Simplified R-vine based forward regression

Zhu, Kailun; Kurowicka, Dorota; Nane, Gabriela F.

doi:10.1016/j.csda.2020.107091

Cited by 9 publications

(10 citation statements)

References 17 publications

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“…The adding a covariates stops if the conditional (penalized) log-likelihood does not increase any more when a further covariate is added. This approach was first developed for D-vine models by Kraus and Czado (2017) and later extended to certain R-vine structures by Zhu et al (2021). Tepegjozova et al (2021) considered both D-and C-vines, but generalized the procedure to look two steps ahead before adding a new covariate.…”

Section: Vine Copula Based Regression Modelsmentioning

confidence: 99%

Analysis of an interventional protein experiment using a vine copula based structural equation model

Czado¹,

Scharl²

2021

Preprint

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While there is considerable effort to identify signaling pathways using linear Gaussian Bayesian networks from data, there is less emphasis of understanding and quantifying conditional densities and probabilities of nodes given its parents from the identified Bayesian network. Most graphical models for continuous data assume a multivariate Gaussian distribution, which might be too restrictive. We reanalyse data from an experimental setting considered in Sachs et al. (2005) to illustrate the effects of such restrictions. For this we propose a novel non Gaussian nonlinear structural equation model based on vine copulas. In particular the D-vine regression approach of Kraus and Czado (2017) is adapted. We show that this model class is more suited to fit the data than the standard linear structural equation model based on the biological consent graph given in Sachs et al. (2005). The modelling approach also allows to study which pathway edges are supported by the data and which can be removed. For data experiment cd3cd28 + aktinhib this approach identified three edges, which are no longer supported by the data. For each of these edges a plausible explanation based on underlying the experimental conditions could be found.

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Section: Vine Copula Based Regression Modelsmentioning

confidence: 99%

Analysis of an interventional protein experiment using a vine copula based structural equation model

Czado¹,

Scharl²

2021

Preprint

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“…One of the most recent approaches for quantile regression are vine copula based quantile regression methods (Kraus and Czado 2017;Tepegjozova et al 2022;Chang and Joe 2019;Zhu et al 2021). Copulas allow for separate modelling of the marginal distributions and the dependence structure in the data, while vine copulas allow the multivariate copula to be constructed using bivariate building blocks only, a so-called pair copula construction.…”

Section: Introductionmentioning

confidence: 99%

“…Chang and Joe (2019) introduced an R-vine based quantile regression by first finding the optimal R-vine structure among all predictors and then adding the response variable to each tree in the vine structure as a leaf node. Another R-vine based regression was introduced in Zhu et al (2021) by optimizing the R-vine structure which gives the largest sum of the absolute value of the partial correlations in each step of the forward extension with predictor variables, while keeping the response as a leaf node. This approach is motivated by the algorithm and results from Zhu et al (2020).…”

Section: Introductionmentioning

confidence: 99%

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Bivariate vine copula based quantile regression

Tepegjozova¹,

Czado²

2022

Preprint

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The statistical analysis of univariate quantiles is a well developed research topic. However, there is a profound need for research in multivariate quantiles. We tackle the topic of bivariate quantiles and bivariate quantile regression using vine copulas. They are graph theoretical models identified by a sequence of linked trees, which allow for separate modelling of marginal distributions and the dependence structure. We introduce a novel graph structure model (given by a tree sequence) specifically designed for a symmetric treatment of two responses in a predictive regression setting. We establish computational tractability of the model and a straight forward way of obtaining different conditional distributions. Using vine copulas the typical shortfalls of regression, as the need for transformations or interactions of predictors, collinearity or quantile crossings are avoided. We illustrate the copula based bivariate quantiles for different copula distributions and provide a data set example. Further, the data example emphasizes the benefits of the joint bivariate response modelling in contrast to two separate univariate regressions or by assuming conditional independence, for bivariate response data set in the presence of conditional dependence.

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“…Comparing multidimensional distributions is important in many fields, including climate science [6], astronomy [7], social sciences [8], or, famously, the quality control of weapons [9]. More recently, machine learning and other data-driven methods have made high dimensional data more common and required the use of multidimensional hypothesis testing, such as in [10]. The literature on divergences and distances between two high-dimensional distributions is robust.…”

Section: Introductionmentioning

confidence: 99%

Accelerated Computation of a High Dimensional Kolmogorov-Smirnov Distance

Hagen¹,

Jackson²,

Kahn³

et al. 2021

Preprint

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Statistical testing is widespread and critical for a variety of scientific disciplines. The advent of machine learning and the increase of computing power has increased the interest in the analysis and statistical testing of multidimensional data. We extend the powerful Kolmogorov-Smirnov two sample test to a high dimensional form in a similar manner to Fasano [1]. We call our result the d-dimensional Kolmogorov-Smirnov test (ddKS) and provide three novel contributions therewith: we develop an analytical equation for the significance of a given ddKS score, we provide an algorithm for computation of ddKS on modern computing hardware that is of constant time complexity for small sample sizes and dimensions, and we provide two approximate calculations of ddKS: one that reduces the time complexity to linear at larger sample sizes, and another that reduces the time complexity to linear with increasing dimension. We perform power analysis of ddKS and its approximations on a corpus of datasets and compare to other common high dimensional two sample tests and distances: Hotelling's T 2 test and Kullback-Leibler divergence. Our ddKS test performs well for all datasets, dimensions, and sizes tests, whereas the other tests and distances fail to reject the null hypothesis on at least one dataset. We therefore conclude that ddKS is a powerful multidimensional two sample test for general use, and can be calculated in a fast and efficient manner using our parallel or approximate methods. Open source code for all methods accompanies this work 1 .

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Simplified R-vine based forward regression

Cited by 9 publications

References 17 publications

Analysis of an interventional protein experiment using a vine copula based structural equation model

Analysis of an interventional protein experiment using a vine copula based structural equation model

Bivariate vine copula based quantile regression

Accelerated Computation of a High Dimensional Kolmogorov-Smirnov Distance

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