arXiv subjects

Sonja Greven

Publications and source records attributed to Sonja Greven.

At least 37 records · Page 2Linked to original sources

arXiv2023

Exploratory functional data analysis of multivariate densities for the identification of agricultural soil contamination by risk elements

Geochemical mapping of risk element concentrations in soils is performed in countries around the world. It results in large datasets of high analytical quality, which can be used to identify soils that violate individual legislative limits for safe food production. However, there is a lack of advanced data mining tools that would be suitable for sensitive exploratory data analysis of big data while respecting the natural variability of soil composition. To distinguish anthropogenic contamination from natural variation, the analysis of the entire data distributions for smaller sub-areas is key. In this article, we propose a new data mining method for geochemical mapping data based on functional data analysis of probability density functions in the framework of Bayes spaces after post-stratification of a big dataset to smaller districts. Proposed tools allow us to analyse the entire distribution, going beyond a superficial detection of extreme concentration anomalies. We illustrate the proposed methodology on a dataset gathered according to the Czech national legislation (1990--2009). Taking into account specific properties of probability density functions and recent results for orthogonal decomposition of multivariate densities enabled us to reveal real contamination patterns that were so far only suspected in Czech agricultural soils. We process the above Czech soil composition dataset by first compartmentalising it into spatial units, in particular the districts, and by subsequently clustering these districts according to diagnostic features of their uni- and multivariate distributions at high concentration ends. Comparison between compartments is key to the reliable distinction of diffuse contamination. In this work, we used soil contamination by Cu-bearing pesticides as an example for empirical testing of the proposed data mining approach.

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arXiv2023

Principal component analysis in Bayes spaces for sparsely sampled density functions

This paper presents a novel approach to functional principal component analysis (FPCA) in Bayes spaces in the setting where densities are the object of analysis, but only few individual samples from each density are observed. We use the observed data directly to account for all sources of uncertainty, instead of relying on prior estimation of the underlying densities in a two-step approach, which can be inaccurate if small or heterogeneous numbers of samples per density are available. To account for the constrained nature of densities, we base our approach on Bayes spaces, which extend the Aitchison geometry for compositional data to density functions. For modeling, we exploit the isometric isomorphism between the Bayes space and the $\mathbb{L}^2$ subspace $\mathbb{L}_0^2$ with integration-to-zero constraint through the centered log-ratio transformation. As only discrete draws from each density are observed, we treat the underlying functional densities as latent variables within a maximum likelihood framework and employ a Monte Carlo Expectation Maximization (MCEM) algorithm for model estimation. Resulting estimates are useful for exploratory analyses of density data, for dimension reduction in subsequent analyses, as well as for improved preprocessing of sparsely sampled density data compared to existing methods. The proposed method is applied to analyze the distribution of maximum daily temperatures in Berlin during the summer months for the last 70 years, as well as the distribution of rental prices in the districts of Munich.

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arXiv2023

Regression in quotient metric spaces with a focus on elastic curves

We propose regression models for curve-valued responses in two or more dimensions, where only the image but not the parametrization of the curves is of interest. Examples of such data are handwritten letters, movement paths or outlines of objects. In the square-root-velocity framework, a parametrization invariant distance for curves is obtained as the quotient space metric with respect to the action of re-parametrization, which is by isometries. With this special case in mind, we discuss the generalization of 'linear' regression to quotient metric spaces more generally, before illustrating the usefulness of our approach for curves modulo re-parametrization. We address the issue of sparsely or irregularly sampled curves by using splines for modeling smooth conditional mean curves. We test this model in simulations and apply it to human hippocampal outlines, obtained from Magnetic Resonance Imaging scans. Here we model how the shape of the irregularly sampled hippocampus is related to age, Alzheimer's disease and sex.

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arXiv2022

Elastic Full Procrustes Analysis of Plane Curves via Hermitian Covariance Smoothing

Determining the mean shape of a collection of curves is not a trivial task, in particular when curves are only irregularly/sparsely sampled at discrete points. We newly propose an elastic full Procrustes mean of shapes of (oriented) plane curves, which are considered equivalence classes of parameterized curves with respect to translation, rotation, scale, and re-parameterization (warping), based on the square-root-velocity (SRV) framework. Identifying the real plane with the complex numbers, we establish a connection to covariance estimation in irregular/sparse functional data analysis. We introduce Hermitian covariance smoothing and show how to employ this extension of existing covariance estimation methods for obtaining an estimator of the (in)elastic full Procrustes mean, also in the sparse case not yet covered by existing (intrinsic) elastic shape means. For this, we provide different groundwork results which are also of independent interest: we characterize (the decomposition of) the covariance structure of rotation-invariant bivariate stochastic processes using complex representations, and we identify sampling schemes that allow for exact observation of derivatives / SRV transforms of sparsely sampled curves. We demonstrate the performance of the approach in a phonetic study on tongue shapes and in different realistic simulation settings, inter alia based on handwriting data.

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arXiv2022

Functional additive models on manifolds of planar shapes and forms

The "shape" of a planar curve and/or landmark configuration is considered its equivalence class under translation, rotation and scaling, its "form" its equivalence class under translation and rotation while scale is preserved. We extend generalized additive regression to models for such shapes/forms as responses respecting the resulting quotient geometry by employing the squared geodesic distance as loss function and a geodesic response function to map the additive predictor to the shape/form space. For fitting the model, we propose a Riemannian $L_2$-Boosting algorithm well suited for a potentially large number of possibly parameter-intensive model terms, which also yields automated model selection. We provide novel intuitively interpretable visualizations for (even non-linear) covariate effects in the shape/form space via suitable tensor-product factorization. The usefulness of the proposed framework is illustrated in an analysis of 1) astragalus shapes of wild and domesticated sheep and 2) cell forms generated in a biophysical model, as well as 3) in a realistic simulation study with response shapes and forms motivated from a dataset on bottle outlines.

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arXiv2022

Classification ensembles for multivariate functional data with application to mouse movements in web surveys

We propose new ensemble models for multivariate functional data classification as combinations of semi-metric-based weak learners. Our models extend current semi-metric-type methods from the univariate to the multivariate case, propose new semi-metrics to compute distances between functions, and consider more flexible options for combining weak learners using stacked generalisation methods. We apply these ensemble models to identify respondents' difficulty with survey questions, with the aim to improve survey data quality. As predictors of difficulty, we use mouse movement trajectories from the respondents' interaction with a web survey, in which several questions were manipulated to create two scenarios with different levels of difficulty.

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arXiv2022

Generalised functional additive mixed models with compositional covariates for areal Covid-19 incidence curves

We extend the generalised functional additive mixed model to include (functional) compositional covariates carrying relative information of a whole. Relying on the isometric isomorphism of the Bayes Hilbert space of probability densities with a subspace of the $L^2$, we include functional compositions as transformed functional covariates with constrained effect function. The extended model allows for the estimation of linear, nonlinear and time-varying effects of scalar and functional covariates, as well as (correlated) functional random effects, in addition to the compositional effects. We use the model to estimate the effect of the age, sex and smoking (functional) composition of the population on regional Covid-19 incidence data for Spain, while accounting for climatological and socio-demographic covariate effects and spatial correlation.

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arXiv2021

Navigating the corporate disclosure gap: Modelling of Missing Not at Random Carbon Data

Corporate carbon emissions data is disclosed by approximately 65% of large and mid-sized companies globally, despite being a key indicator of corporate climate performance. With investors increasingly looking to integrate climate risk into their investment strategies and risk reporting, this creates demand for robust prediction models that can generate reliable estimates for missing carbon disclosures. However, these estimates lack transparency and are frequently used in the investment decisions process with the same confidence as corporate reported data. As disclosures remain mostly voluntary and the propensity to disclose is shaped by several factors (e.g. size, sector, geography), missing emissions data should be assumed to be missing not at random (MNAR). However, widely used estimation methods (e.g. linear regression models) typically do not correct for MNAR bias and do not accurately reflect the uncertainty of estimated data. The objective of this paper is to address these issues: (1) account for the uncertainty of the missing data and thus obtain regression coefficients by multiple imputation (MI) (2) correct for potential bias by using MI algorithms based on Heckman's sample selection model introduced by Galimard et al. (3) estimate missing carbon disclosures with linear models based on MI and report on the uncertainty of predicted values, measured as the length of the prediction interval. In the simulation, our approach resulted in an accuracy gain based on root mean squared error of up to 30%, and up to a 40% higher coverage rate than the existing models. When applied to commercial data, the results suggested up to 20% higher coverage for proposed methods.

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arXiv2021

Multivariate Functional Additive Mixed Models

Multivariate functional data can be intrinsically multivariate like movement trajectories in 2D or complementary like precipitation, temperature, and wind speeds over time at a given weather station. We propose a multivariate functional additive mixed model (multiFAMM) and show its application to both data situations using examples from sports science (movement trajectories of snooker players) and phonetic science (acoustic signals and articulation of consonants). The approach includes linear and nonlinear covariate effects and models the dependency structure between the dimensions of the responses using multivariate functional principal component analysis. Multivariate functional random intercepts capture both the auto-correlation within a given function and cross-correlations between the multivariate functional dimensions. They also allow us to model between-function correlations as induced by e.g.\ repeated measurements or crossed study designs. Modeling the dependency structure between the dimensions can generate additional insight into the properties of the multivariate functional process, improves the estimation of random effects, and yields corrected confidence bands for covariate effects. Extensive simulation studies indicate that a multivariate modeling approach is more parsimonious than fitting independent univariate models to the data while maintaining or improving model fit.

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arXiv2021

Elastic analysis of irregularly or sparsely sampled curves

We provide statistical analysis methods for samples of curves when the image but not the parametrisation of the curves is of interest. A parametrisation invariant analysis can be based on the elastic distance of the curves modulo warping, but existing methods have limitations in common realistic settings where curves are irregularly and potentially sparsely observed. We provide methods and algorithms to approximate the elastic distance for such curves via interpreting them as polygons. Moreover, we propose to use spline curves for modelling smooth or polygonal Fréchet means of open or closed curves with respect to the elastic distance and show identifiability of the spline model modulo warping. We illustrate the use of our methods for elastic mean and distance computation by application to two datasets. The first application clusters sparsely sampled GPS tracks based on the elastic distance and computes smooth means for each cluster to find new paths on Tempelhof field in Berlin. The second classifies irregularly sampled handwritten spirals of Parkinson's patients and controls based on the elastic distance to a mean spiral curve computed using our approach. All developed methods are implemented in the \texttt{R}-package \texttt{elasdics} and evaluated in simulations.

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arXiv2021

Adaptive Step-Length Selection in Gradient Boosting for Generalized Additive Models for Location, Scale and Shape

Tuning of model-based boosting algorithms relies mainly on the number of iterations, while the step-length is fixed at a predefined value. For complex models with several predictors such as Generalized Additive Models for Location, Scale and Shape (GAMLSS), imbalanced updates of predictors, where some distribution parameters are updated more frequently than others, can be a problem that prevents some submodels to be appropriately fitted within a limited number of boosting iterations. We propose an approach using adaptive step-length (ASL) determination within a non-cyclical boosting algorithm for GAMLSS to prevent such imbalance. Moreover, for the important special case of the Gaussian distribution, we discuss properties of the ASL and derive a semi-analytical form of the ASL that avoids manual selection of the search interval and numerical optimization to find the optimal step-length, and consequently improves computational efficiency. We show competitive behavior of the proposed approaches compared to penalized maximum likelihood and boosting with a fixed step-length for GAMLSS models in two simulations and two applications, in particular for cases of large variance and/or more variables than observations. In addition, the idea of the ASL is also applicable to other models with more than one predictor like zero-inflated count model, and brings up insights into the choice of the reasonable defaults for the step-length in simpler special case of (Gaussian) additive models.

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arXiv2020

Selective Inference for Additive and Linear Mixed Models

This work addresses the problem of conducting valid inference for additive and linear mixed models after model selection. One possible solution to overcome overconfident inference results after model selection is selective inference, which constitutes a post-selection inference framework, yielding valid inference statements by conditioning on the selection event. We extend recent work on selective inference to the class of additive and linear mixed models for any type of model selection mechanism that can be expressed as a function of the outcome variable (and potentially on covariates on which it conditions). We investigate the properties of our proposal in simulation studies and apply the framework to a data set in monetary economics. Due to the generality of our proposed approach, the presented approach also works for non-standard selection procedures, which we demonstrate in our application. Here, the final additive mixed model is selected using a hierarchical selection procedure, which is based on the conditional Akaike information criterion and involves varying data set sizes.

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arXiv2020

Predicting respondent difficulty in web surveys: A machine-learning approach based on mouse movement features

A central goal of survey research is to collect robust and reliable data from respondents. However, despite researchers' best efforts in designing questionnaires, respondents may experience difficulty understanding questions' intent and therefore may struggle to respond appropriately. If it were possible to detect such difficulty, this knowledge could be used to inform real-time interventions through responsive questionnaire design, or to indicate and correct measurement error after the fact. Previous research in the context of web surveys has used paradata, specifically response times, to detect difficulties and to help improve user experience and data quality. However, richer data sources are now available, in the form of the movements respondents make with the mouse, as an additional and far more detailed indicator for the respondent-survey interaction. This paper uses machine learning techniques to explore the predictive value of mouse-tracking data with regard to respondents' difficulty. We use data from a survey on respondents' employment history and demographic information, in which we experimentally manipulate the difficulty of several questions. Using features derived from the cursor movements, we predict whether respondents answered the easy or difficult version of a question, using and comparing several state-of-the-art supervised learning methods. In addition, we develop a personalization method that adjusts for respondents' baseline mouse behavior and evaluate its performance. For all three manipulated survey questions, we find that including the full set of mouse movement features improved prediction performance over response-time-only models in nested cross-validation. Accounting for individual differences in mouse movements led to further improvements.

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arXiv2019

Inference for $L_2$-Boosting

We propose a statistical inference framework for the component-wise functional gradient descent algorithm (CFGD) under normality assumption for model errors, also known as $L_2$-Boosting. The CFGD is one of the most versatile tools to analyze data, because it scales well to high-dimensional data sets, allows for a very flexible definition of additive regression models and incorporates inbuilt variable selection. Due to the variable selection, we build on recent proposals for post-selection inference. However, the iterative nature of component-wise boosting, which can repeatedly select the same component to update, necessitates adaptations and extensions to existing approaches. We propose tests and confidence intervals for linear, grouped and penalized additive model components selected by $L_2$-Boosting. Our concepts also transfer to slow-learning algorithms more generally, and to other selection techniques which restrict the response space to more complex sets than polyhedra. We apply our framework to an additive model for sales prices of residential apartments and investigate the properties of our concepts in simulation studies.

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arXiv2019

Boosting Functional Response Models for Location, Scale and Shape with an Application to Bacterial Competition

We extend Generalized Additive Models for Location, Scale, and Shape (GAMLSS) to regression with functional response. This allows us to simultaneously model point-wise mean curves, variances and other distributional parameters of the response in dependence of various scalar and functional covariate effects. In addition, the scope of distributions is extended beyond exponential families. The model is fitted via gradient boosting, which offers inherent model selection and is shown to be suitable for both complex model structures and highly auto-correlated response curves. This enables us to analyze bacterial growth in \textit{Escherichia coli} in a complex interaction scenario, fruitfully extending usual growth models.

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arXiv2018

A General Framework for Multivariate Functional Principal Component Analysis of Amplitude and Phase Variation

Functional data typically contains amplitude and phase variation. In many data situations, phase variation is treated as a nuisance effect and is removed during preprocessing, although it may contain valuable information. In this note, we focus on joint principal component analysis (PCA) of amplitude and phase variation. As the space of warping functions has a complex geometric structure, one key element of the analysis is transforming the warping functions to $L^2(\mathcal{T})$. We present different transformation approaches and show how they fit into a general class of transformations. This allows us to compare their strengths and limitations. In the context of PCA, our results offer arguments in favour of the centered log-ratio transformation. We further embed existing approaches from Hadjipantelis et al. (2015) and Lee and Jung (2017) for joint PCA of amplitude and phase variation into the framework of multivariate functional PCA, where we study the properties of the estimators based on an appropriate metric. The approach is illustrated through an application from seismology.

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arXiv2018

Boosting Functional Regression Models with FDboost

The R add-on package FDboost is a flexible toolbox for the estimation of functional regression models by model-based boosting. It provides the possibility to fit regression models for scalar and functional response with effects of scalar as well as functional covariates, i.e., scalar-on-function, function-on-scalar and function-on-function regression models. In addition to mean regression, quantile regression models as well as generalized additive models for location scale and shape can be fitted with FDboost. Furthermore, boosting can be used in high-dimensional data settings with more covariates than observations. We provide a hands-on tutorial on model fitting and tuning, including the visualization of results. The methods for scalar-on-function regression are illustrated with spectrometric data of fossil fuels and those for functional response regression with a data set including bioelectrical signals for emotional episodes.

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arXiv2018

The Impact of Model Assumptions in Scalar-on-Image Regression

Complex statistical models such as scalar-on-image regression often require strong assumptions to overcome the issue of non-identifiability. While in theory it is well understood that model assumptions can strongly influence the results, this seems to be underappreciated, or played down, in practice. The article gives a systematic overview of the main approaches for scalar-on-image regression with a special focus on their assumptions. We categorize the assumptions and develop measures to quantify the degree to which they are met. The impact of model assumptions and the practical usage of the proposed measures are illustrated in a simulation study and in an application to neuroimaging data. The results show that different assumptions indeed lead to quite different estimates with similar predictive ability, raising the question of their interpretability. We give recommendations for making modeling and interpretation decisions in practice, based on the new measures and simulations using hypothetic coefficient images and the observed data.

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