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

Boosting functional regression models

In functional data analysis, the data consist of functions that are defined on a continuous domain. In practice, functional variables are observed on some discrete grid. Regression models are important tools to capture the impact of explanatory variables on the response and are challenging in the case of functional data. In this thesis, a generic framework is proposed that includes scalar-on-function, function-on-scalar and function-on-function regression models. Within this framework, quantile regression models, generalized additive models and generalized additive models for location, scale and shape can be derived by optimizing the corresponding loss functions. The additive predictors can contain a variety of covariate effects, for example linear, smooth and interaction effects of scalar and functional covariates. In the first part, the functional linear array model is introduced. This model is suited for responses observed on a common grid and covariates that do not vary over the domain of the response. Array models achieve computational efficiency by taking advantage of the Kronecker product in the design matrix. In the second part, the focus is on models without array structure, which are capable to capture situations with responses observed on irregular grids and/or time-varying covariates. This includes in particular models with historical functional effects. For situations, in which the functional response and covariate are both observed over the same time domain, a historical functional effect induces an association between response and covariate such that only past values of the covariate influence the current value of the response. In this model class, effects with more general integration limits, like lag and lead effects, can be specified. In the third part, the framework is extended to generalized additive models for location, scale and shape where all parameters of the conditional response distribution can depend on covariate effects. The conditional response distribution can be modeled very flexibly by relating each distribution parameter with a link function to a linear predictor. For all parts, estimation is conducted by a component-wise gradient boosting algorithm. Boosting is an ensemble method that pursues a divide-and-conquer strategy for optimizing an expected loss criterion. This provides great flexibility for the regression models. For example, minimizing the check function yields quantile regression and minimizing the negative log-likelihood generalized additive models for location, scale and shape. The estimator is updated iteratively to minimize the loss criterion along the steepest gradient descent. The model is represented as a sum of simple (penalized) regression models, the so called base-learners, that separately fit the negative gradient in each step where only the best-fitting base-learner is updated. Component-wise boosting allows for high-dimensional data settings and for automatic, data-driven variable selection. To adapt boosting for regression with functional data, the loss is integrated over the domain of the response and base-learners suited to functional effects are implemented. To enhance the availability of functional regression models for practitioners, a comprehensive implementation of the methods is provided in the \textsf{R} add-on package \pkg{FDboost}. The flexibility of the regression framework is highlighted by several applications from different fields. Some features of the functional linear array model are illustrated using data on curing resin for car production, heat values of fossil fuels and Canadian climate data. These require function-on-scalar, scalar-on-function and function-on-function regression models, respectively. The methodological developments for non-array models are motivated by biotechnological data on fermentations, modeling a key process variable by a historical functional model. The motivating application for functional generalized additive models for location, scale and shape is a time series on stock returns where expectation and standard deviation are modeled depending on scalar and functional covariates

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.Comment: bootstrap confidence interval type uncertainty bounds added; minor changes in formulation

Magnets, magic, and other anomalies:In defense of methodological naturalism

Funding for this research was provided by the John Templeton Foundation, grant number 59023Recent critiques of methodological naturalism (MN) claim that it fails by conflicting with Christian belief and being insufficiently humble. We defend MN by tracing the real history of the debate, contending that the story as it is usually told is mythic. We show how MN works in practice, including among real scientists. The debate is a red herring. It only appears problematic because of confusion among its opponents about how scientists respond to experimental anomalies. We conclude by introducing our preferred approach, Science‐Engaged Theology.PostprintPeer reviewe

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 analyse bacterial growth inEscherichia coliin a complex interaction scenario, fruitfully extending usual growth models

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 analyse bacterial growth in Escherichia coli in a complex interaction scenario, fruitfully extending usual growth models.Peer Reviewe

Rapid and robust generation of long-term self-renewing human neural stem cells with the ability to generate mature astroglia

Induced pluripotent stem cell bear the potential to differentiate into any desired cell type and hold large promise for disease-in-a-dish cell-modeling approaches. With the latest advances in the field of reprogramming technology, the generation of patient-specific cells has become a standard technology. However, directed and homogenous differentiation of human pluripotent stem cells into desired specific cell types remains an experimental challenge. Here, we report the development of a novel hiPSCs-based protocol enabling the generation of expandable homogenous human neural stem cells (hNSCs) that can be maintained under self-renewing conditions over high passage numbers. Our newly generated hNSCs retained differentiation potential as evidenced by the reliable generation of mature astrocytes that display typical properties as glutamate up-take and expression of aquaporin-4. The hNSC-derived astrocytes showed high activity of pyruvate carboxylase as assessed by stable isotope assisted metabolic profiling. Moreover, using a cell transplantation approach, we showed that grafted hNSCs were not only able to survive but also to differentiate into astroglial in vivo. Engraftments of pluripotent stem cells derived from somatic cells carry an inherent tumor formation potential. Our results demonstrate that hNSCs with self-renewing and differentiation potential may provide a safer alternative strategy, with promising applications especially for neurodegenerative disorders