Testing Conditional Independence in Psychometric Networks: An Analysis of Three Bayesian Methods

It is a common saying that testing for conditional independence, that is, testing whether whether two random vectors $X$ and $Y$ are independent, given $Z$, is a hard statistical problem if $Z$ is a continuous random variable (or vector). In this paper, we prove that conditional independence is indeed a particularly difficult hypothesis to test for. Valid statistical tests are required to have a size that is smaller than a pre-defined significance level, and different tests usually have power against a different class of alternatives. We prove that a valid test for conditional independence does not have power against any alternative. Given the nonexistence of a uniformly valid conditional independence test, we argue that tests must be designed so their suitability for a particular problem may be judged easily. To address this need, we propose in the case where $X$ and $Y$ are univariate to nonlinearly regress $X$ on $Z$, and $Y$ on $Z$ and then compute a test statistic based on the sample covariance between the residuals, which we call the generalised covariance measure (GCM). We prove that validity of this form of test relies almost entirely on the weak requirement that the regression procedures are able to estimate the conditional means $X$ given $Z$, and $Y$ given $Z$, at a slow rate. We extend the methodology to handle settings where $X$ and $Y$ may be multivariate or even high dimensional. While our general procedure can be tailored to the setting at hand by combining it with any regression technique, we develop the theoretical guarantees for kernel ridge regression. A simulation study shows that the test based on GCM is competitive with state of the art conditional independence tests. Code is available as the R package $\mathtt{GeneralisedCovarianceMeasure}$ on CRAN.

Conditional independence (CI) testing is an important problem, especially in causal discovery. Most testing methods assume that all variables are fully observable and then test the CI among the observed data. Such an assumption is often untenable beyond applications dealing with, e.g., psychological analysis about the mental health status and medical diagnosing (researchers need to consider the existence of latent variables in these scenarios); and typically adopted latent CI test schemes mainly suffer from robust or efficient issues. Accordingly, this article investigates the problem of testing CI between latent variables. To this end, we offer an auxiliary regression-based CI (AReCI) test by taking the measured variable as the surrogate variable of the latent variables to conduct the regression over the latent variables under the linear causal models, in which each latent variable has some certain measured variables. Specifically, given a pair of latent variables LX and LY , and a corresponding latent variable set LO , [Formula: see text] holds if and only if [Formula: see text] and [Formula: see text] are statistically independent, where A' and A'' are the two disjoint subset of the measured variable for the corresponding latent variables, A'{LO} ∩A''{LO} = ∅ , and ω1 is a parameter vector characterized from the cross covariance between A{LX} and A'{LO} , and ω2 is a parameter vector characterized from the cross covariance between A{LY} and A''{LO} . We theoretically show that the AReCI test is capable of addressing both Gaussian and non-Gaussian data. In addition, we find that the well-known partial correlation test can be seen as a special case of the AReCI test. Finally, we devise a causal discovery method by using the AReCI test as the CI test. The experimental results on synthetic and real-world data illustrate the effectiveness of our method.

The main purpose of this study aims to compare the scale level average scores of Dark Triad personality in China and the USA, as well as the correlation differences between three subscales of dark personality. The present study examined Dark Triad personality perceptions, and three big adult samples are selected in China and the USA separately (N1 = 507, N2 = 925, N3 = 1251). They all finished the Short Dark Triad (SD3) personality scale in paper-pencil or online format. Descriptive statistics of two comparison samples are presented. We took classical NHST and Bayesian method to test the cultural differences on scale scores. In Bayesian statistics, the results are relatively reliable. There are significant differences between China and the USA samples on narcissism and psychopathy, East get higher scores. China participants get lower scores than the USA on Machiavellianism. For the intercorrelations of subscales, some values and patterns are different significantly. Moreover, the results should be replicated in more research. The limitations and future directions of the present study also be discussed at the end of the study.

Causal knowledge is vital for effective reasoning in science, as causal relations, unlike correlations, allow one to reason about the outcomes of interventions. Algorithms that can discover causal relations from observational data are based on the assumption that all variables have been jointly measured in a single dataset. In many cases this assumption fails. Previous approaches to overcoming this shortcoming devised algorithms that returned all joint causal structures consistent with the conditional independence information contained in each individual dataset. But, as conditional independence tests only determine causal structure up to Markov equivalence, the number of consistent joint structures returned by these approaches can be quite large. The last decade has seen the development of elegant algorithms for discovering causal relations beyond conditional independence, which can distinguish among Markov equivalent structures. In this work we adapt and extend these so-called bivariate causal discovery algorithms to the problem of learning consistent causal structures from multiple datasets with overlapping variables belonging to the same generating process, providing a sound and complete algorithm that outperforms previous approaches on synthetic and real data.

A consistent characteristic function-based test for conditional independence

Bayesian networks are formal knowledge representation tools that provide reasoning under uncertainty. The applications of Bayesian networks are widespread, including data mining, information retrieval, and various diagnostic systems. Although Bayesian networks are useful, the learning problem, namely to construct a network automatically from data, remains a difficult problem. Recently, some researchers have adopted evolutionary computation for learning. However, the drawback is that the approach is slow. In this chapter, we propose a hybrid framework for Bayesian network learning. By combining the merits of two different learning approaches, we expect an improvement in learning speed. In brief, the new learning algorithm consists of two phases: the conditional independence (CI) test phase and the search phase. In the CI test phase, we conduct dependency analysis, which helps to reduce the search space. In the search phase, we perform model searching using an evolutionary approach, called cooperative coevolution. When comparing our new algorithm with an existing algorithm, we find that our algorithm performs faster and is more accurate in many cases.

. A new metric, called variation of conditional mean (VCM), is proposed to measure the dependence of conditional mean of a response variable on a predictor variable. The VCM has several appealing merits. It equals zero if and only if the conditional mean of the response is independent of the predictor; it can be used for both real vector-valued variables and functional data. An estimator of the VCM is given through kernel smoothing, and a test for the conditional mean independence based on the estimated VCM is constructed. The limit distributions of the test statistic under the null hypothesis and alternative hypothesis are deduced, respectively. We further use VCM as a marginal utility to do high-dimensional feature screening to screen out variables that do not contribute to the conditional mean of the response given the predictors and prove the validity of the sure screening property. Furthermore, we find the cross variation of conditional mean (CVCM), a variant of the VCM, has a faster convergence rate than the VCM under conditional mean independence. Numerical comparison shows that the VCM and CVCM performs well in both conditional independence testing and feature screening. We also illustrate their applications to real data sets.

Current estimates of the contribution of education to economic growth have been questioned because they ignore the interaction of education with ability. Whether the neglect of ability differences in the analyses of the income-education relationship results in estimates that are too high was considered in an earlier paper by one of the authors (Griliches 1970), and a negative answer was conjectured. In this paper, we pursue this question a bit further, using a new and larger body of data. Unfortunately, a definitive answer to this question is hampered both by the vagueness and elasticity of "education" and "ability" as analytical concepts and by the lack of data on early (preschooling) intelligence. The data examined in this paper are based on a 1964 sample of U.S. military veterans. The variables measured include scores on a mental ability test, indicators of parental status, region of residence while growing up, school years completed before service, and school years completed during or after service. These have allowed us to inquire into the separate effects of parental background, intelligence, and schooling. The basic problem and analytical framework can be set out very simply. Let income be a linear function of education and ability, or, Y a + P1E + P(2G + u, where Y is income, E is education, G is ability,

Recently, regression based conditional independence (CI) tests have been employed to solve the problem of causal discovery. These methods provide an alternative way to test for CI by transforming CI to independence between residuals. Generally, it is nontrivial to check for independence when these residuals are linearly uncorrelated. With the ability to represent high-order moments, kernel-based methods are usually used to achieve this goal, but at a cost of considerable time. In this paper, we investigate the independence between two linear combinations under linear non-Gaussian structural equation model (SEM). We show that generally the 1-st to 4-th moments of the two linear combinations contain enough information to infer whether or not they are independent. The proposed method provides a simpler but more effective way to measure CIs, with only calculating the 1-st to 4-th moments of the input variables. When applied to causal discovery, the proposed method outperforms kernel-based methods in terms of both speed and accuracy. which is validated by extensive experiments.

In the genotyped-proband design, a proband is selected based on an observed phenotype, the genotype of the proband is observed, and then the phenotypes of all first-degree relatives are obtained. The genotypes of these first-degree relatives are not observed. Gail et al. [(1999) Genet Epidemiol] discuss likelihood analysis of this design under the assumption that the phenotypes are conditionally independent of one another given the observed and unobserved genotypes. Li and Thompson [(1997) Biometrics 53:282–293] give an example where this assumption is suspect, thus suggesting that it is important to develop tests for conditional independence. In this paper, we develop a score test for the conditional independence assumption in models that might include covariates or observation of genotypes for some of the first degree relatives. The problem can be cast more generally as one of score testing in the presence of missing covariates. A standard analysis would require specifying a distribution for the covariates, which is not convenient and could lead to a lack of model-robustness. We show that by considering a natural conditional likelihood, and basing the score test on it, a simple analysis results. The methods are applied to a study of the penetrance for breast cancer of BRCA1 and BRCA2 mutations among Ashkenazi Jews. Genet. Epidemiol. 18:293–306, 2000. © 2000 Wiley-Liss, Inc.

Based on benchmarking various methods and analyzing multiple real scRNA-seq datasets, a computational platform/workflow and a set of tips for best practices are developed for analyzing causal interactions or relationships in single cells.

The understanding of co-movements, dependence, and influence between variables of interest is key in many applications. Broadly speaking such understanding can lead to better predictions and decision making in many settings. We propose Quantile Graphical Models (QGMs) to characterize prediction and conditional independence relationships within a set of random variables of interest. Although those models are of interest in a variety of applications, we draw our motivation and contribute to the financial risk management literature. Importantly, the proposed framework is intended to be applied to non-Gaussian settings, which are ubiquitous in many real applications, and to handle a large number of variables and conditioning events. We propose two distinct QGMs. First, Condition Independence Quantile Graphical Models (CIQGMs) characterize conditional independence at each quantile index revealing the distributional dependence structure. Second, Prediction Quantile Graphical Models (PQGMs) characterize the best linear predictor under asymmetric loss functions. A key difference between those models is the (non-vanishing) misspecification between the best linear predictor and the conditional quantile functions. We also propose estimators for those QGMs. Due to high-dimensionality, the two distinct QGMs require different estimators. The estimators are based on high-dimensional techniques including (a continuum of) `1-penalized quantile regressions (and low biased equations), which allow us to handle the potential large number of variables. We build upon a recent literature to obtain new results for valid choice of the penalty parameters, rates of convergence, and confidence regions that are simultaneously valid. We illustrate how to use QGMs to quantify tail interdependence (instead of mean dependence) between a large set of variables which is relevant in applications concerning with extreme events. We show that the associated tail risk network can be used for measuring systemic risk contributions. We also apply the framework to study international financial contagion and the impact of market downside movement on the dependence structure of assets' returns.

DT-Planner: an environment for managing dynamic decision problems

Markov decision processes (MDPs) allow to represent a wide class of problems in medical decision making and control. The complexity of the algorithms used to search the best policy of a MDP is directly related with the dimensionality of the state space. A careful structuring of the state space is hence an important task in the MDP specification. Graphical models are particularly appealing to cope with this task. Here, the authors describe a novel graphical formalism for MDP knowledge acquisition called Influence View (IV). An IV is a directed acyclic graph that depicts the probabilistic relationships between the problem state variables in a generic time transition; additional variables, called event variables, may be added, in order to describe the conditional independencies between state variables. By using the specified conditional independence structure, an TV may allow a parsimonious specification of a MDP. The authors have applied this methodology to the GVHD prophylaxis after Bone Marrow Transplantation.

Streaming feature-based causal structure learning algorithm with symmetrical uncertainty