Constraint-based Causal Discovery Research Articles

Construction of time series causal network based on partial rank correlation

Discovering causal relationships from time series data is a significant research area in data mining. To tackle the challenges of identifying and constructing causal networks in non-linear, high-dimensional time series data, we introduce the partial rank correlation coefficient and propose two new structure learning algorithms suitable for time-series causal network modeling. In this paper, we make three main contributions. Firstly, we demonstrate the suitability of the partial rank correlation as a criterion for independence testing. Secondly, by integrating the partial rank correlation with constraint-based causal discovery methods, we propose the TS-PRCS algorithm for temporal causal network discovery. Thirdly, we combine ideas from local learning, constraint-based methods, and score-based search to propose the TS-MCHC algorithm, which combines mixed constraints and hill-climbing search for time-series causal discovery. Finally, we validate the effectiveness of the TS-PRCS and TS-MCHC algorithms through experiments on both simulated and real-world data. Compared to existing methods, our proposed algorithms exhibit robust causal detection capabilities in diverse non-linear environments and demonstrate efficient performance in high-dimensional time series networks. The experimental results affirm the ability of our methods to effectively uncover causal relationships among time series data, presenting promising prospects for practical applications.

Differentially Private Nonlinear Causal Discovery from Numerical Data

Recently, several methods such as private ANM, EM-PC and Priv-PC have been proposed to perform differentially private causal discovery in various scenarios including bivariate, multivariate Gaussian and categorical cases. However, there is little effort on how to conduct private nonlinear causal discovery from numerical data. This work tries to challenge this problem. To this end, we propose a method to infer nonlinear causal relations from observed numerical data by using regression-based conditional independence test (RCIT) that consists of kernel ridge regression (KRR) and Hilbert-Schmidt independence criterion (HSIC) with permutation approximation. Sensitivity analysis for RCIT is given and a private constraint-based causal discovery framework with differential privacy guarantee is developed. Extensive simulations and real-world experiments for both conditional independence test and causal discovery are conducted, which show that our method is effective in handling nonlinear numerical cases and easy to implement. The source code of our method and data are available at https://github.com/Causality-Inference/PCD.

The structure of dimensions of psychopathology in normative and clinical samples: Applying causal discovery to MMPI-2-RF scales to investigate clustering of psychopathology spectra and p-factors.

We applied a Bayesian Constraint-based Causal Discovery method (BCCD) to examine the hierarchical structure of the Minnesota Multiphasic Personality Inventory-2-Restructured Form (MMPI-2-RF) Restructured Clinical (RC) scales. Two different general psychopathology super spectra (p-factor) scales were extracted from (1) all RC scales and (2) all RC scales except the RCd (Demoralization) scale. These p-factor scales were included in separate models to investigate the structure of dimensions of psychopathology in a normative (n = 3,242) and clinical (n = 2,466) sample, as well as the combined normative/clinical sample (N = 5,708), by applying the BCCD algorithm to obtain a data-driven reconstruction of the internal hierarchical structure of the MMPI-2-RF. Research on the underlying structure of the MMPI-2-RF has clinical relevance as well as conceptual relevance in the context of the HiTOP model. Results demonstrated that the syndromes measured with the RC-scales-in presence of a p-factor-cluster into six spectra: internalizing, disinhibited-externalizing, antagonistic-externalizing, thought disorder, detachment, and somatoform. These results may support a super spectrum construct, as it was necessary for obtaining a bottom-up reconstruction of this six-spectrum structure. We found support for superiority of a broad super spectrum with additional variance over and above demoralization, as it resulted in the clearest structure (i.e., clustering of the RC scales). Furthermore, our results indicate independent support for the bifactor structure model of psychopathology.

Multiple imputation and test‐wise deletion for causal discovery with incomplete cohort data

Causal discovery algorithms estimate causal graphs from observational data. This can provide a valuable complement to analyses focusing on the causal relation between individual treatment-outcome pairs. Constraint-based causal discovery algorithms rely on conditional independence testing when building the graph. Until recently, these algorithms have been unable to handle missing values. In this article, we investigate two alternative solutions: test-wise deletion and multiple imputation. We establish necessary and sufficient conditions for the recoverability of causal structures under test-wise deletion, and argue that multiple imputation is more challenging in the context of causal discovery than for estimation. We conduct an extensive comparison by simulating from benchmark causal graphs: as one might expect, we find that test-wise deletion and multiple imputation both clearly outperform list-wise deletion and single imputation. Crucially, our results further suggest that multiple imputation is especially useful in settings with a small number of either Gaussian or discrete variables, but when the dataset contains a mix of both neither method is uniformly best. The methods we compare include random forest imputation and a hybrid procedure combining test-wise deletion and multiple imputation. An application to data from the IDEFICS cohort study on diet- and lifestyle-related diseases in European children serves as an illustrating example.

Causal Discovery of Gene Regulation with Incomplete Data

SummaryCausal discovery algorithms aim to identify causal relations from observational data and have become a popular tool for analysing genetic regulatory systems. In this work, we applied causal discovery to obtain novel insights into the genetic regulation underlying head-and-neck squamous cell carcinoma. Some methodological challenges needed to be resolved first. The available data contained missing values, but most approaches to causal discovery require complete data. Hence, we propose a new procedure combining constraint-based causal discovery with multiple imputation. This is based on using Rubin's rules for pooling tests of conditional independence. A second challenge was that causal discovery relies on strong assumptions and can be rather unstable. To assess the robustness of our results, we supplemented our investigation with sensitivity analyses, including a non-parametric bootstrap to quantify the variability of the estimated causal structures. We applied these methods to investigate how the high mobility group AT-Hook 2 (HMGA2) gene is incorporated in the protein 53 signalling pathway playing an important role in head-and-neck squamous cell carcinoma. Our results were quite stable and found direct associations between HMGA2 and other relevant proteins, but they did not provide clear support for the claim that HMGA2 itself is a key regulator gene.

Discovering causal graphs with cycles and latent confounders: An exact branch-and-bound approach

Understanding causal relationships is a central challenge in many research endeavours. Recent research has shown the importance of accounting for feedback (cycles) and latent confounding variables, as they are prominently present in many data analysis settings. However, allowing for cycles and latent confounders makes the structure learning task especially challenging. The constraint-based approach is able to learn causal graphs even over such general search spaces, but to obtain high accuracy, the conflicting (in)dependence information in sample data need to be resolved optimally. In this work, we develop a new practical algorithmic approach to solve this computationally challenging combinatorial optimization problem. While recent advances in exact algorithmic approaches for constraint-based causal discovery build upon off-the-shelf declarative optimization solvers, we propose a first specialized branch-and-bound style exact search algorithm. Our problem-oriented approach enables directly incorporating domain knowledge for developing a wider range of specialized search techniques for the problem, including problem-specific propagators and reasoning rules, and branching heuristics together with linear programming based bounding techniques, as well as directly incorporating different constraints on the search space, such as sparsity and acyclicity constraints. We empirically evaluate our implementation of the approach, showing that it outperforms current state of art in exact constraint-based causal discovery on real-world instances.

A constraint-based algorithm for causal discovery with cycles, latent variables and selection bias

Causal processes in nature may contain cycles, and real datasets may violate causal sufficiency as well as contain selection bias. No constraint-based causal discovery algorithm can currently handle cycles, latent variables and selection bias (CLS) simultaneously. I therefore introduce an algorithm called cyclic causal inference (CCI) that makes sound inferences with a conditional independence oracle under CLS, provided that we can represent the cyclic causal process as a non-recursive linear structural equation model with independent errors. Empirical results show that CCI outperforms the cyclic causal discovery algorithm in the cyclic case as well as rivals the fast causal inference and really fast causal inference algorithms in the acyclic case. An R implementation is available at https://github.com/ericstrobl/CCI .

Correction to: Constraint-based causal discovery with mixed data

The article “Constraint-based causal discovery with mixed data,” written by Michail Tsagris, Giorgos Borboudakis, Vincenzo Lagani, and Ioannis Tsamardinos, was originally published electronically on the publisher’s internet portal (currently SpringerLink) on February 2, 2018, without open access.

Constraint-based causal discovery with mixed data

We address the problem of constraint-based causal discovery with mixed data types, such as (but not limited to) continuous, binary, multinomial, and ordinal variables. We use likelihood-ratio tests based on appropriate regression models and show how to derive symmetric conditional independence tests. Such tests can then be directly used by existing constraint-based methods with mixed data, such as the PC and FCI algorithms for learning Bayesian networks and maximal ancestral graphs, respectively. In experiments on simulated Bayesian networks, we employ the PC algorithm with different conditional independence tests for mixed data and show that the proposed approach outperforms alternatives in terms of learning accuracy.

Causal Discovery from Nonstationary/Heterogeneous Data: Skeleton Estimation and Orientation Determination.

It is commonplace to encounter nonstationary or heterogeneous data, of which the underlying generating process changes over time or across data sets (the data sets may have different experimental conditions or data collection conditions). Such a distribution shift feature presents both challenges and opportunities for causal discovery. In this paper we develop a principled framework for causal discovery from such data, called Constraint-based causal Discovery from Nonstationary/heterogeneous Data (CD-NOD), which addresses two important questions. First, we propose an enhanced constraint-based procedure to detect variables whose local mechanisms change and recover the skeleton of the causal structure over observed variables. Second, we present a way to determine causal orientations by making use of independence changes in the data distribution implied by the underlying causal model, benefiting from information carried by changing distributions. Experimental results on various synthetic and real-world data sets are presented to demonstrate the efficacy of our methods.

Evaluating WAIS–IV structure through a different psychometric lens: structural causal model discovery as an alternative to confirmatory factor analysis

Objective: Since the publication of the WAIS–IV in the U.S. in 2008, efforts have been made to explore the structural validity by applying factor analysis to various samples. This study aims to achieve a more fine-grained understanding of the structure of the Dutch language version of the WAIS–IV (WAIS–IV–NL) by applying an alternative analysis based on causal modeling in addition to confirmatory factor analysis (CFA). The Bayesian Constraint-based Causal Discovery (BCCD) algorithm learns underlying network structures directly from data and assesses more complex structures than is possible with factor analysis. Method: WAIS–IV–NL profiles of two clinical samples of 202 patients (i.e. patients with temporal lobe epilepsy and a mixed psychiatric outpatient group) were analyzed and contrasted with a matched control group (N = 202) selected from the Dutch standardization sample of the WAIS–IV–NL to investigate internal structure by means of CFA and BCCD. Results: With CFA, the four-factor structure as proposed by Wechsler demonstrates acceptable fit in all three subsamples. However, BCCD revealed three consistent clusters (verbal comprehension, visual processing, and processing speed) in all three subsamples. The combination of Arithmetic and Digit Span as a coherent working memory factor could not be verified, and Matrix Reasoning appeared to be isolated. Conclusions: With BCCD, some discrepancies from the proposed four-factor structure are exemplified. Furthermore, these results fit CHC theory of intelligence more clearly. Consistent clustering patterns indicate these results are robust. The structural causal discovery approach may be helpful in better interpreting existing tests, the development of new tests, and aid in diagnostic instruments.

Discovery of Causal Models that Contain Latent Variables through Bayesian Scoring of Independence Constraints.

Discovering causal structure from observational data in the presence of latent variables remains an active research area. Constraint-based causal discovery algorithms are relatively efficient at discovering such causal models from data using independence tests. Typically, however, they derive and output only one such model. In contrast, Bayesian methods can generate and probabilistically score multiple models, outputting the most probable one; however, they are often computationally infeasible to apply when modeling latent variables. We introduce a hybrid method that derives a Bayesian probability that the set of independence tests associated with a given causal model are jointly correct. Using this constraint-based scoring method, we are able to score multiple causal models, which possibly contain latent variables, and output the most probable one. The structure-discovery performance of the proposed method is compared to an existing constraint-based method (RFCI) using data generated from several previously published Bayesian networks. The structural Hamming distances of the output models improved when using the proposed method compared to RFCI, especially for small sample sizes.

Handling hybrid and missing data in constraint-based causal discovery to study the etiology of ADHD

Causal discovery is an increasingly important method for data analysis in the field of medical research. In this paper, we consider two challenges in causal discovery that occur very often when working with medical data: a mixture of discrete and continuous variables and a substantial amount of missing values. To the best of our knowledge, there are no methods that can handle both challenges at the same time. In this paper, we develop a new method that can handle these challenges based on the assumption that data are missing at random and that continuous variables obey a non-paranormal distribution. We demonstrate the validity of our approach for causal discovery on simulated data as well as on two real-world data sets from a monetary incentive delay task and a reversal learning task. Our results help in the understanding of the etiology of attention-deficit/hyperactivity disorder (ADHD).

On Estimation of Functional Causal Models

Compared to constraint-based causal discovery, causal discovery based on functional causal models is able to identify the whole causal model under appropriate assumptions [Shimizu et al. 2006; Hoyer et al. 2009; Zhang and Hyvärinen 2009b]. Functional causal models represent the effect as a function of the direct causes together with an independent noise term. Examples include the linear non-Gaussian acyclic model (LiNGAM), nonlinear additive noise model, and post-nonlinear (PNL) model. Currently, there are two ways to estimate the parameters in the models: dependence minimization and maximum likelihood. In this article, we show that for any acyclic functional causal model, minimizing the mutual information between the hypothetical cause and the noise term is equivalent to maximizing the data likelihood with a flexible model for the distribution of the noise term. We then focus on estimation of the PNL causal model and propose to estimate it with the warped Gaussian process with the noise modeled by the mixture of Gaussians. As a Bayesian nonparametric approach, it outperforms the previous one based on mutual information minimization with nonlinear functions represented by multilayer perceptrons; we also show that unlike the ordinary regression, estimation results of the PNL causal model are sensitive to the assumption on the noise distribution. Experimental results on both synthetic and real data support our theoretical claims.

Causal discovery in an adult ADHD data set suggests indirect link between DAT1 genetic variants and striatal brain activation during reward processing.

Attention-deficit/hyperactivity disorder (ADHD) is a common and highly heritable disorder affecting both children and adults. One of the candidate genes for ADHD is DAT1, encoding the dopamine transporter. In an attempt to clarify its mode of action, we assessed brain activity during the reward anticipation phase of the Monetary Incentive Delay (MID) task in a functional MRI paradigm in 87 adult participants with ADHD and 77 controls (average age 36.5 years). The MID task activates the ventral striatum, where DAT1 is most highly expressed. A previous analysis based on standard statistical techniques did not show any significant dependencies between a variant in the DAT1 gene and brain activation [Hoogman et al. (2013); Neuropsychopharm 23:469-478]. Here, we used an alternative method for analyzing the data, that is, causal modeling. The Bayesian Constraint-based Causal Discovery (BCCD) algorithm [Claassen and Heskes (2012); Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence] is able to find direct and indirect dependencies between variables, determines the strength of the dependencies, and provides a graphical visualization to interpret the results. Through BCCD one gets an opportunity to consider several variables together and to infer causal relations between them. Application of the BCCD algorithm confirmed that there is no evidence of a direct link between DAT1 genetic variability and brain activation, but suggested an indirect link mediated through inattention symptoms and diagnostic status of ADHD. Our finding of an indirect link of DAT1 with striatal activity during reward anticipation might explain existing discrepancies in the current literature. Further experiments should confirm this hypothesis. © 2015 Wiley Periodicals, Inc.

Constraint-based causal discovery from multiple interventions over overlapping variable sets

Scientific practice typically involves repeatedly studying a system, each time trying to unravel a different perspective. In each study, the scientist may take measurements under different experime...

A causal discovery algorithm using multiple regressions

The purpose of a constraint-based causal discovery algorithm (CDA) is to find a directed acyclic graph which is observationally equivalent to the non-interventional data. Limiting the data to follow multivariate Gaussian distribution, existing such algorithms perform conditional independence (CI) tests to compute the graph structure by comparing pairs of nodes independently. In this paper, however, we propose Multiple Search algorithm which performs CI tests on multiple pairs of nodes simultaneously. Furthermore, compared to existing CDAs, the proposed algorithm searches a smaller number of conditioning sets because it continuously removes irrelevant nodes, and generates more-reliable solutions by double-checking the graph structures. We show the effectiveness of the proposed algorithm by comparison with Grow–Shrink and Collider Set algorithms through numerical experiments based on six networks.