Causal Edges Research Articles

InfoFlowNet: A multi-head attention-based self-supervised learning model with surrogate approach for uncovering brain effective connectivity

Deciphering brain network topology can enhance the depth of neuroscientific knowledge and facilitate the development of neural engineering methods. Effective connectivity, which gauges the directional influences among brain regions, is pivotal for these studies. This research introduces InfoFlowNet, a novel self-supervised learning model designed to infer causal relationships in electroencephalogram (EEG) data, aiming at capturing the complex information flow among brain regions. Specifically, InfoFlowNet employs convolution operations and multi-head self-attention mechanisms with a masking feature, which ignores self-connections to focus on inter-regional dynamics. Additionally, a new causal magnitude estimation is introduced by assessing the impact of shuffled surrogate data on signal prediction to quantify causal influence. Experiments using synthetic data and real EEG datasets demonstrate that InfoFlowNet effectively uncovers time-varying causal relationships. Compared with the Granger causality model (GCM) and the temporal causal discovery framework (TCDF), InfoFlowNet shows superior sensitivity in detecting significant causal edges. For instance, in a psychomotor vigilance task, InfoFlowNet identified 8 out of 16 significant causal edges, significantly outperforming GCM and TCDF. Furthermore, InfoFlowNet successfully passes the whiteness test on the model's residuals, and advanced analyses illustrate the advantages of utilizing multi-head attention and masking mechanisms to capture effective connectivity. In sum, InfoFlowNet represents a significant advancement in the analysis of effective connectivity, offering a deeper understanding of brain network dynamics. The model's ability to discern complex causal interactions supports its potential application in broader neuroscientific research and applications.

Identification of Causal Structure with Latent Variables Based on Higher Order Cumulants

Causal discovery with latent variables is a crucial but challenging task. Despite the emergence of numerous methods aimed at addressing this challenge, they are not fully identified to the structure that two observed variables are influenced by one latent variable and there might be a directed edge in between. Interestingly, we notice that this structure can be identified through the utilization of higher-order cumulants. By leveraging the higher-order cumulants of non-Gaussian data, we provide an analytical solution for estimating the causal coefficients or their ratios. With the estimated (ratios of) causal coefficients, we propose a novel approach to identify the existence of a causal edge between two observed variables subject to latent variable influence. In case when such a causal edge exits, we introduce an asymmetry criterion to determine the causal direction. The experimental results demonstrate the effectiveness of our proposed method.

ВИЯВЛЕННЯ КАУЗАЛЬНИХ ВІДНОШЕНЬ З МАРКОВСЬКИХ ВЛАСТИВОСТЕЙ В УМОВАХ ЛАТЕНТНИХ КОНФАУНДЕРІВ

We address the problems of causal structure reconstruction given conditional independence facts when latent confounders are allowed. We examine the conditions that allow one to partially or fully identify authentic causal links and latent confounders. The updated implicative rules for orienting edges under confounding are suggested. As demonstrated, it is possible to construct the new rules, which can reveal confounded causal edges and bows. The rules rely on facts of the absence of certain authentic edges (such facts may be justified by non-independence constraints, like Verma constraint, or subject-based requirements). Keywords: causal relation, d-separation, conditional independence, latent confounder, edge orientation, bow (arc).

Success concepts for causal discovery

Existing causal discovery algorithms are often evaluated using two success criteria, one that is typically unachievable and the other which is too weak for practical purposes. The unachievable criterion—uniform consistency—requires that a discovery algorithm identify the correct causal structure at a known sample size. The weak but achievable criterion— pointwise consistency—requires only that one identify the correct causal structure in the limit. We investigate two intermediate success criteria—decidability and progressive solvability—that are stricter than mere consistency but weaker than uniform consistency. To do so, we review several topological theorems characterizing which discovery problems are decidable and/or progressively solvable. These theorems apply to any problem of statistical model selection, but in this paper, we apply the theorems only to selection of causal models. We show, under several common modeling assumptions, that there is no uniformly consistent procedure for identifying the direction of a causal edge, but there are statistical decision procedures and progressive solutions. We focus on linear models in which the error terms are either non-Gaussian or contain no Gaussian components; the latter modeling assumption is novel to this paper. We focus especially on which success criteria remain feasible when confounders are present.

Prior Knowledge-Based Causal Inference Algorithms and Their Applications for China COVID-19 Analysis

Causal inference has become an important research direction in the field of computing. Traditional methods have mainly used Bayesian networks to discover the causal effects between variables. These methods have limitations, namely, on the one hand, the computing cost is expensive if one wants to achieve accurate results, i.e., exponential growth along with the number of variables. On the other hand, the accuracy is not good enough if one tries to reduce the computing cost. In this study, we use prior knowledge iteration or time series trend fitting between causal variables to resolve the limitations and discover bidirectional causal edges between the variables. Subsequently, we obtain real causal graphs, thus establishing a more accurate causal model for the evaluation and calculation of causal effects. We present two new algorithms, namely, the PC+ algorithm and the DCM algorithm. The PC+ algorithm is used to address the problem of the traditional PC algorithm, which needs to enumerate all Markov equivalence classes at a high computational cost or with immediate output of non-directional causal edges. In the PC+ algorithm, the causal tendency among some variables was analyzed via partial exhaustive analysis. By fixing the relatively certain causality as prior knowledge, a causal graph of higher accuracy is the final output at a low running cost. The DCM algorithm uses the d-separation strategy to improve the traditional CCM algorithm, which can only handle the pairwise fitting of variables, and thus identify the indirect causality as the direct one. By using the d-separation strategy, our DCM algorithm achieves higher accuracy while following the basic criteria of Bayesian networks. In this study, we evaluate the proposed algorithms based on the COVID-19 pandemic with experimental and theoretical analysis. The experimental results show that our improved algorithms are effective and efficient. Compared to the exponential cost of the PC algorithm, the time complexity of the PC+ algorithm is reduced to a linear level. Moreover, the accuracies of the PC+ algorithm and DCM algorithm are improved to different degrees; specifically, the accuracy of the PC+ algorithm reaches 91%, much higher than the 33% of the PC algorithm.

D-BIAS: A Causality-Based Human-in-the-Loop System for Tackling Algorithmic Bias.

With the rise of AI, algorithms have become better at learning underlying patterns from the training data including ingrained social biases based on gender, race, etc. Deployment of such algorithms to domains such as hiring, healthcare, law enforcement, etc. has raised serious concerns about fairness, accountability, trust and interpretability in machine learning algorithms. To alleviate this problem, we propose D-BIAS, a visual interactive tool that embodies human-in-the-loop AI approach for auditing and mitigating social biases from tabular datasets. It uses a graphical causal model to represent causal relationships among different features in the dataset and as a medium to inject domain knowledge. A user can detect the presence of bias against a group, say females, or a subgroup, say black females, by identifying unfair causal relationships in the causal network and using an array of fairness metrics. Thereafter, the user can mitigate bias by refining the causal model and acting on the unfair causal edges. For each interaction, say weakening/deleting a biased causal edge, the system uses a novel method to simulate a new (debiased) dataset based on the current causal model while ensuring a minimal change from the original dataset. Users can visually assess the impact of their interactions on different fairness metrics, utility metrics, data distortion, and the underlying data distribution. Once satisfied, they can download the debiased dataset and use it for any downstream application for fairer predictions. We evaluate D-BIAS by conducting experiments on 3 datasets and also a formal user study. We found that D-BIAS helps reduce bias significantly compared to the baseline debiasing approach across different fairness metrics while incurring little data distortion and a small loss in utility. Moreover, our human-in-the-loop based approach significantly outperforms an automated approach on trust, interpretability and accountability.

Data-driven identification model for associated fault propagation path

In this paper, a data-driven identification model of the associated fault propagation path is proposed. Different from traditional fault diagnosis methods, the alternative approach is focused more on identifying the fault propagation path. Firstly, the KPCA method is used for fault detection. Then, a new transfer entropy method is proposed to construct the causality diagram. Finally, a kernel extreme learning machine-based search approach is proposed for fault propagation path identification. To demonstrate the effectiveness and applicability, the proposed model is applied to the Tennessee-Eastman Process and the real telemetry data of the satellite in orbit. Experimental results show that the number of causal edges obtained by the proposed method is only 12.62% of the traditional transfer entropy method, and 24.45% of the multivariate transfer entropy method.

Spreading of correlations and entanglement in the long-range transverse Ising chain

Whether long-range interactions allow for a form of causality in non-relativistic quantum models remains an open question with far-reaching implications for the propagation of information and thermalization processes. Here, we study the out-of-equilibrium dynamics of the one-dimensional transverse Ising model with algebraic long-range exchange coupling. Using a state of the art tensor-network approach, complemented by analytic calculations and considering various observables, we show that a weak form of causality emerges, characterized by non-universal dynamical exponents. While the local spin and spin correlation causal edges are sub-ballistic, the causal region has a rich internal structure, which, depending on the observable, displays ballistic or super-ballistic features. In contrast, the causal region of entanglement entropy is featureless and its edge is always ballistic, irrespective of the interaction range. Our results shed light on the propagation of information in long-range interacting lattice models and pave the way to future experiments, which are discussed.

Autonomous root-cause fault diagnosis using symbolic dynamic based causality analysis

This paper proposes a general framework for autonomous root-cause fault diagnosis in a complex process. In this framework, as a prerequisite step after conducting fault detection, the potential root-cause candidates are selected using a contribution score-based method (e.g. accumulative rate contribution scores). Then a fully automated procedure is proposed to determine the root-cause(s) of the detected fault amongst potential candidates without a priori knowledge of the base-line model or intervention of an expert. To locate the root-cause variable(s), firstly symbolic dynamic-based normalized transfer entropy (SDNTE) is proposed to generate an initial causal graph of root-cause candidates. Then symbolic dynamic-based normalized direct transfer entropy (SDNDTE) is proposed and utilized for pruning the initial graph (i.e. discard indirect and spurious causal edges). To this aim, explicit definitions of immediate intermediate variables (IIV) and source intermediate variables (SIV) are given and systematic algorithms are developed to find them efficiently. At last, a topological approach is proposed to locate the root-cause variables according to the pruned causal graph. The proposed generalized SDNDTE approach overcomes the computational complexity in the calculation of normalized direct transfer entropy (NDTE) using conventional multi-dimensional kernel probability density functions (PDFs) fitting, which enables real-time root-cause fault diagnosis. To demonstrate the effectiveness and applicability, the proposed autonomous scheme is tested on a numerical example at first, and its computational complexity is analysed and compared to other existing works. Finally, it is validated on the Tennessee Eastman process (TEP) benchmark model.

Integrated Causal Network and Model‐based Analysis of Ca2+ Wave Propagation in Liver Lobules

Intracellular free Ca2+ in hepatocytes regulates a wide range of hepatic functions. Whole tissue Ca2+ imaging studies show wave‐like spatial patterns of cytosolic Ca2+ in response to circulating hormonal stimuli in liver lobules. Ca2+ waves elicited by hormones such as vasopressin are rooted in cell‐autonomous GPCR activation and the downstream canonical signaling cascade. Spatial Ca2+ waves are caused by gap junction‐mediated molecule exchange between adjacent hepatocytes. Ca2+ waves override cellular heterogeneity with regards to intracellular Ca2+ dynamics leading to a coordinated response to stimuli.Although a wealth of knowledge exists on intracellular Ca2+ dynamics, a quantitative description of lobular scale Ca2+ waves is lacking. We acquired data on vasopressin induced Ca2+ transients imaged in a 2D optical slice in perfused rat liver for 1300 hepatocytes across several lobules. We used a combination of causal time series modeling and model‐based analysis to identify what factors contribute towards propagation of Ca2+ waves in liver lobules.Time series modeling of our data suggested that although Ca2+ waves appeared to traverse entire lobules, only a subset of hepatocytes residing in any lobule formed causally connected “islands”. Within these islands, hepatocytes were causally connected to up to six neighbors. However information flow between adjacent hepatocytes within these islands was not aligned in a unidirectional fashion, as required for wave‐like propagation. Visualization of the Ca2+ profiles within an island revealed existence of cell‐autonomous Ca2+ transients superimposed on spatially propagating waves.We next analyzed our data using a receptor oriented, ODE‐based computational model of Ca2+ wave propagation. Our model suggested that Ca2+ waves originated from extended regions near the pericentral lobular zone and propagated towards the periportal region. Ca2+ waves in our model resulted from parameter gradients and IP3 exchange. Our analysis also revealed that Ca2+ wave propagation was robust to some non‐interacting hepatocytes due to high degree of causal connections for a given hepatocyte.Our analyses revealed that robust lobular scale Ca2+ waves arise due spatial gradients of intracellular signaling components and IP3 exchange between a hepatocyte and several of its neighbors residing within the same island. The existence of multidirectional causal edges as seen in our causal analysis could arise due to cell‐autonomous Ca2+ response of hepatocytes within a small region which do not propagate beyond a few cells. Although we modeled intercellular interactions as gap junction mediated IP3 exchange, additional phenomena such as paracrine signaling as well as cellular arrangement in 3D could contribute towards coupling of hepatocyte Ca2+ responses across sinusoids. These aspects must be included to improve our description of spatial Ca2+ wave dynamics in liver lobules.Support or Funding InformationNIH NIAAA: R01 AA018873This abstract is from the Experimental Biology 2018 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Comorbidity Scoring with Causal Disease Networks.

In recent years, there has been numerous studies constructing a disease network with diverse sources of data. Many researchers attempted to extend the usage of the disease network by employing machine learning algorithms on various problems such as prediction of comorbidity. The relations between diseases can further be specified into causal relations. When causality is laid on the edges in the network, prediction for comorbid diseases can be more improved. However, not many machine learning algorithms have been developed to concern causality. In this study, we exploit a network based machine learning algorithm that generates comorbidity scores from a causal disease network. In order to find comorbid diseases, semi-supervised scoring for causal networks is proposed. It computes scores of entire nodes in the network when a specific node is labeled. Each score is calculated one at a time and affects to the others along causal edges. The algorithm iterates until it converges. We compared the scoring results of the causal disease network and those of simple association network. As a gold standard, we referenced the values of relative risk from prevalence database, HuDiNe. Scoring by the proposed method provides clearer distinguishability between the top-ranked diseases in the comorbidity list. This is a benefit because it allows the choosing of the most significant ones on an easier fashion. To present typical use of the resulting list, comorbid diseases of Huntington disease and pnuemonia are validated via PubMed literature, respectively.

Sophisticated Merging Over Random Partitions: A Scalable and Robust Causal Discovery Approach.

Scalable causal discovery is an essential technology to a wide spectrum of applications, including biomedical studies and social network evolution analysis. To tackle the difficulty of high dimensionality, a number of solutions are proposed in the literature, generally dividing the original variable domain into smaller subdomains by computation intensive partitioning strategies. These approaches usually suffer significant structural errors when the partitioning strategies fail to recognize true causal edges across the output subdomains. Such a structural error accumulates quickly with the growing depth of recursive partitioning, due to the lack of correction mechanism over causally connected variables when they are wrongly divided into two subdomains, finally jeopardizing the robustness of the integrated results. This paper proposes a completely different strategy to solve the problem, powered by a lightweight random partitioning scheme together with a carefully designed merging algorithm over results from the random partitions. Based on the randomness properties of the partitioning scheme, we design a suite of tricks for the merging algorithm, in order to support propagation-based significance enhancement, maximal acyclic subgraph causal ordering, and order-sensitive redundancy elimination. Theoretical studies as well as empirical evaluations verify the genericity, effectiveness, and scalability of our proposal on both simulated and real-world causal structures when the scheme is used in combination with a variety of causal solvers known effective on smaller domains.

Fuzzy cognitive maps of public support for insurgency and terrorism

Feedback fuzzy cognitive maps (FCMs) can model the complex structure of public support for insurgency and terrorism (PSOT). FCMs are fuzzy causal signed digraphs that model degrees of causality in interwoven webs of feedback causality and policy variables. Their nonlinear dynamics permit forward-chaining inference from input causes and policy options to output effects. We show how a concept node causally affects downstream nodes through a weighted product of the intervening causal edge strengths. FCMs allow users to add detailed dynamics and feedback links directly to the causal model. Users can also fuse or combine FCMs from multiple experts by weighting and adding the underlying FCM fuzzy edge matrices. The combined FCM tends to better represent domain knowledge as the expert sample size increases if the expert sample approximates a random sample. Statistical or machine-learning algorithms can use numerical sample data to learn and tune a FCM’s causal edges. A differential Hebbian learning law can approximate a PSOT FCM’s directed edges of partial causality using time-series training data. The PSOT FCM adapts to the computational factor-tree PSOT model that Davis and OMahony based on prior social science research and case studies. Simulation experiments compare the PSOT models with the adapted FCM models.

Interpreting transcriptional changes using causal graphs: new methods and their practical utility on public networks.

BackgroundInference of active regulatory cascades under specific molecular and environmental perturbations is a recurring task in transcriptional data analysis. Commercial tools based on large, manually curated networks of causal relationships offering such functionality have been used in thousands of articles in the biomedical literature. The adoption and extension of such methods in the academic community has been hampered by the lack of freely available, efficient algorithms and an accompanying demonstration of their applicability using current public networks.ResultsIn this article, we propose a new statistical method that will infer likely upstream regulators based on observed patterns of up- and down-regulated transcripts. The method is suitable for use with public interaction networks with a mix of signed and unsigned causal edges. It subsumes and extends two previously published approaches and we provide a novel algorithmic method for efficient statistical inference. Notably, we demonstrate the feasibility of using the approach to generate biological insights given current public networks in the context of controlled in-vitro overexpression experiments, stem-cell differentiation data and animal disease models. We also provide an efficient implementation of our method in the R package QuaternaryProd available to download from Bioconductor.ConclusionsIn this work, we have closed an important gap in utilizing causal networks to analyze differentially expressed genes. Our proposed Quaternary test statistic incorporates all available evidence on the potential relevance of an upstream regulator. The new approach broadens the use of these types of statistics for highly curated signed networks in which ambiguities arise but also enables the use of networks with unsigned edges. We design and implement a novel computational method that can efficiently estimate p-values for upstream regulators in current biological settings. We demonstrate the ready applicability of the implemented method to analyze differentially expressed genes using the publicly available networks.

Causal structure in the scalar–tensor theory with field derivative coupling to the Einstein tensor

We investigate the causal structure in the scalar–tensor theory with the field derivative coupling to the Einstein tensor, which is a class of the Horndeski theory in the four-dimensional spacetime. We show that in general the characteristic hypersurface is non-null, which admits the superluminal propagations. We also derive the conditions that the characteristic hypersurface becomes null and show that a Killing horizon can be the causal edge for all the propagating degrees of freedom, if the additional conditions for the scalar field are satisfied. Finally, we find the position of the characteristic hypersurface in the dynamical spacetime with the maximally symmetric space, and that the fastest propagation can be superluminal, especially if the coupling constant becomes positive. We also argue that the superluminality itself may not lead to the acausality of the theory.

Causal structures in Gauss-Bonnet gravity

We analyze causal structures in Gauss-Bonnet gravity. It is known that Gauss-Bonnet gravity potentially has superluminal propagation of gravitons due to its noncanonical kinetic terms. In a theory with superluminal modes, an analysis of causality based on null curves makes no sense, and thus, we need to analyze them in a different way. In this paper, using the method of the characteristics, we analyze the causal structure in Gauss-Bonnet gravity. We have the result that, on a Killing horizon, gravitons can propagate in the null direction tangent to the Killing horizon. Therefore, a Killing horizon can be a causal edge as in the case of general relativity; i.e. a Killing horizon is the ``event horizon'' in the sense of causality. We also analyze causal structures on nonstationary solutions with $(D\ensuremath{-}2)$-dimensional maximal symmetry, including spherically symmetric and flat spaces. If the geometrical null energy condition, ${R}_{AB}{N}^{A}{N}^{B}\ensuremath{\ge}0$ for any null vector ${N}^{A}$, is satisfied, the radial velocity of gravitons must be less than or equal to that of light. However, if the geometrical null energy condition is violated, gravitons can propagate faster than light. Hence, on an evaporating black hole where the geometrical null energy condition is expected not to hold, classical gravitons can escape from the ``black hole'' defined with null curves. That is, the causal structures become nontrivial. It may be one of the possible solutions for the information loss paradox of evaporating black holes.

Quantization effects on the equilibrium behavior of combined fuzzy cognitive maps

Fuzzy cognitive maps (FCMs) allow experts to express their knowledge by drawing weighted causal digraphs. Experts can pool or fuse their knowledge by adding the underlying FCM causal matrices. This naturally extends the ordered-weighted-averaging (OWA) technique to averaging dynamical systems and can create complex dynamical systems from several simpler ones. Edge quantization allows experts to state their knowledge in the simpler terms of causal increase (1), decrease (−1), or absence (0). We model the expert FCMs as a sequence of random fields to study the small-sample effects of quantizing both the causal edges and the fuzzy-set concept nodes. The averaged quantized random matrices exhibit large-sample convergence to the population means of the unquantized matrices in accordance with the Strong Law of Large Numbers. But the small-sample averages can show substantial diversity of equilibrium attractors (fixed points or limit cycles). We use statistical tests—chi-square tests, Spearman's rank coefficient, the Kolmogorov–Smirnov test, and the fuzzy equality of limit cycle histograms—to show that this small-sample equilibrium diversity increases as the node multivalence or fuzzy-set quantization increases. The appendix presents a new probabilistic convergence theorem that shows that edge quantization or thresholding does not affect FCM combination for large expert sample sizes: the sample mean of quantized expert causal edge values converges with probability one to the population mean causal edge values. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 181–202, 2007.