cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.26820293
title: TSLiNGAM: DirectLiNGAM Under Heavy Tails

description: One of the established approaches to causal discovery consists of combining directed acyclic graphs (DAGs) with structural causal models (SCMs) to describe the functional dependencies of effects on their causes. Possible identifiability of SCMs given data depends on assumptions made on the noise variables and the functional classes in the SCM. For instance, in the LiNGAM model, the functional class is restricted to linear functions and the disturbances have to be non-Gaussian. In this work, we propose TSLiNGAM, a new method for identifying the DAG of a causal model based on observational data. TSLiNGAM builds on DirectLiNGAM, a popular algorithm which uses simple OLS regression for identifying causal directions between variables. TSLiNGAM leverages the non-Gaussianity assumption of the error terms in the LiNGAM model to obtain more efficient and robust estimation of the causal structure. TSLiNGAM is justified theoretically and is studied empirically in an extensive simulation study. It performs significantly better on heavy-tailed and skewed data and demonstrates a high small-sample efficiency. In addition, TSLiNGAM also shows better robustness properties as it is more resilient to contamination. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.26820293.v2
title: TSLiNGAM: DirectLiNGAM Under Heavy Tails

description: One of the established approaches to causal discovery consists of combining directed acyclic graphs (DAGs) with structural causal models (SCMs) to describe the functional dependencies of effects on their causes. Possible identifiability of SCMs given data depends on assumptions made on the noise variables and the functional classes in the SCM. For instance, in the LiNGAM model, the functional class is restricted to linear functions and the disturbances have to be non-Gaussian. In this work, we propose TSLiNGAM, a new method for identifying the DAG of a causal model based on observational data. TSLiNGAM builds on DirectLiNGAM, a popular algorithm which uses simple OLS regression for identifying causal directions between variables. TSLiNGAM leverages the non-Gaussianity assumption of the error terms in the LiNGAM model to obtain more efficient and robust estimation of the causal structure. TSLiNGAM is justified theoretically and is studied empirically in an extensive simulation study. It performs significantly better on heavy-tailed and skewed data and demonstrates a high small-sample efficiency. In addition, TSLiNGAM also shows better robustness properties as it is more resilient to contamination. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.27122583
title: Multivariate Moment Least-Squares Variance Estimators for Reversible Markov Chains

description: Markov chain Monte Carlo (MCMC) is a commonly used method for approximating expectations with respect to probability distributions. Uncertainty assessment for MCMC estimators is essential in practical applications. Moreover, for multivariate functions of a Markov chain, it is important to estimate not only the auto-correlation for each component but also to estimate cross-correlations, in order to better assess sample quality, improve estimates of effective sample size, and use more effective stopping rules. <i>Berg and Song</i> introduced the moment least squares (momentLS) estimator, a shape-constrained estimator for the autocovariance sequence from a reversible Markov chain, for univariate functions of the Markov chain. Based on this sequence estimator, they proposed an estimator of the asymptotic variance of the sample mean from MCMC samples. In this study, we propose novel autocovariance sequence and asymptotic variance estimators for Markov chain functions with multiple components, based on the univariate momentLS estimators from <i>Berg and Song</i>. We demonstrate strong consistency of the proposed auto(cross)-covariance sequence and asymptotic variance matrix estimators. We conduct empirical comparisons of our method with other state-of-the-art approaches on simulated and real-data examples, using popular samplers including the random-walk Metropolis sampler and the No-U-Turn sampler from STAN. Supplemental materials for this article are available online.
DOI: 10.6084/m9.figshare.27629156
title: Ms.FPOP: A Fast Exact Segmentation Algorithm with a Multiscale Penalty

description: Given a time series in Rn with a piecewise constant mean and independent noises, we propose an exact dynamic programming algorithm for minimizing a least-squares criterion with a multiscale penalty, favoring well-spread changepoints. This penalty was proposed by Verzelen et al. and achieves optimal rates for changepoint detection and changepoint localization in a non-asymptotic scenario. Our proposed algorithm, Multiscale Functional Pruning Optimal Partitioning (Ms.FPOP), extends functional pruning ideas presented in Rigaill and Maidstone et al. to multiscale penalties. For large signals (n≥105) with sparse changepoints, Ms.FPOP is shown empirically to be quasi-linear and faster than the Pruned Exact Linear Time (PELT) method of Killick et al. applied to the multiscale penalty of Verzelen et al. which exhibits quadratic slowdown in these cases. We propose an efficient implementation of Ms.FPOP coded in C++ interfaced with R that can segment profiles of up to n=106 in a matter of seconds. Our algorithm works for slightly more general multiscale penalties. In particular, it allows a minimum segment length to be imposed. Using simple simulations we then show that where profiles are sufficiently large (n≥104), Ms.FPOP using the multiscale penalty of Verzelen et al. is typically more powerful than optimizing a least-squares criterion with the BIC penalty of Yao, a criterion that was shown by Fearnhead and Rigaill to perfom well across a wide range of scenarios. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.27629156.v2
title: Ms.FPOP: A Fast Exact Segmentation Algorithm with a Multiscale Penalty

description: Given a time series in Rn with a piecewise constant mean and independent noises, we propose an exact dynamic programming algorithm for minimizing a least-squares criterion with a multiscale penalty, favoring well-spread changepoints. This penalty was proposed by Verzelen et al. and achieves optimal rates for changepoint detection and changepoint localization in a non-asymptotic scenario. Our proposed algorithm, Multiscale Functional Pruning Optimal Partitioning (Ms.FPOP), extends functional pruning ideas presented in Rigaill and Maidstone et al. to multiscale penalties. For large signals (n≥105) with sparse changepoints, Ms.FPOP is shown empirically to be quasi-linear and faster than the Pruned Exact Linear Time (PELT) method of Killick et al. applied to the multiscale penalty of Verzelen et al. which exhibits quadratic slowdown in these cases. We propose an efficient implementation of Ms.FPOP coded in C++ interfaced with R that can segment profiles of up to n=106 in a matter of seconds. Our algorithm works for slightly more general multiscale penalties. In particular, it allows a minimum segment length to be imposed. Using simple simulations we then show that where profiles are sufficiently large (n≥104), Ms.FPOP using the multiscale penalty of Verzelen et al. is typically more powerful than optimizing a least-squares criterion with the BIC penalty of Yao, a criterion that was shown by Fearnhead and Rigaill to perfom well across a wide range of scenarios. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.26504002
title: Using Rejection Sampling Probability of Acceptance as a Measure of Independence

description: This article proposes a new association statistic for determining whether random variables are statistically independent. The proposed association statistic can also be used to examine the strength of both linear and nonlinear dependency between variables. This statistic is derived by examining how the conditional probabilities of events differ from their corresponding marginal probabilities. The new statistic is defined in terms of the probability of acceptance commonly associated with the Accept–Reject algorithm and has a very simple formula. The simulated density of the probability of acceptance can be used to measure the degree of uncertainty of the estimated values of the new association statistic. The results from simulations as well as examples that employ real data indicate that this new association statistic is very powerful in detecting linear and nonlinear associations between two random variables. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.26504002.v2
title: Using Rejection Sampling Probability of Acceptance as a Measure of Independence

description: This article proposes a new association statistic for determining whether random variables are statistically independent. The proposed association statistic can also be used to examine the strength of both linear and nonlinear dependency between variables. This statistic is derived by examining how the conditional probabilities of events differ from their corresponding marginal probabilities. The new statistic is defined in terms of the probability of acceptance commonly associated with the Accept–Reject algorithm and has a very simple formula. The simulated density of the probability of acceptance can be used to measure the degree of uncertainty of the estimated values of the new association statistic. The results from simulations as well as examples that employ real data indicate that this new association statistic is very powerful in detecting linear and nonlinear associations between two random variables. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.26820293.v1
title: TSLiNGAM: DirectLiNGAM under heavy tails

description: One of the established approaches to causal discovery consists of combining directed acyclic graphs (DAGs) with structural causal models (SCMs) to describe the functional dependencies of effects on their causes. Possible identifiability of SCMs given data depends on assumptions made on the noise variables and the functional classes in the SCM. For instance, in the LiNGAM model, the functional class is restricted to linear functions and the disturbances have to be non-Gaussian. In this work, we propose TSLiNGAM, a new method for identifying the DAG of a causal model based on observational data. TSLiNGAM builds on DirectLiNGAM, a popular algorithm which uses simple OLS regression for identifying causal directions between variables. TSLiNGAM leverages the non-Gaussianity assumption of the error terms in the LiNGAM model to obtain more efficient and robust estimation of the causal structure. TSLiNGAM is justified theoretically and is studied empirically in an extensive simulation study. It performs significantly better on heavy-tailed and skewed data and demonstrates a high small-sample efficiency. In addition, TSLiNGAM also shows better robustness properties as it is more resilient to contamination. Supplementary Materials for this article are available online.
DOI: 10.6084/m9.figshare.27122583.v1
title: Multivariate moment least-squares variance estimators for reversible Markov chains

description: Markov chain Monte Carlo (MCMC) is a commonly used method for approximating expectations with respect to probability distributions. Uncertainty assessment for MCMC estimators is essential in practical applications. Moreover, for multivariate functions of a Markov chain, it is important to estimate not only the auto-correlation for each component but also to estimate cross-correlations, in order to better assess sample quality, improve estimates of effective sample size, and use more effective stopping rules. Berg and Song (2023) introduced the moment least squares (momentLS) estimator, a shape-constrained estimator for the autocovariance sequence from a reversible Markov chain, for univariate functions of the Markov chain. Based on this sequence estimator, they proposed an estimator of the asymptotic variance of the sample mean from MCMC samples. In this study, we propose novel autocovariance sequence and asymptotic variance estimators for Markov chain functions with multiple components, based on the univariate momentLS estimators from Berg and Song (2023). We demonstrate strong consistency of the proposed auto(cross)-covariance sequence and asymptotic variance matrix estimators. We conduct empirical comparisons of our method with other state-of-the-art approaches on simulated and real-data examples, using popular samplers including the random-walk Metropolis sampler and the No-U-Turn sampler from STAN. Supplemental materials for this article are available online.
DOI: 10.6084/m9.figshare.27122583.v2
title: Multivariate Moment Least-Squares Variance Estimators for Reversible Markov Chains

description: Markov chain Monte Carlo (MCMC) is a commonly used method for approximating expectations with respect to probability distributions. Uncertainty assessment for MCMC estimators is essential in practical applications. Moreover, for multivariate functions of a Markov chain, it is important to estimate not only the auto-correlation for each component but also to estimate cross-correlations, in order to better assess sample quality, improve estimates of effective sample size, and use more effective stopping rules. <i>Berg and Song</i> introduced the moment least squares (momentLS) estimator, a shape-constrained estimator for the autocovariance sequence from a reversible Markov chain, for univariate functions of the Markov chain. Based on this sequence estimator, they proposed an estimator of the asymptotic variance of the sample mean from MCMC samples. In this study, we propose novel autocovariance sequence and asymptotic variance estimators for Markov chain functions with multiple components, based on the univariate momentLS estimators from <i>Berg and Song</i>. We demonstrate strong consistency of the proposed auto(cross)-covariance sequence and asymptotic variance matrix estimators. We conduct empirical comparisons of our method with other state-of-the-art approaches on simulated and real-data examples, using popular samplers including the random-walk Metropolis sampler and the No-U-Turn sampler from STAN. Supplemental materials for this article are available online.
DOI: 10.6084/m9.figshare.27629156.v1
title: Ms.FPOP: a fast exact segmentation algorithm with a multiscale penalty

description: Given a time series in Rn with a piecewise constant mean and independent noises, we propose an exact dynamic programming algorithm for minimizing a least-squares criterion with a multiscale penalty, favoring well-spread changepoints. This penalty was proposed by Verzelen <i>et al.</i> (2023) and achieves optimal rates for changepoint detection and changepoint localization in a non-asymptotic scenario. Our proposed algorithm, Multiscale Functional Pruning Optimal Partitioning (Ms.FPOP), extends functional pruning ideas presented in Rigaill (2015) and Maidstone <i>et al.</i> (2017) to multiscale penalties. For large signals ( n≥105) with sparse changepoints, Ms.FPOP is shown empirically to be quasi-linear and faster than the Pruned Exact Linear Time (PELT) method of Killick <i>et al.</i> (2012) applied to the multiscale penalty of Verzelen <i>et al.</i> (2023), which exhibits quadratic slowdown in these cases. We propose an efficient implementation of Ms.FPOP coded in C++ interfaced with R that can segment profiles of up to n=106 in a matter of seconds. Our algorithm works for slightly more general multiscale penalties. In particular, it allows a minimum segment length to be imposed. Using simple simulations we then show that where profiles are sufficiently large ( n≥104), Ms.FPOP using the multiscale penalty of Verzelen <i>et al.</i> (2023) is typically more powerful than optimizing a least-squares criterion with the BIC penalty of Yao (1989), a criterion that was shown by Fearnhead and Rigaill 2020 to perfom well across a wide range of scenarios. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.26504002.v1
title: Using rejection sampling probability of acceptance as a measure of independence

description: This paper proposes a new association statistic for determining whether random variables are statistically independent. The proposed association statistic can also be used to examine the strength of both linear and non-linear dependency between variables. This statistic is derived by examining how the conditional probabilities of events differ from their corresponding marginal probabilities. The new statistic is defined in terms of the probability of acceptance commonly associated with the Accept-Reject algorithm and has a very simple formula. The simulated density of the probability of acceptance can be used to measure the degree of uncertainty of the estimated values of the new association statistic. The results from simulations as well as examples that employ real data indicate that this new association statistic is very powerful in detecting linear and non-linear associations between two random variables. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.27011401
title: Efficient Convex PCA with Applications to Wasserstein GPCA and Ranked Data

description: Convex PCA, which was introduced by <i>Bigot et al.</i> modifies Euclidean PCA by restricting the data and the principal components to lie in a given convex subset of a Hilbert space. This setting arises naturally in many applications, including distributional data in the Wasserstein space of an interval, and ranked compositional data under the Aitchison geometry. Our contribution in this article is 3-fold. First, we present several new theoretical results including consistency as well as continuity and differentiability of the objective function in the finite dimensional case. Second, we develop a numerical implementation of finite dimensional convex PCA when the convex set is polyhedral, and show that this provides a natural approximation of Wasserstein GPCA. Third, we illustrate our results with two financial applications, namely distributions of stock returns ranked by size and the capital distribution curve, both of which are of independent interest in stochastic portfolio theory. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.27011401.v2
title: Efficient Convex PCA with Applications to Wasserstein GPCA and Ranked Data

description: Convex PCA, which was introduced by <i>Bigot et al.</i> modifies Euclidean PCA by restricting the data and the principal components to lie in a given convex subset of a Hilbert space. This setting arises naturally in many applications, including distributional data in the Wasserstein space of an interval, and ranked compositional data under the Aitchison geometry. Our contribution in this article is 3-fold. First, we present several new theoretical results including consistency as well as continuity and differentiability of the objective function in the finite dimensional case. Second, we develop a numerical implementation of finite dimensional convex PCA when the convex set is polyhedral, and show that this provides a natural approximation of Wasserstein GPCA. Third, we illustrate our results with two financial applications, namely distributions of stock returns ranked by size and the capital distribution curve, both of which are of independent interest in stochastic portfolio theory. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.26250448
title: Computational Methods for Fast Bayesian Model Assessment via Calibrated Posterior <i>p</i>-values

description: Posterior predictive <i>p</i>-values (ppps) have become popular tools for Bayesian model assessment, being general-purpose and easy to use. However, interpretation can be difficult because their distribution is not uniform under the hypothesis that the model did generate the data. Calibrated ppps (cppps) can be obtained via a bootstrap-like procedure, yet remain unavailable in practice due to high computational cost. This article introduces methods to enable efficient approximation of cppps and their uncertainty for fast model assessment. We first investigate the computational tradeoff between the number of calibration replicates and the number of MCMC samples per replicate. Provided that the MCMC chain from the real data has converged, using short MCMC chains per calibration replicate can save significant computation time compared to naive implementations, without significant loss in accuracy. We propose different variance estimators for the cppp approximation, which can be used to confirm quickly the lack of evidence against model misspecification. As variance estimation uses effective sample sizes of many short MCMC chains, we show these can be approximated well from the real-data MCMC chain. The procedure for cppp is implemented in NIMBLE, a flexible framework for hierarchical modeling that supports many models and discrepancy measures. Supplementary materials for this article are available online.
DOI: 10.6084/m9.figshare.26250448.v2
title: Computational Methods for Fast Bayesian Model Assessment via Calibrated Posterior <i>p</i>-values

description: Posterior predictive <i>p</i>-values (ppps) have become popular tools for Bayesian model assessment, being general-purpose and easy to use. However, interpretation can be difficult because their distribution is not uniform under the hypothesis that the model did generate the data. Calibrated ppps (cppps) can be obtained via a bootstrap-like procedure, yet remain unavailable in practice due to high computational cost. This article introduces methods to enable efficient approximation of cppps and their uncertainty for fast model assessment. We first investigate the computational tradeoff between the number of calibration replicates and the number of MCMC samples per replicate. Provided that the MCMC chain from the real data has converged, using short MCMC chains per calibration replicate can save significant computation time compared to naive implementations, without significant loss in accuracy. We propose different variance estimators for the cppp approximation, which can be used to confirm quickly the lack of evidence against model misspecification. As variance estimation uses effective sample sizes of many short MCMC chains, we show these can be approximated well from the real-data MCMC chain. The procedure for cppp is implemented in NIMBLE, a flexible framework for hierarchical modeling that supports many models and discrepancy measures. Supplementary materials for this article are available online.