Spherical regression models with general covariates and anisotropic errors

Paine, Phillip J.; Preston, Simon; Tsagris, Michail; Wood, Andrew

doi:10.1007/s11222-019-09872-2

Cited by 9 publications

(5 citation statements)

References 18 publications

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“…Under the kernel mean embedding framework that is surveyed by Muandet et al (2017), one can focus on kernel mean E[k(X, •)] in the function space, rather a physical mean that exist in the compositional domain. The latter is known to be difficult to even define properly (Paine et al, 2020;Scealy and Welsh, 2011). On the other hand, the kernel mean is endowed with flexibility and linear structure of the function space.…”

Section: Discussionmentioning

confidence: 99%

Reproducing Kernels and New Approaches in Compositional Data Analysis

Li¹,

Ahn²

2022

Preprint

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Compositional data, such as human gut microbiomes, consist of non-negative variables whose only the relative values to other variables are available. Analyzing compositional data such as human gut microbiomes needs a careful treatment of the geometry of the data. A common geometrical understanding of compositional data is via a regular simplex. Majority of existing approaches rely on a log-ratio or power transformations to overcome the innate simplicial geometry. In this work, based on the key observation that a compositional data are projective in nature, and on the intrinsic connection between projective and spherical geometry, we re-interpret the compositional domain as the quotient topology of a sphere modded out by a group action. This re-interpretation allows us to understand the function space on compositional domains in terms of that on spheres and to use spherical harmonics theory along with reflection group actions for constructing a compositional Reproducing Kernel Hilbert Space (RKHS). This construction of RKHS for compositional data will widely open research avenues for future methodology developments. In particular, well-developed kernel embedding methods can be now introduced to compositional data analysis. The polynomial nature of compositional RKHS has both theoretical and computational benefits. The wide applicability of the proposed theoretical framework is exemplified with nonparametric density estimation and kernel exponential family for compositional data.

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Section: Discussionmentioning

confidence: 99%

Reproducing Kernels and New Approaches in Compositional Data Analysis

Li¹,

Ahn²

2022

Preprint

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“…Furthermore, a LRT was also performed to determine the overall difference in frontal angles of the CHD subgroups and the control group. In addition, a spherically projected multivariate linear (SPML) regression model with the frontal angle as the outcome and the subgroup as a categorically independent variable (control group was considered as the reference level) was fitted to the data, under the assumption that the data follows a von Mises-Fisher distribution (analogous to the normal distribution in linear regression) [ 37 , 38 ].…”

Section: Methodsmentioning

confidence: 99%

The electrical heart axis in fetuses with congenital heart disease, measured with non-invasive fetal electrocardiography

Noben

Lempersz²,

Heuvel³

et al. 2022

PLoS ONE

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Objectives To determine if the electrical heart axis in different types of congenital heart defects (CHD) differs from that of a healthy cohort at mid-gestation. Methods Non-invasive fetal electrocardiography (NI-fECG) was performed in singleton pregnancies with suspected CHD between 16 and 30 weeks of gestation. The mean electrical heart axis (MEHA) was determined from the fetal vectorcardiogram after correction for fetal orientation. Descriptive statistics were used to determine the MEHA with corresponding 95% confidence intervals (CI) in the frontal plane of all fetuses with CHD and the following subgroups: conotruncal anomalies (CTA), atrioventricular septal defects (AVSD) and hypoplastic right heart syndrome (HRHS). The MEHA of the CHD fetuses as well as the subgroups was compared to the healthy control group using a spherically projected multivariate linear regression analysis. Discriminant analysis was applied to calculate the sensitivity and specificity of the electrical heart axis for CHD detection. Results The MEHA was determined in 127 fetuses. The MEHA was 83.0° (95% CI: 6.7°; 159.3°) in the total CHD group, and not significantly different from the control group (122.7° (95% CI: 101.7°; 143.6°). The MEHA was 105.6° (95% CI: 46.8°; 164.4°) in the CTA group (n = 54), -27.4° (95% CI: -118.6°; 63.9°) in the AVSD group (n = 9) and 26.0° (95% CI: -34.1°; 86.1°) in the HRHS group (n = 5). The MEHA of the AVSD and the HRHS subgroups were significantly different from the control group (resp. p = 0.04 and p = 0.02). The sensitivity and specificity of the MEHA for the diagnosis of CHD was 50.6% (95% CI 47.5% - 53.7%) and 60.1% (95% CI 57.1% - 63.1%) respectively. Conclusion The MEHA alone does not discriminate between healthy fetuses and fetuses with CHD. However, the left-oriented electrical heart axis in fetuses with AVSD and HRHS was significantly different from the control group suggesting altered cardiac conduction along with the structural defect. Trial registration Clinical trial registration number: NL48535.015.14.

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“…Cornea et al (2017) proposed a more general semiparametric intrinsic manifold-manifold regression model that incorporates parametric link functions and a nonparametric error structure. Very recently, Paine et al (2020) introduced a very general regression model for an S 2 -valued response with covariates that can be spherical, linear or categorical, and two kinds of anisotropic error distributions. In its most general formulation, a preliminary orthogonal transformation of the response is assumed to follow an anisotropic distribution with covariate-dependent parameters.…”

Section: Spherical Responsementioning

confidence: 99%

Recent advances in directional statistics

Pewsey

García‐Portugués

2021

TEST

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Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere, and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper, we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (Wiley 1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, space situational awareness, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. AnWe are most grateful to three anonymous referees and, in alphabetical order, to

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Spherical regression models with general covariates and anisotropic errors

Cited by 9 publications

References 18 publications

Reproducing Kernels and New Approaches in Compositional Data Analysis

Reproducing Kernels and New Approaches in Compositional Data Analysis

The electrical heart axis in fetuses with congenital heart disease, measured with non-invasive fetal electrocardiography

Recent advances in directional statistics

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