A Fourier-based Solving Approach for the Transport of Intensity Equation without Typical Restrictions

The Transport-of-Intensity equation (TIE) has been proven as a standard approach for phase retrieval. Some high efficiency solving methods for the TIE, extensively used in many works, are based on a Fourier-Transform (FT). However, to solve the TIE by these methods several assumptions have to be made. A common assumption is that there are no zero values for the intensity distribution allowed. The two most widespread Fourier-based approaches have further restrictions. One of these requires the uniformity of the intensity distribution and the other assumes the collinearity of the intensity and phase gradients. In this paper, we present an approach, which does not need any of these assumptions and consequently extends the application domain of the TIE

Solving phase‐field fracture problems in the tensor train format

Phase-field models for the quasi-static simulation of brittle fracture where the crack is approximated by a damage phase-field are limited by the necessary memory and computation time. In this contribution, we study the applicability of low-rank methods to phase-field fracture models, specifically the tensor train (TT) format. To this end, we investigate the low-rank structure of the crack phase-field. Additionally, we present an implementation of an alternating minimization scheme to solve the coupled displacement and damage problem in the TT format. We show the evolution of the TT ranks of the displacement and damage fields for a specific example

Q(D)O-ES: Population-based Quality (Diversity) Optimisation for Post Hoc Ensemble Selection in AutoML

Automated machine learning (AutoML) systems commonly ensemble models post hoc to improve predictive performance, typically via greedy ensemble selection (GES). However, we believe that GES may not always be optimal, as it performs a simple deterministic greedy search. In this work, we introduce two novel population-based ensemble selection methods, QO-ES and QDO-ES, and compare them to GES. While QO-ES optimises solely for predictive performance, QDO-ES also considers the diversity of ensembles within the population, maintaining a diverse set of well-performing ensembles during optimisation based on ideas of quality diversity optimisation. The methods are evaluated using 71 classification datasets from the AutoML benchmark, demonstrating that QO-ES and QDO-ES often outrank GES, albeit only statistically significant on validation data. Our results further suggest that diversity can be beneficial for post hoc ensembling but also increases the risk of overfitting.Comment: 10 pages main paper, 24 pages references and appendix, 4 figures, 16 subfigures, 13 tables, to be published in: International Conference on Automated Machine Learning 2023; affiliations corrected. arXiv admin note: text overlap with arXiv:2307.0028

HPO × ELA:Investigating Hyperparameter Optimization Landscapes by Means of Exploratory Landscape Analysis

Hyperparameter optimization (HPO) is a key component of machine learning models for achieving peak predictive performance. While numerous methods and algorithms for HPO have been proposed over the last years, little progress has been made in illuminating and examining the actual structure of these black-box optimization problems. Exploratory landscape analysis (ELA) subsumes a set of techniques that can be used to gain knowledge about properties of unknown optimization problems. In this paper, we evaluate the performance of five different black-box optimizers on 30 HPO problems, which consist of two-, three- and five-dimensional continuous search spaces of the XGBoost learner trained on 10 different data sets. This is contrasted with the performance of the same optimizers evaluated on 360 problem instances from the black-box optimization benchmark (BBOB). We then compute ELA features on the HPO and BBOB problems and examine similarities and differences. A cluster analysis of the HPO and BBOB problems in ELA feature space allows us to identify how the HPO problems compare to the BBOB problems on a structural meta-level. We identify a subset of BBOB problems that are close to the HPO problems in ELA feature space and show that optimizer performance is comparably similar on these two sets of benchmark problems. We highlight open challenges of ELA for HPO and discuss potential directions of future research and applications.</p

Hpo X Ela:Investigating Hyperparameter Optimization Landscapes by Means of Exploratory Landscape Analysis

Hyperparameter optimization (HPO) is a key component of machine learning models for achieving peak predictive performance. While numerous methods and algorithms for HPO have been proposed over the last years, little progress has been made in illuminating and examining the actual structure of these black-box optimization problems. Exploratory landscape analysis (ELA) subsumes a set of techniques that can be used to gain knowledge about properties of unknown optimization problems. In this paper, we evaluate the performance of five different black-box optimizers on 30 HPO problems, which consist of two-, three- and five-dimensional continuous search spaces of the XGBoost learner trained on 10 different data sets. This is contrasted with the performance of the same optimizers evaluated on 360 problem instances from the black-box optimization benchmark (BBOB). We then compute ELA features on the HPO and BBOB problems and examine similarities and differences. A cluster analysis of the HPO and BBOB problems in ELA feature space allows us to identify how the HPO problems compare to the BBOB problems on a structural meta-level. We identify a subset of BBOB problems that are close to the HPO problems in ELA feature space and show that optimizer performance is comparably similar on these two sets of benchmark problems. We highlight open challenges of ELA for HPO and discuss potential directions of future research and applications

An R toolbox for score-based measurement invariance tests in IRT models

The detection of differential item functioning (DIF) is a central topic in psychometrics and educational measurement. In the past few years, a new family of score-based tests of measurement invariance has been proposed, which allows the detection of DIF along arbitrary person covariates in a variety of item response theory (IRT) models. This paper illustrates the application of these tests within the R system for statistical computing, making them accessible to a broad range of users. This presentation also includes IRT models for which these tests have not previously been investigated, such as the generalized partial credit model. The paper has three goals: First, we review the ideas behind score-based tests of measurement invariance. Second, we describe the implementation of these tests within the R system for statistical computing, which is based on the interaction of the R packages mirt, psychotools and strucchange. Third, we illustrate the application of this software and the interpretation of its output in two empirical datasets. The complete R code for reproducing our results is reported in the paper