have reported that abnormal functional connectivity patterns within the default mode network (DMN) were associated with social dysfunction in ASD. However, how the altered causal connectivity pattern within the DMN affects the social functioning in ASD remains largely unclear. Here, we introduced the Liang information flow method, widely applied to climate science and quantum mechanics, to uncover the brain causal network patterns in ASD. Compared with the healthy controls (HC), we observed that the interactions among the dorsal medial prefrontal cortex (dMPFC), ventral medial prefrontal cortex (vMPFC), hippocampal formation, and temporo-parietal junction showed more inter-regional causal connectivity differences in ASD. For the topological property analysis, we also found the clustering coefficient of DMN and the In-Out degree of anterior medial prefrontal cortex were significantly decreased in ASD. Furthermore, we found that the causal connectivity from dMPFC to vMPFC was correlated with the clinical symptoms of ASD. These altered causal connectivity patterns indicated that the DMN inter-regions information processing was perturbed in ASD. In particular, we found that the dMPFC acts as a causal source in the DMN in HC, whereas it plays a causal target in ASD. Overall, our findings indicated that the Liang information flow method could serve as an important way to explore the DMN causal connectivity patterns, and it also can provide novel insights into the nueromechanisms underlying DMN dysfunction in ASD.

The dynamic causality in sporadic bursts between CO2 emission allowance prices and clean energy index

This study examines the dynamic causality between the carbon emission market and the clean energy market, using an information flow-based, quantitative Liang causality analysis which is firmly grounded on physics and derived from first principles. The dynamic causal relationships between European Union Allowance (EUA) prices and clean energy index allow us to explore whether the causality in return or in variance from CO2 emission allowances to the clean energy index is time-varying. The results show that the causal relationships in return and in variance between EUA and Clean Energy Index (CEI) are drastically time-varying. For the causality in return, a significant unidirectional long-term and stable causality from CEI to EUA is identified after March 2020. For that in variance, a bidirectional causality is found after March 2020, but values after 2020 are opposite to those in return. It seems when fluctuations in the clean energy market are low, the clean energy market has a weak causal effect on the carbon emission market but when volatility in the clean energy market is increasing, causalities between the two markets are significantly strengthened. These results obtained through this rigorous causality analysis can serve as a reference for academics, market participants, and policymakers to understand the underlying links between EUA prices and clean energy index.

Quantum Liang Information Flow as Causation Quantifier

Liang information flow is widely used in classical systems and network theory for causality quantification and has been applied widely, for example, to finance, neuroscience, and climate studies. The key part of the theory is to freeze a node of a network to ascertain its causal influence on other nodes. Such a theory is yet to be applied to quantum network dynamics. Here, we generalize the Liang information flow to the quantum domain with respect to von Neumann entropy and exemplify its usage by applying it to a variety of small quantum networks.

Phase-based causality analysis with partial mutual information from mixed embedding

Instantaneous phases extracted from multivariate time series can retain information about the relationships between the underlying mechanisms that generate the series. Although phases have been widely used in the study of nondirectional coupling and connectivity, they have not found similar appeal in the study of causality. Herein, we present a new method for phase-based causality analysis, which combines ideas from the mixed embedding technique and the information-theoretic approach to causality in coupled oscillatory systems. We then use the introduced method to investigate causality in simulated datasets of bivariate, unidirectionally paired systems from combinations of Rössler, Lorenz, van der Pol, and Mackey-Glass equations. We observe that causality analysis using the phases can capture the true causal relation for coupling strength smaller than the analysis based on the amplitudes can capture. On the other hand, the causality estimation based on the phases tends to have larger variability, which is attributed more to the phase extraction process than the actual phase-based causality method. In addition, an application on real electroencephalographic data from an experiment on elicited human emotional states reinforces the usefulness of phases in causality identification.

Beyond randomness: Evaluating measures of information entropy in binary series

The enormous amount of currently available data demands efforts to extract meaningful information. For this purpose, different measurements are applied, including Shannon's entropy, permutation entropy, and the Lempel-Ziv complexity. These methods have been used in many applications, such as pattern recognition, series classification, and several other areas (e.g., physical, financial, and biomedical). Data in these applications are often presented in binary series with temporal correlations. Herein, we compare the measures of information entropy in binary series conveying short- and long-range temporal correlations characterized by the Hurst exponent H. Combining numerical and analytical approaches, we scrutinize different methods that were not efficient in detecting temporal correlations. To surpass this limitation, we propose a measure called the binary permutation index (BPI). We will demonstrate that BPI efficiently discriminates patterns embedded in the series, offering advantages over previous methods. Subsequently, we collect stock market time series and rain precipitation data as well as perform in vivo electrophysiological recordings in the hippocampus of an experimental animal model of temporal lobe epilepsy, in which the BPI application in both public open source and experimental data is demonstrated. An index is proposed to evaluate information entropy, allowing the ability to discriminate randomness and extract meaningful information in binary time series.

The Causal Interaction between Complex Subsystems

Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the bulk information flow between two complex subsystems of a large-dimensional parental system. Analytical formulas have been obtained in a closed form. Under a Gaussian assumption, their maximum likelihood estimators have also been obtained. These formulas have been validated using different subsystems with preset relations, and they yield causalities just as expected. On the contrary, the commonly used proxies for the characterization of subsystems, such as averages and principal components, generally do not work correctly. This study can help diagnose the emergence of patterns in complex systems and is expected to have applications in many real world problems in different disciplines such as climate science, fluid dynamics, neuroscience, financial economics, etc.

El Niño Modoki can be mostly predicted more than 10 years ahead of time

The 2014-2015 "Monster"/"Super" El Niño failed to be predicted one year earlier due to the growing importance of a new type of El Niño, El Niño Modoki, which reportedly has much lower forecast skill with the classical models. In this study, we show that, so far as of today, this new El Niño actually can be mostly predicted at a lead time of more than 10 years. This is achieved through tracing the predictability source with an information flow-based causality analysis, which has been rigorously established from first principles during the past 16 years (e.g., Liang in Phys Rev E 94:052201, 2016). We show that the information flowing from the solar activity 45 years ago to the sea surface temperature results in a causal structure resembling the El Niño Modoki mode. Based on this, a multidimensional system is constructed out of the sunspot number series with time delays of 22-50 years. The first 25 principal components are then taken as the predictors to fulfill the prediction, which through causal AI based on the Liang-Kleeman information flow reproduces rather accurately the events thus far 12 years in advance.

Measuring the importance of individual units in producing the collective behavior of a complex network

A quantitative evaluation of the contribution of individual units in producing the collective behavior of a complex network can allow us to understand the potential damage to the structure integrity due to the failure of local nodes. Given a time series for each unit, a natural way to do this is to find the information flowing from the unit of concern to the rest of the network. In this study, we show that this flow can be rigorously derived in the setting of a continuous-time dynamical system. With a linear assumption, a maximum likelihood estimator can be obtained, allowing us to estimate it in an easy way. As expected, this "cumulative information flow" does not equal the sum of the information flows to other individual units, reflecting the collective phenomenon that a group is not the addition of individual members. For the purpose of demonstration and validation, we have examined a network made of Stuart-Landau oscillators. Depending on the topology, the computed information flow may differ. In some situations, the most crucial nodes for the network are not the hubs, i.e., nodes with high degrees; they may have low degrees and, if depressed or attacked, will cause the failure of the entire network. This study can help diagnose neural network problems, control epidemic diseases, trace city traffic bottlenecks, identify the potential cause of power grid failure (e.g., the 2003 great power outage that darkened much of North America), build robust computer networks, and so forth.

The Role of Instrumental Variables in Causal Inference Based on Independence of Cause and Mechanism

Causal inference methods based on conditional independence construct Markov equivalent graphs and cannot be applied to bivariate cases. The approaches based on independence of cause and mechanism state, on the contrary, that causal discovery can be inferred for two observations. In our contribution, we pose a challenge to reconcile these two research directions. We study the role of latent variables such as latent instrumental variables and hidden common causes in the causal graphical structures. We show that methods based on the independence of cause and mechanism indirectly contain traces of the existence of the hidden instrumental variables. We derive a novel algorithm to infer causal relationships between two variables, and we validate the proposed method on simulated data and on a benchmark of cause-effect pairs. We illustrate by our experiments that the proposed approach is simple and extremely competitive in terms of empirical accuracy compared to the state-of-the-art methods.