Definition Of Causality Research Articles

Mixed orthogonality graphs for continuous-time stationary processes

In this paper, we introduce different concepts of Granger causality and contemporaneous correlation for multivariate stationary continuous-time processes to model different dependencies between the component processes. Several equivalent characterisations are given for the different definitions, in particular by orthogonal projections. We then define two mixed graphs based on different definitions of Granger causality and contemporaneous correlation, the (mixed) orthogonality graph and the local (mixed) orthogonality graph. In these graphs, the components of the process are represented by vertices, directed edges between the vertices visualise Granger causal influences and undirected edges visualise contemporaneous correlation between the component processes. Further, we introduce various notions of Markov properties in analogy to Eichler (2012), which relate paths in the graphs to different dependence structures of subprocesses, and we derive sufficient criteria for the (local) orthogonality graph to satisfy them. Finally, as an example, for the popular multivariate continuous-time AR (MCAR) processes, we explicitly characterise the edges in the (local) orthogonality graph by the model parameters.

A Causal Analysis of Harm

As autonomous systems rapidly become ubiquitous, there is a growing need for a legal and regulatory framework that addresses when and how such a system harms someone. There have been several attempts within the philosophy literature to define harm, but none of them has proven capable of dealing with the many examples that have been presented, leading some to suggest that the notion of harm should be abandoned and “replaced by more well-behaved notions”. As harm is generally something that is caused, most of these definitions have involved causality at some level. Yet surprisingly, none of them makes use of causal models and the definitions of actual causality that they can express. In this paper, which is an expanded version of the conference paper Beckers et al. (Adv Neural Inform Process Syst 35:2365–2376, 2022), we formally define a qualitative notion of harm that uses causal models and is based on a well-known definition of actual causality. The key features of our definition are that it is based on contrastive causation and uses a default utility to which the utility of actual outcomes is compared. We show that our definition is able to handle the examples from the literature, and illustrate its importance for reasoning about situations involving autonomous systems.

Detecting dynamical causality via intervened reservoir computing

An abundance of complex dynamical phenomena exists in nature and human society, requiring sophisticated analytical tools to understand and explain. Causal analysis through observational time series data is essential in comprehending complex systems when controlled experiments are not feasible or ethical. Although data-based causal discovery methods have been widely used, there is still a lack of direct ways more aligned with the intuitive definition of causality, i.e., whether interventions on one element lead to changes in the subsequent development of others. To solve this problem, we propose the method of intervened reservoir computing (IRC) based on constructing a neural network replica of the original system and applying interventions to it. This approach enables controlled trials, thus observing the intervened evolution, in the digital twins of the underlying systems. Simulated and real-world data are used to test our approach and demonstrate its accuracy in inferring causal networks. Given the importance of causality in understanding complex dynamics, we anticipate that IRC could serve as a powerful tool for various disciplines to decipher the intrinsic mechanisms of natural systems from observational data.

Personal Time and Transmigration Time Travel

Lewis argued that although paradoxes such as the famous Grandfather Paradox can be solved, only a limited set of time travel fiction is consistent. In this paper, I discuss how to extend a Lewisian approach to a class of time travel fiction not considered by Lewis: transmigration or mental time travel fiction. To this end, Lewis’s definition of personal time needs refining, and this is the primary focus of my paper. I discuss some alternative refinements of Lewis’s definition: a Solely Mental definition and a Causal definition. I end by also applying these definitions to cases of reverse aging.

Causalized Convergent Cross Mapping and Its Implementation in Causality Analysis.

Rooted in dynamic systems theory, convergent cross mapping (CCM) has attracted increased attention recently due to its capability in detecting linear and nonlinear causal coupling in both random and deterministic settings. One limitation with CCM is that it uses both past and future values to predict the current value, which is inconsistent with the widely accepted definition of causality, where it is assumed that the future values of one process cannot influence the past of another. To overcome this obstacle, in our previous research, we introduced the concept of causalized convergent cross mapping (cCCM), where future values are no longer used to predict the current value. In this paper, we focus on the implementation of cCCM in causality analysis. More specifically, we demonstrate the effectiveness of cCCM in identifying both linear and nonlinear causal coupling in various settings through a large number of examples, including Gaussian random variables with additive noise, sinusoidal waveforms, autoregressive models, stochastic processes with a dominant spectral component embedded in noise, deterministic chaotic maps, and systems with memory, as well as experimental fMRI data. In particular, we analyze the impact of shadow manifold construction on the performance of cCCM and provide detailed guidelines on how to configure the key parameters of cCCM in different applications. Overall, our analysis indicates that cCCM is a promising and easy-to-implement tool for causality analysis in a wide spectrum of applications.

Causal Mediation Analysis with the Parallel Process Latent Growth Curve Mediation Model

In parallel process latent growth curve mediation models, the mediation pathways from treatment to the intercept or slope of outcome through the intercept or slope of mediator are often of interest. In this study, we developed causal mediation analysis methods for these mediation pathways. Particularly, we provided causal definitions and identification results for the interventional indirect effects via the mediator intercept (or slope) alone and due to their mutual dependence. For estimation, we proposed an interaction model that incorporates interactions among the mediator intercept/slope and treatment, coupled with a Bayesian method. We evaluated the studied methods through simulations, and illustrated their applications using an empirical example.

A phenomenological account for causality in terms of elementary actions

Abstract Discussions on causal relations in real life often consider variables for which the definition of causality is unclear since the notion of interventions on the respective variables is obscure. Asking “what qualifies an action for being an intervention on the variable X X ” raises the question whether the action impacted all other variables only through X or directly, which implicitly refers to a causal model. To avoid this known circularity, we instead suggest a notion of “phenomenological causality” whose basic concept is a set of elementary actions. Then the causal structure is defined such that elementary actions change only the causal mechanism at one node (e.g. one of the causal conditionals in the Markov factorization). This way, the principle of independent mechanisms becomes the defining property of causal structure in domains where causality is a more abstract phenomenon rather than being an objective fact relying on hard-wired causal links between tangible objects. In other words, causal relations between variables get defined by the interface between the system and an external agent (who is able to perform the elementary actions), rather than being an internal property of links between the variables. We describe this phenomenological approach to causality for toy and hypothetical real-world examples and argue that it is consistent with the causal Markov condition when the system under consideration interacts with other variables that control the elementary actions.

Discovering Agents (Abstract Reprint)

Causal models of agents have been used to analyse the safety aspects of machine learning systems. But identifying agents is non-trivial – often the causal model is just assumed by the modeller without much justification – and modelling failures can lead to mistakes in the safety analysis. This paper proposes the first formal causal definition of agents – roughly that agents are systems that would adapt their policy if their actions influenced the world in a different way. From this we derive the first causal discovery algorithm for discovering the presence of agents from empirical data, given a set of variables and under certain assumptions. We also provide algorithms for translating between causal models and game-theoretic influence diagrams. We demonstrate our approach by resolving some previous confusions caused by incorrect causal modelling of agents.

Rethinking ‘causality’ in quantitative human geography

AbstractCausality is at the core of much contemporary discussion in social sciences, philosophy, and computer science—from the establishment of basic definitions of causality to developing methods for causal inference, this discussion is increasingly finding voice within geographical literature. However, geographers have long discussed (and differed) about the role “causality” plays in our work. We present a history of contemporary definitions of causality arising from philosophy and examine how these intellectual currents interact with past and present geographical thinking about causal relations. In particular, we focus on how new thinking about counterfactual causality can help re‐route inquiry around a well‐known impasse: law‐based causality in geography. In other words, while different perspectives around “laws” of geography exist, we argue that it is more productive to put aside these differences and find common ground in counterfactual causal thinking. To demonstrate, we outline new kinds of scholarship enabled by counterfactual causality and contemporary challenges that counterfactual causality faces in spatial analysis. Throughout, we refer interested readers to contemporary work on spatial causal inference and methods useful for scholars interested in analysing causal relationships in geographical systems.

Concepts of Statistical Causality and Strong and Weak Properties of Predictable Representation

The paper considers the statistical concept of causality in continuous time, which is based on Granger’s definition of causality. We give necessary and sufficient conditions, in terms of statistical causality, for the preservation of the strong property of predictable representation for stopped martingales when filtration is decreased. This concept of causality is also connected to the preservation of the strong property of predictable representation under a change in measure. In addition, we give conditions, in terms of statistical causality, for martingales to have strong and weak properties of predictable representation. The results are applied to the problem of pricing claims in incomplete financial markets.

Application of the Concept of Statistical Causality in Integrable Increasing Processes and Measures

In this paper, we investigate an application of the statistical concept of causality, based on Granger’s definition of causality, on raw increasing processes as well as on optional and predictable measures. A raw increasing process is optional (predictable) if the bounded (left-continuous) process X, associated with the measure μA(X), is self-caused. Also, the measure μA(X) is optional (predictable) if an associated process X is self-caused with some additional assumptions. Some of the obtained results, in terms of self-causality, can be directly applied to defining conditions for an optional stopping time to become predictable.

Feature causality

The detection and understanding of reasons for defects and inadvertent behavior in software is challenging due to its ever increasing complexity. One major aspect contributing to this complexity is the multitude of features a user might select from in configurable systems. In this article, we tackle this challenge by introducing the notion of feature causality that identifies features and their interactions which are the reasons for a system showing certain functional and non-functional properties seen as effects. Feature causality operates at the level of system configurations and is based on counterfactual reasoning, inspired by the seminal definition of actual causality by Halpern and Pearl.Towards turning feature causality into meaningful explanations for the reasons why an effect emerges, we present various explication methods, e.g., by cause–effect covers, quantifications of causal impacts based on notions like responsibility and blame, causal reasoning with uncertainty, and feature interactions. Through a close connection of feature causality to prime implicants, we derive algorithms to effectively compute feature causes and causal explications. By means of an evaluation on a wide range of configurable software systems, including community benchmarks and real-world systems, we demonstrate the feasibility of our approach: We illustrate how our notion of causality facilitates to identify root causes, estimate the impact of features on effect properties, and detect feature interactions.

Discovering agents

Causal models of agents have been used to analyse the safety aspects of machine learning systems. But identifying agents is non-trivial – often the causal model is just assumed by the modeller without much justification – and modelling failures can lead to mistakes in the safety analysis. This paper proposes the first formal causal definition of agents – roughly that agents are systems that would adapt their policy if their actions influenced the world in a different way. From this we derive the first causal discovery algorithm for discovering the presence of agents from empirical data, given a set of variables and under certain assumptions. We also provide algorithms for translating between causal models and game-theoretic influence diagrams. We demonstrate our approach by resolving some previous confusions caused by incorrect causal modelling of agents.

Causal predictability between stochastic processes and filtrations

In this paper we further develop a notion of causal predictability defined in [A. Merkle, Predictability and Uniqueness of Weak Solutions of Stochastic Differential Equations, Analele Stiintifice ale Universitatii Ovidius Constanta, 2022] as a concept of dependence which is based on Granger's definition of causality. More precisely, in [A. Merkle, Predictability and Uniqueness of Weak Solutions of Stochastic Differential Equations, Analele Stiintifice ale Universitatii Ovidius Constanta, 2022] causal predictability is defined between filtrations, but now we introduce causal predictability between stochastic processes and filtrations. Also, we provide some properties of this new concept. Then we apply the given causality concept to the uniqueness of weak solutions of the stochastic differential equations and in financial mathematics. Granger [Investigating causal relations by econometric models and cross spectral methods, Econometrica. 37 (1969), pp. 424–438] has considered causality concept between time series. In this paper we consider continuous time processes, since continuous time models represent the first step in various applications, such as in finance, econometric practice, neuroscience, epidemiology, climatology, demographic, etc.

Analysis of the Impact of Global Oil Prices On GDP (on the Example of the Azerbaijan Republic)

Purpose of the study. The article analyzes the impact of world oil prices (external and internal factors) on the country’s GDP, considers fluctuations in world oil prices, their impact on the national economy of Azerbaijan and the integrability of these macroeconomic indexes. Materials and methods. The study of the dynamics of the functioning of time series based on the initial data revealed their non-stationarity, which does not allow creating a “qualitative” predictive model. In order to achieve the goals of the study and “improve the quality” of the model being formed, which is used to calculate predictive estimates, appropriate econometric procedures were carried out and the integrability of time series was investigated. In particular, the method of vector error correction model VECM is used. The test is based on the use of cointegration equations between variables, where lag lengths and Granger causality definitions are solved within this model. When forming the VECM model, the hypotheses put forward in the work were tested using econometric tests. The responses of the impulse function to the independent variables of the model were studied by the method of graphical representation based on the values of the model and its residuals.Results. It has been determined that the long-term equilibrium relationship between variables can be considered stable, since after short-term disturbances from shock reactions, stability is restored. The applied method of decomposition of forecast error variances to determine the influence of exogenous variables on the endogenous variable showed that the greatest uncertainty in the forecast for GDP, Azeri_light, Brent and West is given by their own changes during the first trimester of the period under consideration.Conclusion. The results obtained can be useful for identifying real trends in Azerbaijan’s GDP and determining its interdependencies with other macroeconomic variables, for determining its interdependencies with variations in energy prices based on an analysis of the dynamics of the indexes under consideration, for developing recommendations and forming directions for the longterm development of GDP.

The Necessity of Primary Causes: A Critique of Denis Edwards

AbstractIn this paper I will investigate a recent development on St Thomas Aquinas’ definition of dual causality and see if it truly develops Aquinas’ thinking or departs from it. Denis Edwards made significant contributions to contemporary Catholic theology especially as it concerns the relationship between science and Christian theology. In one very interesting publication, ‘Toward a Theology of Divine Action’, Edwards employs the developments of William R Stoeger, a Jesuit theologian who has also contributed a great deal to Catholic thought on science, to reconcile Stoeger's work with the Thomist tradition. Edwards argued that Stoeger's account of the laws of nature creates a space for the development which is built on Aquinas’ account of divine causality and miracles. However, I hope to show that Edwards’ account of divine causality does not actually offer anything new and opposes key features of Thomist thought. This paper will investigate Edward's understanding of the Thomist position and the consequences of departing from it.

Causal structure of interacting Weyl fermions in condensed matter systems

The spacetime light cone is central to the definition of causality in the theory of relativity. Recently, links between relativistic and condensed matter physics have been uncovered, where relativistic particles can emerge as quasiparticles in the energy-momentum space of matter. Here, we unveil an energy-momentum analogue of the spacetime light cone by mapping time to energy, space to momentum, and the light cone to the Weyl cone. We show that two Weyl quasiparticles can only interact to open a global energy gap if they lie in each other’s energy-momentum dispersion cones–analogous to two events that can only have a causal connection if they lie in each other’s light cones. Moreover, we demonstrate that the causality of surface chiral modes in quantum matter is entangled with the causality of bulk Weyl fermions. Furthermore, we identify a unique quantum horizon region and an associated ‘thick horizon’ in the emergent causal structure.

Deep recurrent modelling of Granger causality with latent confounding

Inferring causal relationships in observational time series data is an important task when interventions cannot be performed. Granger causality is a popular framework to infer potential causal mechanisms between different time series. The original definition of Granger causality is restricted to linear processes and leads to spurious conclusions in the presence of a latent confounder. To this end, we propose a deep learning model to detect non-linear Granger causality and directly account for latent confounders. Our approach consists of two components: 1. feed-forward neural networks to infer representations of the confounder from available proxy variables; 2. recurrent neural networks to construct forecasting models for the target time series with and without additional information. Conditioned on the proxy, if the target time series can be better predicted without extra information, our model concludes that the confounder alone Granger causes the target, and vice versa. To assess the proposed approach, we tested the model on both synthetic and real world time series with known causal relationships; results showed the superiority of our model relative to existing benchmarks.

Granger causality from quantized measurements

An approach is proposed for inferring Granger causality between jointly stationary, Gaussian signals from quantized data. First, a necessary and sufficient rank criterion for the equality of two conditional Gaussian distributions is proved. Assuming a partial finite-order Markov property, a characterization of Granger causality in terms of the rank of a matrix involving the covariances is presented. We call this the causality matrix. The smallest singular value of the causality matrix gives a lower bound on the distance between the two conditional Gaussian distributions appearing in the definition of Granger causality and yields a new measure of causality. Then, conditions are derived under which Granger causality between jointly Gaussian processes can be reliably inferred from the second order moments of quantized measurements. A necessary and sufficient condition is proposed for Granger causality inference under binary quantization. Furthermore, sufficient conditions are introduced to infer Granger causality between jointly Gaussian signals through measurements quantized via non-uniform or high resolution quantizers. Apart from the assumed partial Markov order and joint Gaussianity, this approach does not require the parameters of a system model to be identified. No assumptions are made on the identifiability of the jointly Gaussian random processes through the quantized observations. The effectiveness of the proposed method is illustrated by simulation results.

Causal mapping of human brain function.

Mapping human brain function is a long-standing goal of neuroscience that promises to inform the development of new treatments for brain disorders. Early maps of human brain function were based on locations of brain damage or brain stimulation that caused a functional change. Over time, this approach was largely replaced by technologies such as functional neuroimaging, which identify brain regions in which activity is correlated with behaviours or symptoms. Despite their advantages, these technologies reveal correlations, not causation. This creates challenges for interpreting the data generated from these tools and using them to develop treatments for brain disorders. A return to causal mapping of human brain function based on brain lesions and brain stimulation is underway. New approaches can combine these causal sources of information with modern neuroimaging and electrophysiology techniques to gain new insights into the functions of specific brain areas. In this Review, we provide a definition of causality for translational research, propose a continuum along which to assess the relative strength of causal information from human brain mapping studies and discuss recent advances in causal brain mapping and their relevance for developing treatments.