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We investigate the problem of inferring the causal predictors of a response Y from a set of d explanatory variables (X 1 , ..., X d ). Classical ordinary least-square regression includes all predictors that reduce the variance of Y. Using only the causal predictors instead leads to models that have the advantage of remaining invariant under interventions; loosely speaking they lead to invariance across different \"environments\" or \"heterogeneity patterns.\" More precisely, the conditional distribution of Y given its causal predictors is the same for all observations, provided that there are no interventions on Y. Recent work exploits such a stability to infer causal relations from data with different but known environments. We show that even without having knowledge of the environments or heterogeneity pattern, inferring causal relations is possible for time-ordered (or any other type of sequentially ordered) data. In particular, this allows detecting instantaneous causal relations in multivariate linear time series, which is usually not the case for Granger causality. Besides novel methodology, we provide statistical confidence bounds and asymptotic detection results for inferring causal predictors, and present an application to monetary policy in macroeconomics. Supplementary materials for this article are available online.

We consider the problem of learning causal information between random variables in directed acyclic graphs (DAGs) when allowing arbitrarily many latent and selection variables. The FCI (Fast Causal Inference) algorithm has been explicitly designed to infer conditional independence and causal information in such settings. However, FCI is computationally infeasible for large graphs. We therefore propose the new RFCI algorithm, which is much faster than FCI. In some situations the output of RFCI is slightly less informative, in particular with respect to conditional independence information. However, we prove that any causal information in the output of RFCI is correct in the asymptotic limit. We also define a class of graphs on which the outputs of FCI and RFCI are identical. We prove consistency of FCI and RFCI in sparse high-dimensional settings, and demonstrate in simulations that the estimation performances of the algorithms are very similar. All software is implemented in the R-package pcalg.

In discrete manufacturing, the knowledge about causal relationships makes it possible to avoid unforeseen production downtimes by identifying their root causes. Learning causal structures from real-world settings remains challenging due to high-dimensional data, a mix of discrete and continuous variables, and requirements for preprocessing log data under the causal perspective. In our work, we address these challenges proposing a process for causal reasoning based on raw machine log data from production monitoring. Within this process, we define a set of transformation rules to extract independent and identically distributed observations. Further, we incorporate a variable selection step to handle high-dimensionality and a discretization step to include continuous variables. We enrich a commonly used causal structure learning algorithm with domain-related orientation rules, which provides a basis for causal reasoning. We demonstrate the process on a real-world dataset from a globally operating precision mechanical engineering company. The dataset contains over 40 million log data entries from production monitoring of a single machine. In this context, we determine the causal structures embedded in operational processes. Further, we examine causal effects to support machine operators in avoiding unforeseen production stops, i.e., by detaining machine operators from drawing false conclusions on impacting factors of unforeseen production stops based on experience.

Childhood obesity is a complex disorder that appears to be influenced by an interacting system of many factors. Taking this complexity into account, we aim to investigate the causal structure underlying childhood obesity. Our focus is on identifying potential early, direct or indirect, causes of obesity which may be promising targets for prevention strategies. Using a causal discovery algorithm, we estimate a cohort causal graph (CCG) over the life course from childhood to adolescence. We adapt a popular method, the so-called PC-algorithm, to deal with missing values by multiple imputation, with mixed discrete and continuous variables, and that takes background knowledge such as the time-structure of cohort data into account. The algorithm is then applied to learn the causal structure among 51 variables including obesity, early life factors, diet, lifestyle, insulin resistance, puberty stage and cultural background of 5112 children from the European IDEFICS/I.Family cohort across three waves (2007–2014). The robustness of the learned causal structure is addressed in a series of alternative and sensitivity analyses; in particular, we use bootstrap resamples to assess the stability of aspects of the learned CCG. Our results suggest some but only indirect possible causal paths from early modifiable risk factors, such as audio-visual media consumption and physical activity, to obesity (measured by age- and sex-adjusted BMI z-scores) 6 years later.

We introduce a new method to estimate the Markov equivalence class of a directed acyclic graph (DAG) in the presence of hidden variables, in settings where the underlying DAG among the observed variables is sparse, and there are a few hidden variables that have a direct effect on many of the observed variables. Building on the so-called low rank plus sparse framework, we suggest a two-stage approach which first removes the effect of the hidden variables and then estimates the Markov equivalence class of the underlying DAG under the assumption that there are no remaining hidden variables. This approach is consistent in certain high dimensional regimes and performs favourably when compared with the state of the art, in terms of both graphical structure recovery and total causal effect estimation.

Digital mental health tools promise to enhance the reach and quality of care. Current tools often recommend content to individuals, typically using generic knowledge-based systems or predictive artificial intelligence (AI). However, predictive AI is problematic for interventional recommendations as cause-effect relationships can be confounded in observed data. Therefore, causal AI is required to compare future outcomes under different interventions. We aimed to develop a causal AI recommendation system that uses an individual's current presentation, their preferences, and the learned dynamics between domains to rank interventions. We frame the recommendation problem within a Bayesian decision-theoretic framework, whereby a preference ordering of decisions is estimated using the expected utility of outcomes under interventions. The causal processes are assumed to follow a structural causal model, where the posterior distribution of structural causal models is estimated using a Markov chain Monte Carlo method. Expected utilities under interventions are estimated using a do-operation, which estimates the effects of changing a variable on outcomes, while accounting for confounders. We apply our approach to rank domains relating to mental health and well-being as intervention targets for adults (n=619) who used the Innowell Fitness app between September 2021 to September 2023 and completed a questionnaire at 2 time points (1 wk-6 mo from baseline). The causal AI recommendation system recommends intervention targets as a function of a user's baseline presentation, the causal effects of the intervention on itself and other domains, and the utility function. In our example, psychological distress was typically the optimal intervention target in complex cases where multiple domains were unhealthy at baseline, due to it affecting multiple domains with paths to personal functioning (probability [p] of path; ppath=86%), social support (ppath=92%), sleep (ppath=88%), and physical activity (ppath=86%). The probability of being the optimal intervention target was personal functioning (popt=30%), psychological distress (popt=29%), social support (popt=18%), nutrition (popt=9.6%), substance use (popt=6.7%), sleep (popt=4.5%), and physical activity (popt=2.2%). This work illustrates the use of causality and decision-theoretic principles to personalize interventions in digital mental health tools.

Learning a directed acyclic graph (DAG) from observational data plays a crucial role in causal inference and machine learning. However, the scarcity of observational data is a common phenomenon in real-world applications, where the current DAG learning methods may cause unsatisfactory performance in the context of small data samples. Data enhancement has been recognized as one of the key techniques for improving the generalization abilities of learning models utilizing small data samples. However, due to the inherent difficulty of sampling small datasets to generate high-quality new data samples, this approach has not been widely used in DAG learning. To alleviate this problem, we propose a data enhancement-based DAG learning (DE-DAG) approach. Specifically, DE-DAG first presents an integrated data sampling strategy for DAG learning and data sampling, then constructs a sample-level adaptive distance computing algorithm for selecting high-quality samples from the sampled datasets, and finally implements a DAG learning method on enhanced datasets consisting of high-quality samples and the original data samples. Experimental results obtained on benchmark datasets demonstrate that our proposed approach outperforms the state-of-the-art baselines.

We consider the problem of estimating a high dimensional p × p covariance matrix Σ, given n observations of confounded data with covariance Σ + ΓΓT, where Γ is an unknown p × q matrix of latent factor loadings. We propose a simple and scalable estimator based on the projection onto the right singular vectors of the observed data matrix, which we call right singular vector projection (RSVP). Our theoretical analysis of this method reveals that, in contrast with approaches based on the removal of principal components, RSVP can cope well with settings where the smallest eigenvalue of ΓTΓ is relatively close to the largest eigenvalue of Σ, as well as when the eigenvalues of ΓTΓ are diverging fast. RSVP does not require knowledge or estimation of the number of latent factors q, but it recovers Σ only up to an unknown positive scale factor. We argue that this suffices in many applications, e.g. if an estimate of the correlation matrix is desired. We also showthat, by using subsampling,we can further improve the performance of the method. We demonstrate the favourable performance of RSVP through simulation experiments and an analysis of gene expression data sets collated by the GTEX consortium.

The development of technology has strongly affected regional urbanization. With development of mobile communication technology, intelligent devices have become increasingly widely used in people’s lives. The application of big data in urban computing is multidimensional; it has been involved in different fields, such as urban planning, network optimization, intelligent transportation, energy consumption and so on. Data analysis becomes particularly important for wireless networks. In this paper, a method for analyzing cellular traffic data was proposed. Firstly, a method to extract trend components, periodic components and essential components from complex traffic time series was proposed. Secondly, we introduced causality data mining. Different from traditional time series causality analysis, the depth of causal mining was increased. We conducted causality verification on different components of time series and the results showed that the causal relationship between base stations is different in trend component, periodic component and essential component in urban wireless network. This is crucial for urban planning and network management. Thirdly, DIC-ST: a spatial temporal time series prediction based on decomposition and integration system with causal structure learning was proposed by combining GCN. Final results showed that the proposed method significantly improves the accuracy of cellular traffic prediction. At the same time, this method can play a crucial role for urban computing in network management, intelligent transportation, base station siting and energy consumption when combined with remote sensing map information.

Personalized (patient-specific) approaches have recently emerged with a precision medicine paradigm that acknowledges the fact that molecular pathway structures and activity might be considerably different within and across tumors. The functional cancer genome and proteome provide rich sources of information to identify patient-specific variations in signaling pathways and activities within and across tumors; however, current analytic methods lack the ability to exploit the diverse and multi-layered architecture of these complex biological networks. We assessed pan-cancer pathway activities for >7700 patients across 32 tumor types from The Cancer Proteome Atlas by developing a personalized cancer-specific integrated network estimation (PRECISE) model. PRECISE is a general Bayesian framework for integrating existing interaction databases, data-driven de novo causal structures, and upstream molecular profiling data to estimate cancer-specific integrated networks, infer patient-specific networks and elicit interpretable pathway-level signatures. PRECISE-based pathway signatures, can delineate pan-cancer commonalities and differences in proteomic network biology within and across tumors, demonstrates robust tumor stratification that is both biologically and clinically informative and superior prognostic power compared to existing approaches. Towards establishing the translational relevance of the functional proteome in research and clinical settings, we provide an online, publicly available, comprehensive database and visualization repository of our findings ( https://mjha.shinyapps.io/PRECISE/ ).