Boosting in Nonlinear Regression Models with an Application to DCE-MRI Data.

BACKGROUND: For the statistical analysis of dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data, compartment models are a commonly used tool. By these models, the observed uptake of contrast agent in some tissue over time is linked to physiologic properties like capillary permeability and blood flow. Up to now, models of different complexity have been used, and it is still unclear which model should be used in which situation. In previous studies, it has been found that for DCE-MRI data, the number of compartments differs for different types of tissue, and that in cancerous tissue, it might actually differ over a region of voxels of one DCE-MR image. OBJECTIVES: To find the appropriate number of compartments and estimate the parameters of a regression model for each voxel in an DCE-MR image. With that, tumors in an DCE-MR image can be located, and for example therapy success can be assessed. METHODS: The observed uptake of contrast agent in a voxel of an image of some tissue is described by a concentration time curve. This curve can be modeled using a nonlinear regression model. We present a boosting approach with nonlinear regression as base procedure, which allows us to estimate the number of compartments and the related parameters for each voxel of an DCE-MR image. In addition, a spatially regularized version of this approach is proposed. RESULTS: With the proposed approach, the number of compartments - and with that the complexity of the model - per voxel is not fixed but data-driven, which allows us to fit models of adequate complexity to the concentration time curves of all voxels. The parameters of the model remain nevertheless interpretable because of the underlying compartment model. CONCLUSIONS: The proposed boosting approaches outperform all competing methods considered in this paper regarding the correct localization of tumors in DCE-MR images as well as the spatial homogeneity of the estimated number of compartments across the image, and the definition of the tumor edge.

Analyzing the BBOB results by means of benchmarking concepts.

We present methods to answer two basic questions that arise when benchmarking optimization algorithms. The first one is: which algorithm is the "best" one? and the second one is: which algorithm should I use for my real-world problem? Both are connected and neither is easy to answer. We present a theoretical framework for designing and analyzing the raw data of such benchmark experiments. This represents a first step in answering the aforementioned questions. The 2009 and 2010 BBOB benchmark results are analyzed by means of this framework and we derive insight regarding the answers to the two questions. Furthermore, we discuss how to properly aggregate rankings from algorithm evaluations on individual problems into a consensus, its theoretical background and which common pitfalls should be avoided. Finally, we address the grouping of test problems into sets with similar optimizer rankings and investigate whether these are reflected by already proposed test problem characteristics, finding that this is not always the case.

Resampling methods for meta-model validation with recommendations for evolutionary computation.

Meta-modeling has become a crucial tool in solving expensive optimization problems. Much of the work in the past has focused on finding a good regression method to model the fitness function. Examples include classical linear regression, splines, neural networks, Kriging and support vector regression. This paper specifically draws attention to the fact that assessing model accuracy is a crucial aspect in the meta-modeling framework. Resampling strategies such as cross-validation, subsampling, bootstrapping, and nested resampling are prominent methods for model validation and are systematically discussed with respect to possible pitfalls, shortcomings, and specific features. A survey of meta-modeling techniques within evolutionary optimization is provided. In addition, practical examples illustrating some of the pitfalls associated with model selection and performance assessment are presented. Finally, recommendations are given for choosing a model validation technique for a particular setting.