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Many algorithms for inferring causality rely heavily on the faithfulness assumption. The main justification for imposing this assumption is that the set of unfaithful distributions has Lebesgue measure zero, since it can be seen as a collection of hypersurfaces in a hypercube. However, due to sampling error the faithfulness condition alone is not sufficient for statistical estimation, and strong-faithfulness has been proposed and assumed to achieve uniform or high-dimensional consistency. In contrast to the plain faithfulness assumption, the set of distributions that is not strong-faithful has nonzero Lebesgue measure and in fact, can be surprisingly large as we show in this paper. We study the strong-faithfulness condition from a geometric and combinatorial point of view and give upper and lower bounds on the Lebesgue measure of strong-faithful distributions for various classes of directed acyclic graphs. Our results imply fundamental limitations for the PC-algorithm and potentially also for other algorithms based on partial correlation testing in the Gaussian case.

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.

This paper introduces a modeling framework that integrates constraint-based causal discovery with predictive algorithms for oil market analysis. The methodology first applies the PC algorithm to identify a causal graph from heterogeneous market data. This graph then informs feature selection for a LightGBM model, constraining it to causally-relevant variables. Empirical results demonstrate that this approach maintains forecasting accuracy while providing interpretability through SHAP analysis and counterfactual reasoning. The derived causal structure corroborates established economic principles, highlighting inventory dynamics and regional arbitrage as primary price drivers.

This study explores dynamic relationships among Chinese housing prices for the years 2010–2019. With monthly data from 99 major cities in China, we use the vector error correction model and directed acyclic graph to characterize contemporaneous causality among housing prices from different tiers of cities. The PC algorithm identifies the causal pattern and the LiNGAM algorithm further identifies the causal path, from which we perform innovation accounting analysis. Complex housing price dynamics are found in the price adjustment process following price shocks, which is not only dominated by the top tiers of cities. This suggests that policies on housing prices in the long run might need to be planned from a national perspective.

We develop a novel hybrid method for Bayesian network structure learning called partitioned hybrid greedy search (pHGS), composed of three distinct yet compatible new algorithms: Partitioned PC (pPC) accelerates skeleton learning via a divide-and-conquer strategy, p-value adjacency thresholding (PATH) effectively accomplishes parameter tuning with a single execution, and hybrid greedy initialization (HGI) maximally utilizes constraint-based information to obtain a high-scoring and well-performing initial graph for greedy search. We establish structure learning consistency of our algorithms in the large-sample limit, and empirically validate our methods individually and collectively through extensive numerical comparisons. The combined merits of pPC and PATH achieve significant computational reductions compared to the PC algorithm without sacrificing the accuracy of estimated structures, and our generally applicable HGI strategy reliably improves the estimation structural accuracy of popular hybrid algorithms with negligible additional computational expense. Our empirical results demonstrate the competitive empirical performance of pHGS against many state-of-the-art structure learning algorithms.

Estimation of the skeleton of a directed acyclic graph (DAG) is of great importance for understanding the underlying DAG and causal effects can be assessed from the skeleton when the DAG is not identifiable. We propose a novel method named PenPC to estimate the skeleton of a high-dimensional DAG by a two-step approach. We first estimate the nonzero entries of a concentration matrix using penalized regression, and then fix the difference between the concentration matrix and the skeleton by evaluating a set of conditional independence hypotheses. For high-dimensional problems where the number of vertices p is in polynomial or exponential scale of sample size n, we study the asymptotic property of PenPC on two types of graphs: traditional random graphs where all the vertices have the same expected number of neighbors, and scale-free graphs where a few vertices may have a large number of neighbors. As illustrated by extensive simulations and applications on gene expression data of cancer patients, PenPC has higher sensitivity and specificity than the state-of-the-art method, the PC-stable algorithm.

Purpose This study aims to investigate dynamic relationships among residential housing price indices of ten major Chinese cities for the years 2005–2021. Design/methodology/approach Using monthly data, this study uses vector error correction modeling and the directed acyclic graph for characterization of contemporaneous causality among the ten indices. Findings The PC algorithm identifies the causal pattern and the Linear Non-Gaussian Acyclic Model algorithm further determines the causal path, from which this study conducts innovation accounting analysis. Sophisticated price dynamics are found in price adjustment processes following price shocks, which are generally dominated by the top tiers of cities. Originality/value This study suggests that policies on residential housing prices in the long run might need to be planned with particular attention paid to these top tiers of cities.

We assume that we have observational data generated from an unknown underlying directed acyclic graph (DAG) model. A DAG is typically not identifiable from observational data, but it is possible to consistently estimate the equivalence class of a DAG. Moreover, for any given DAG, causal effects can be estimated using intervention calculus. In this paper, we combine these two parts. For each DAG in the estimated equivalence class, we use intervention calculus to estimate the causal effects of the covariates on the response. This yields a collection of estimated causal effects for each covariate. We show that the distinct values in this set can be consistently estimated by an algorithm that uses only local information of the graph. This local approach is computationally fast and feasible in high-dimensional problems. We propose to use summary measures of the set of possible causal effects to determine variable importance. In particular, we use the minimum absolute value of this set, since that is a lower bound on the size of the causal effect. We demonstrate the merits of our methods in a simulation study and on a data set about riboflavin production.

Purpose This study aims to investigate dynamic relations among office property price indices of 10 major cities in China for the years 2005–2021. Design/methodology/approach Using monthly data, the authors adopt vector error correction modeling and the directed acyclic graph for the characterization of contemporaneous causality among the 10 indices. Findings The PC algorithm identifies the causal pattern, and the linear non-Gaussian acyclic model algorithm further determines the causal path from which we perform innovation accounting analysis. Sophisticated price dynamics are found in price adjustment processes following price shocks, which are generally dominated by the top tier of cities. Originality/value This suggests that policies on office property prices, in the long run, might need to be planned with particular attention paid to the top tier of cities.