Boosting flexible functional regression models with a high number of functional historical effects

Brockhaus, Sarah; Melcher, Michael; Leisch, Friedrich; Greven, Sonja

doi:10.1007/s11222-016-9662-1

Cited by 27 publications

(87 citation statements)

References 26 publications

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“…We used the FDboost package in R (Brockhaus, Melcher, Leisch, & Greven, ; Brockhaus, Scheipl, Hothorn, & Greven, ) to fit a model of the following form:

y false(t false) = α + \int_{0}^{t} β_{1} (s, t) x_{1} (s) d s + \int_{0}^{t} β_{2} (s, t) x_{2} (s) d s

where the functional response variable y ( t ) is the rate of spring onion growth over time in each school. An important note in this model is that s is always less than t , so only past temperature can inform the current growth rate.…”

Section: Methodsmentioning

confidence: 99%

A mass participatory experiment provides a rich temporal profile of temperature response in spring onions

Brestovitsky

Ezer

2019

Plant Direct

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Plants modulate their growth rates based on the environmental signals; however, it is difficult to experimentally test how natural temperature and light fluctuations affect growth, since realistic outdoor environments are difficult to replicate in controlled laboratory conditions, and it is expensive to conduct experiments in many environmentally diverse regions. In partnership with BBC Terrific Scientific, over 50 primary schools from around the UK grew spring onions outside of hydroponic growth chambers that they constructed. Over 2 weeks, students measured the height of the spring onions daily, while the hourly temperature and visibility data were determined for each school based on the UK Meteorological Office data. This rich time series data allowed us to model how plants integrate temperature and light signals to determine how much to grow, using techniques from functional data analysis. We determined that under nutrient‐poor hydroponic conditions, growth of spring onion is sensitive to even a few degrees change in temperature, and is most correlated with warm nighttime temperatures, high temperatures at the start of the experiment, and light exposure near the end of the experiment. We show that scientists can leverage schools to conduct experiments that leverage natural environmental variability to develop complex models of plant‐environment interactions.

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“…We used the FDboost package in R (Brockhaus, Melcher, Leisch, & Greven, ; Brockhaus, Scheipl, Hothorn, & Greven, ) to fit a model of the following form:

y false(t false) = α + \int_{0}^{t} β_{1} (s, t) x_{1} (s) d s + \int_{0}^{t} β_{2} (s, t) x_{2} (s) d s

Section: Methodsmentioning

confidence: 99%

A mass participatory experiment provides a rich temporal profile of temperature response in spring onions

Brestovitsky

Ezer

2019

Plant Direct

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“…In the case considered here, it is more appropriate to introduce the historical functional linear model (HFLM) as it allows to restrict the domain where the predictor influences the predictand (Malfait and Ramsay ; Harezlak et al ; Gervini ). The HFLM has known recent developments regarding its implementation (Brockhaus et al ; Brockhaus, Melcher, et al ) and is defined as follows:

y_{i} (t) = α (t) + \int_{l (t)}^{u (t)} β false(t, s false) x_{i} false(s false) d s + ε_{i} (t), t \in {normalΩ}_{1},

where l ( t ) and u ( t ) are, respectively, the lower and the upper bound where the predictor x i ( . ) can influence y i (.)…”

Section: Methodsmentioning

confidence: 99%

“…In order to fit functional models, the functional linear array model (FLAM) implemented in R (R Core Team ) by Brockhaus et al () in the package FDboost (Brockhaus, Ruegamer, et al ) was used as it can fit both model (3) and (4) with different configurations of l ( t ) and u ( t ). The FLAM is fitted using a component‐wise gradient boosting algorithm, a machine learning procedure that estimates the model parameters by minimizing an empirical loss function (Freund et al ; Bühlmann and Hothorn ; Brockhaus, Melcher, et al ). In our case, the minimized loss function is the root mean squared error (Brockhaus et al ):

\sqrt{\frac{1}{n} {\sum_{i = 1}^{n} \int_{Ω_{1}} [y_{i} (t) - {\overset{y}{true}}_{i} (t)]}^{2} d t,}

where

{\overset{y}{true}}_{i} (.)

is the simulated stream temperature curve by the functional model.…”

Section: Methodsmentioning

confidence: 99%

Stream Temperature Modeling Using Functional Regression Models

Boudreault

Bergeron

St‐Hilaire

et al. 2019

J American Water Resour Assoc

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Stream temperature is one of the most important environmental variables in lotic habitats as it has important and direct impacts on the ecosystem. Given the continuous nature of this variable, the aim of this paper was to introduce functional regression for the air‐stream temperature relation, being capable to model an entire seasonal or annual curve of temperatures as one entity, rather than multiple daily or weekly values in classical models. Three types of functional models were explored in the study and compared to two classical models (Generalized Additive Model and Logistic Model) for six rivers from the United States The results show the functional models have the best performance for all the considered rivers. When comparing functional models between them, one variant of the historical functional model performs better than the two other models and is the most parsimonious. Functional regression leads to encouraging results to model the complete annual stream temperature curve as one entity compared to other classical approaches.

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“…They fit their models either using existing generalized additive models software (Wood, 2016) in the R package refund (Huang et al 2016) or through a component-wise gradient boosting (Buhlmann and Hothorn, 2007) in the R package FDboost (Brockhaus, 2016). …”

Section: Summary Of Functional Linear Array Model Frameworkmentioning

confidence: 99%

“…The formulation and building up of this general framework has been a topic in this research group’s work over the past few years, introducing much of this structure for Gaussian functions largely represented by splines and fit using generalized additive model (GAM) software in Scheipl, Staicu and Greven (2015), incorporating functional principal components (fPC) to flexibly model sparse, irregularly sampled outcomes in Cederbaum, et al (2015), extending to generalized outcomes in Scheipl, Gertheiss, and Greven (2016), and introducing a new boosting-based fitting procedure that allows extension to robust functional regression and confers other benefits in Brockhaus, et al (2015). Other specific work has been done developing details for additive scalar-on function models (McLean et al 2014) and function-on-function regression (Ivanescu, et al 2015; Scheipl and Greven 2016; Brockhaus, et al 2016), and undoubtedly this productive group will continue to further develop this framework in the coming years.…”

Section: Introductionmentioning

confidence: 99%

Comparison and contrast of two general functional regression modelling frameworks

Morris

2017

Statistical Modelling

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In this article, Greven and Scheipl describe an impressively general framework for performing functional regression that builds upon the generalized additive modeling framework. Over the past number of years, my collaborators and I have also been developing a general framework for functional regression, functional mixed models, which shares many similarities with this framework, but has many differences as well. In this discussion, I compare and contrast these two frameworks, to hopefully illuminate characteristics of each, highlighting their respecitve strengths and weaknesses, and providing recommendations regarding the settings in which each approach might be preferable.

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Boosting flexible functional regression models with a high number of functional historical effects

Cited by 27 publications

References 26 publications

A mass participatory experiment provides a rich temporal profile of temperature response in spring onions

A mass participatory experiment provides a rich temporal profile of temperature response in spring onions

Stream Temperature Modeling Using Functional Regression Models

Comparison and contrast of two general functional regression modelling frameworks

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