Causality Detection Methods Research Articles

A Comparative Study of Causality Detection Methods in Root Cause Diagnosis: From Industrial Processes to Brain Networks.

Abstracting causal knowledge from process measurements has become an appealing topic for decades, especially for fault root cause analysis (RCA) based on signals recorded by multiple sensors in a complex system. Although many causality detection methods have been developed and applied in different fields, some research communities may have an idiosyncratic implementation of their preferred methods, with limited accessibility to the wider community. Targeting interested experimental researchers and engineers, this paper provides a comprehensive comparison of data-based causality detection methods in root cause diagnosis across two distinct domains. We provide a possible taxonomy of those methods followed by descriptions of the main motivations of those concepts. Of the two cases we investigated, one is a root cause diagnosis of plant-wide oscillations in an industrial process, while the other is the localization of the epileptogenic focus in a human brain network where the connectivity pattern is transient and even more complex. Considering the differences in various causality detection methods, we designed several sets of experiments so that for each case, a total of 11 methods could be appropriately compared under a unified and reasonable evaluation framework. In each case, these methods were implemented separately and in a standard way to infer causal interactions among multiple variables to thus establish the causal network for RCA. From the cross-domain investigation, several findings are presented along with insights into them, including an interpretative pitfall that warrants caution.

High Resilient Asymmetry and Anomaly Detection Based on Data Causality

In the tunnel construction practice, multiple buildings’ tilt rate data are collected. In this study, data causality is defined to reflect the causal relation between the input and output of the building tilt rate detection data. Upon defining and calculating the data causality, a new high resilient causality detection (HiReCau) method is proposed for abnormal building tilt rate detection. A numerical case and another practical case are studied for validation purposes. The case study results show that the proposed HiReCau method can accurately detect high-causality data and low-causality data among the building tilt rate detection data and produces superior results compared with the direct adoption of a machine learning approach. Furthermore, the resilience of HiReCau is validated by investigations testing varied levels of additional low-causality data in the training dataset. Presently, HiReCau is limited to handling problems with a single output. Furthermore, only the back-propagation neural network (BPNN) is tested as the baseline model and there is also room to further expand the data size. The proposed approach is versatile and able to be adjusted to handle fault diagnosis and safety assessment problems in varied theoretical and engineering backgrounds.

Robust inference of causality in high-dimensional dynamical processes from the Information Imbalance of distance ranks

We introduce an approach which allows detecting causal relationships between variables for which the time evolution is available. Causality is assessed by a variational scheme based on the Information Imbalance of distance ranks, a statistical test capable of inferring the relative information content of different distance measures. We test whether the predictability of a putative driven system Y can be improved by incorporating information from a potential driver system X, without explicitly modeling the underlying dynamics and without the need to compute probability densities of the dynamic variables. This framework makes causality detection possible even between high-dimensional systems where only few of the variables are known or measured. Benchmark tests on coupled chaotic dynamical systems demonstrate that our approach outperforms other model-free causality detection methods, successfully handling both unidirectional and bidirectional couplings. We also show that the method can be used to robustly detect causality in human electroencephalography data.

Usefulness and limitations of convergent cross sorting and continuity scaling methods for their application in simulated and real-world time series

Causality detection methods are valuable tools for detecting causal links in complex systems. The efficiency of continuity scaling (CS) and the convergent cross sorting (CSS) methods to detect causality was analysed. Usefulness and limitations of both methods in their application to simulated and real-world time series was explored under different scenarios. We find that CS is more robust and efficient than the CSS method for all simulated systems, even when increasing noise levels were considered. Both methods were not able to infer causality when time series with a marked difference in their main frequencies were analysed. Minimum time-series length required for the detection of a causal link depends on intrinsic system dynamics and on the method selected to detect it. Using simulated time series, only the CS method was capable to detect bidirectional causality. Causality detection, using the CS method, should at least include: (i) causality strength convergence analysis, (ii) statistical tests of significance, (iii) time-series standardization, and (iv) causality strength ratios as a strength indicator of relative causality between systems. Causality cannot be detected by either method in simulated time series that exhibit generalized synchronization.

Conditional cross-map-based technique: From pairwise dynamical causality to causal network reconstruction.

Causality detection methods based on mutual cross mapping have been fruitfully developed and applied to data originating from nonlinear dynamical systems, where the causes and effects are non-separable. However, these pairwise methods still have shortcomings in discriminating typical network structures, including common drivers, indirect dependencies, and facing the curse of dimensionality, when they are stepping to causal network reconstruction. A few endeavors have been devoted to conquer these shortcomings. Here, we propose a novel method that could be regarded as one of these endeavors. Our method, named conditional cross-map-based technique, can eliminate third-party information and successfully detect direct dynamical causality, where the detection results can exactly be categorized into four standard normal forms by the designed criterion. To demonstrate the practical usefulness of our model-free, data-driven method, data generated from different representative models covering all kinds of network motifs and measured from real-world systems are investigated. Because correct identification of the direct causal links is essential to successful modeling, predicting, and controlling the underlying complex systems, our method does shed light on uncovering the inner working mechanisms of real-world systems only using the data experimentally obtained in a variety of disciplines.

A Data-Driven Two-Phase Multi-Split Causal Ensemble Model for Time Series

Causal inference is a fundamental research topic for discovering the cause–effect relationships in many disciplines. Inferring causality means identifying asymmetric relations between two variables. In real-world systems, e.g., finance, healthcare, and industrial processes, time series data from sensors and other data sources offer an especially good basis to infer causal relationships. Therefore, many different time series causal inference algorithms have been proposed in recent years. However, not all algorithms are equally well-suited for a given dataset. For instance, some approaches may only be able to identify linear relationships, while others are applicable for non-linearities. Algorithms further vary in their sensitivity to noise and their ability to infer causal information from coupled vs. non-coupled time series. As a consequence, different algorithms often generate different causal relationships for the same input. In order to achieve a more robust causal inference result, this publication proposes a novel data-driven two-phase multi-split causal ensemble model to combine the strengths of different causality base algorithms. In comparison to existing approaches, the proposed ensemble method reduces the influence of noise through a data partitioning scheme in a first phase. To achieve this, the data are initially divided into several partitions and the base causal inference algorithms are applied to each partition. Subsequently, Gaussian mixture models are used to identify the causal relationships derived from the different partitions that are likely to be valid. In the second phase, the identified relationships from each base algorithm are then merged based on three combination rules. The proposed ensemble approach is evaluated using multiple metrics, among them a newly developed evaluation index for causal ensemble approaches. We perform experiments using three synthetic datasets with different volumes and complexity, which have been specifically designed to test causality detection methods under different circumstances while knowing the ground truth causal relationships. In these experiments, our causality ensemble outperforms each of its base algorithms. In practical applications, the use of the proposed method could hence lead to more robust and reliable causality results.

A new method of nonlinear causality detection: Reservoir computing Granger causality

Identifying causal and interaction relationships from observational time series is a key step toward understanding complex systems and is also a challenging problem. Many methods have been developed to detect and identify the possible causal link between two variables. However, most of them often suffer from the false detection problems, including false-positive (detected causal links do not exist) and false-negative (an existing causal link fails to be detected). Compared to false-negative problem, false-positive is a more serious problem found in nonlinear systems or processes for almost all causality detection methods. In this study, a new method combining the advantages of Reservoir Computing (RC, a machine learning method) and classical Granger causality detection was developed to fully solve false-positive problems or considerably lower the false-positive rate in detecting causal links of nonlinear systems. Three typical coupled systems with known causal links are applied to show the better performance of new Reservoir Computing Granger (RCG) method over traditional nonlinear Granger causality and its extension methods, which indicates that RCG can accurately detect causal relationships in complex systems and its great potential in exploring the causal and interaction relationships from observational time series.

Granger Causality on forward and Reversed Time Series.

In this study, the information flow time arrow is investigated for stochastic data defined by vector autoregressive models. The time series are analyzed forward and backward by different Granger causality detection methods. Besides the normal distribution, which is usually required for the validity of Granger causality analysis, several other distributions of predictive errors are considered. A clear effect of a change in the order of cause and effect on the time-reversed series of unidirectionally connected variables was detected with standard Granger causality test (GC), when the product of the connection strength and the ratio of the predictive errors of the driver and the recipient was below a certain level, otherwise bidirectional causal connection was detected. On the other hand, opposite causal link was detected unconditionally by the methods based on the time reversal testing, but they were not able to detect correct bidirectional connection. The usefulness of the backward analysis is manifested in cases where falsely detected unidirectional connections can be rejected by applying the result obtained after the time reversal, and in cases of uncorrelated causally independent variables, where the absence of a causal link detected by GC on the original series should be confirmed on the time-reversed series.

Non-Uniform Embedding Scheme and Low-Dimensional Approximation Methods for Causality Detection.

Information causality measures have proven to be very effective in uncovering the connectivity patterns of multivariate systems. The non-uniform embedding (NUE) scheme has been developed to address the “curse of dimensionality”, since the estimation relies on high-dimensional conditional mutual information (CMI) terms. Although the NUE scheme is a dimension reduction technique, the estimation of high-dimensional CMIs is still required. A possible solution is the utilization of low-dimensional approximation (LA) methods for the computation of CMIs. In this study, we aim to provide useful insights regarding the effectiveness of causality measures that rely on NUE and/or on LA methods. In a comparative study, three causality detection methods are evaluated, namely partial transfer entropy (PTE) defined using uniform embedding, PTE using the NUE scheme (PTENUE), and PTE utilizing both NUE and an LA method (LATE). Results from simulations on well known coupled systems suggest the superiority of PTENUE over the other two measures in identifying the true causal effects, having also the least computational cost. The effectiveness of PTENUE is also demonstrated in a real application, where insights are presented regarding the leading forces in financial data.

Reconstructing directional causal networks with random forest: Causality meeting machine learning.

Inspired by the decision tree algorithm in machine learning, a novel causal network reconstruction framework is proposed with the name Importance Causal Analysis (ICA). The ICA framework is designed in a network level and fills the gap between traditional mutual causality detection methods and the reconstruction of causal networks. The potential of the method to identify the true causal relations in complex networks is validated by both benchmark systems and real-world data sets.

Causality Detection Methods Applied to the Investigation of Malaria Epidemics.

Malaria, a disease with major health and socio-economic impacts, is driven by multiple factors, including a complex interaction with various climatic variables. In this paper, five methods developed for inferring causal relations between dynamic processes based on the information encapsulated in time series are applied on cases previously studied in literature by means of statistical methods. The causality detection techniques investigated in the paper are: a version of the kernel Granger causality, transfer entropy, recurrence plot, causal decomposition and complex networks. The methods provide coherent results giving a quite good confidence in the conclusions.

Hydrological natural inflow and climate variables: Time and frequency causality analysis

Numbers of studies have proved the significant influence of climate variables on hydrological series. Considering the pivotal role of the hydroelectric power plants play in the electricity production in Brazil this paper considers the natural hydrological inflow data from 15 major basins and 8 climate variables containing 7 El Niño Southern Oscillation proxies and the sunspot numbers. The causal relationships between hydrological natural inflows and climate variables are investigated by adopting and comparing 5 different causality detection methods (Granger Causality test, Frequency Domain Causality test, Convergent Cross Mapping Causality test, Single Spectrum Analysis (SSA) Causality test and Periodic Autoregressive Model Causality test) that cover both well established and novel empirical approaches. Both time domain and frequency domain causality tests gain valid evidences of unidirectional causality for a group of series; CCM achieved unidirectional causality for 18% of pairs and overwhelmingly indicated the opposite direction of causality; a mixture of results are concluded by SSA causality test; PAR based causality test obtained six unidirectional causality, but only one is really significant.

Comparison of six methods for the detection of causality in a bivariate time series.

In this comparative study, six causality detection methods were compared, namely, the Granger vector autoregressive test, the extended Granger test, the kernel version of the Granger test, the conditional mutual information (transfer entropy), the evaluation of cross mappings between state spaces, and an assessment of predictability improvement due to the use of mixed predictions. Seven test data sets were analyzed: linear coupling of autoregressive models, a unidirectional connection of two Hénon systems, a unidirectional connection of chaotic systems of Rössler and Lorenz type and of two different Rössler systems, an example of bidirectionally connected two-species systems, a fishery model as an example of two correlated observables without a causal relationship, and an example of mediated causality. We tested not only 20000 points long clean time series but also noisy and short variants of the data. The standard and the extended Granger tests worked only for the autoregressive models. The remaining methods were more successful with the more complex test examples, although they differed considerably in their capability to reveal the presence and the direction of coupling and to distinguish causality from mere correlation.

Time-Varying Nonlinear Causality Detection Using Regularized Orthogonal Least Squares and Multi-Wavelets With Applications to EEG

A new transient Granger causality detection method is proposed based on a time-varying parametric modeling framework, and is applied to the real EEG signals to reveal the causal information flow during motor imagery (MI) tasks. The time-varying parametric modeling approach employs a nonlinear autoregressive with external input model, whose parameters are approximated by a set of multi-wavelet basis functions. A regularized orthogonal least squares (ROLS) algorithm is then used to produce a parsimonious or sparse regression model and estimate the associated model parameters. The time-varying Granger causality between nonstationary signals can be detected accurately by making use of both the good approximation properties of multi-wavelets and the good generalization performance of the ROLS in the presence of high-level noise. Two simulation examples are presented to demonstrate the effectiveness of the proposed method for both linear and nonlinear causal detection respectively. The proposed method is then applied to real EEG signals of MI tasks. It follows that transient causal information flow over the time course between various sensorimotor related channels can be successfully revealed during the whole reaction processes. Experimental results from these case studies confirm the applicability of the proposed scheme and show its utility for the understanding of the associated neural mechanism and the potential significance for developing MI tasks based brain-computer interface systems.

Real-Time Assessment and Diagnosis of Process Operating Performance

Over time, the performance of processes may deviate from the initial design due to process variations and uncertainties, making it necessary to develop systematic methods for online optimality assessment based on routine operating process data. Some processes have multiple operating modes caused by the set point change of the critical process variables to achieve different product specifications. On the other hand, the operating region in each operating mode can alter, due to uncertainties. In this paper, we will establish an optimality assessment framework for processes that typically have multi-mode, multi-region operations, as well as transitions between different modes. The kernel density approach for mode detection is adopted and improved for operating mode detection. For online mode detection, the model-based clustering discriminant analysis (MclustDA) approach is incorporated with some a priori knowledge of the system. In addition, multi-modal behavior of steady-state modes is tackled utilizing the mixture probabilistic principal component regression (MPPCR) method, and dynamic principal component regression (DPCR) is used to investigate transitions between different modes. Moreover, a probabilistic causality detection method based on the sequential forward floating search (SFFS) method is introduced for diagnosing poor or non-optimum behavior. Finally, the proposed method is tested on the Tennessee Eastman (TE) benchmark simulation process in order to evaluate its performance.

Isolation of plant-wide faults using causality detection methods

Isolation of plant-wide faults in large-scale complex systems is particularly challenging. A methodology to detect and isolate faults is proposed, detecting the faulty variables using univariate control charts and the causality information between them to indicate the source. The clustering of faulty variables uses univariate analysis to avoid the smearing effect brought by multivariate analysis. The variable where the fault took place is indicated, handling fault novelties in a very natural manner. The proposed method is discussed and illustrated through its application to the Tennessee Eastman Process and to routine operating data from a thermoelectric power plant.

A Causality Capturing Method for Diagnosis Based on Transfer Entropy by Analyzing Trends of Time Series

Since modern industrial processes become much larger and more complex, efficient and effective causality detection methods are needed to capture the process topology, diagnose root causes of widespread or even plant-wide process malfunction, and further ensure the safety of processes. A modified transfer entropy method, named trend transfer entropy, is proposed in this paper, which focuses on analyzing trends of time series rather than the original series themselves and thus, compared to the traditional transfer entropy, proves to be more robust in conditions of data drifting and noise disturbance. Moreover, the new method can reduce computational load effectively, saving valuable time before the occurrence of an accident. Simulation studies are presented to illustrate the procedure and features of the proposed method.

Causality detection and turbulence in fusion plasmas

This work explores the potential of an information-theoretical causality detection method for unravelling the relation between fluctuating variables in complex non-linear systems. The method is tested on some simple though non-linear models, and guidelines for the choice of analysis parameters are established. Then, measurements from magnetically confined fusion plasmas are analysed. The selected data bear relevance to the all-important spontaneous confinement transitions often observed in fusion plasmas, fundamental for the design of an economically attractive fusion reactor. It is shown how the present method is capable of clarifying the interaction between fluctuating quantities such as the turbulence amplitude, turbulent flux and zonal flow amplitude, and uncovers several interactions that were missed by traditional methods.

A Parametric Method to Measure Time-Varying Linear and Nonlinear Causality With Applications to EEG Data

A linear and nonlinear causality detection method called the error-reduction-ratio causality (ERRC) test is introduced in this paper to investigate if linear or nonlinear models should be considered in the study of human electroencephalograph (EEG) data. In comparison to the traditional Granger methods, one significant advantage of the ERRC approach is that it can effectively detect the time-varying linear and nonlinear causalities between two signals without fitting a complete nonlinear model. Two numerical simulation examples are employed to compare the performance of the new method with other widely used methods in the presence of noise and in tracking time-varying causality. Finally, an application to measure the linear and nonlinear relationships between two EEG signals from different cortical sites for patients with childhood absence epilepsy is discussed.

Quantification of Effective Connectivity in the Brain Using a Measure of Directed Information

Effective connectivity refers to the influence one neural system exerts on another and corresponds to the parameter of a model that tries to explain the observed dependencies. In this sense, effective connectivity corresponds to the intuitive notion of coupling or directed causal influence. Traditional measures to quantify the effective connectivity include model-based methods, such as dynamic causal modeling (DCM), Granger causality (GC), and information-theoretic methods. Directed information (DI) has been a recently proposed information-theoretic measure that captures the causality between two time series. Compared to traditional causality detection methods based on linear models, directed information is a model-free measure and can detect both linear and nonlinear causality relationships. However, the effectiveness of using DI for capturing the causality in different models and neurophysiological data has not been thoroughly illustrated to date. In addition, the advantage of DI compared to model-based measures, especially those used to implement Granger causality, has not been fully investigated. In this paper, we address these issues by evaluating the performance of directed information on both simulated data sets and electroencephalogram (EEG) data to illustrate its effectiveness for quantifying the effective connectivity in the brain.