Real-world optimization scenarios under uncertainty and noise are typically handled with robust optimization techniques, which re-formulate the original optimization problem into a robust... Show moreReal-world optimization scenarios under uncertainty and noise are typically handled with robust optimization techniques, which re-formulate the original optimization problem into a robust counterpart, e.g., by taking an average of the function values over different perturbations to a specific input. Solving the robust counterpart instead of the original problem can significantly increase the associated computational cost, which is often overlooked in the literature to the best of our knowledge. Such an extra cost brought by robust optimization might depend on the problem landscape, the dimensionality, the severity of the uncertainty, and the formulation of the robust counterpart.This paper targets an empirical approach that evaluates and compares the computational cost brought by different robustness formulations in Kriging-based optimization on a wide combination (300 test cases) of problems, uncertainty levels, and dimensions. We mainly focus on the CPU time taken to find robust solutions, and choose five commonly-applied robustness formulations: `"mini-max robustness'', "mini-max regret robustness'', "expectation-based robustness'', ``dispersion-based robustness'', and "composite robustness'' respectively. We assess the empirical performance of these robustness formulations in terms of a fixed budget and a fixed target analysis, from which we find that "mini-max robustness'' is the most practical formulation w.r.t.~the associated computational cost. Show less
Automated Machine Learning (AutoML) frameworks are designed to select the optimal combination of operators and hyperparameters. Classical AutoML-based Bayesian Optimization (BO) approaches often... Show moreAutomated Machine Learning (AutoML) frameworks are designed to select the optimal combination of operators and hyperparameters. Classical AutoML-based Bayesian Optimization (BO) approaches often integrate all operator search spaces into a single search space. However, a disadvantage of this history-based strategy is that it can be less robust when initialized randomly than optimizing each operator algorithm combination independently. To overcome this issue, a novel contesting procedure algorithm, Divide And Conquer Optimization (DACOpt), is proposed to make AutoML more robust. DACOpt partitions the AutoML search space into a reasonable number of sub-spaces based on algorithm similarity and budget constraints. Furthermore, throughout the optimization process, DACOpt allocates resources to each sub-space to ensure that (1) all areas of the search space are covered and (2) more resources are assigned to the most promising sub-space. Two extensive sets of experiments on 117 benchmark datasets demonstrate that DACOpt achieves significantly better results in 36% of AutoML benchmark datasets: 5% when to compared to TPOT, 8% - to AutoSklearn, 15% - to H20 and 18% - to ATM. Show less
Saha, S.; de Jesus de Araujo Rios, T.; Minku, L.L.; Stein, B. van; Wollstadt, P.; Yao, X.; ... ; Menzel, S. 2022
Automated machine learning (AutoML) aims to automatically produce the best machine learning pipeline, i.e., a sequence of operators and their optimized hyperparameter settings, to maximize the... Show moreAutomated machine learning (AutoML) aims to automatically produce the best machine learning pipeline, i.e., a sequence of operators and their optimized hyperparameter settings, to maximize the performance of an arbitrary machine learning problem. Typically, AutoML based Bayesian optimization (BO) approaches convert the AutoML optimization problem into a Hyperparameter Optimization (HPO) problem, where the choice of algorithms is modeled as an additional categorical hyperparameter. In this way, algorithms and their local hyper-parameters are referred to as the same level. Consequently, this approach makes the resulting initial sampling less robust. In this study, we describe a first attempt to formulate the AutoML optimization problem as its nature instead of transfer it into a HPO problem. To take advantage of this paradigm, we propose a novel initial sampling approach to maximize the coverage of the AutoML search space to help BO construct a robust surrogate model. We experiment with 2 independent scenarios of AutoML with 2 operators and 6 operators over 117 benchmark datasets. Results of our experiments demonstrate that the performance of BO significantly improved by using our sampling approach. Show less
The imbalanced classification problem is very relevant in both academic and industrial applications. The task of finding the best machine learning model to use for a specific imbalanced dataset is... Show moreThe imbalanced classification problem is very relevant in both academic and industrial applications. The task of finding the best machine learning model to use for a specific imbalanced dataset is complicated due to a large number of existing algorithms, each with its own hyperparameters. The Combined Algorithm Selection and Hyperparameter optimization (CASH) has been introduced to tackle both aspects at the same time. However, CASH has not been studied in detail in the class imbalance domain, where the best combination of resampling technique and classification algorithm is searched for, together with their optimized hyperparameters. Thus, we target the CASH problem for imbalanced classification. We experiment with a search space of 5 classification algorithms, 21 resampling approaches and 64 relevant hyperparameters in total. Moreover, we investigate performance of 2 well-known optimization approaches: Random search and Tree Parzen Estimators approach which is a kind of Bayesian optimization. For comparison, we also perform grid search on all combinations of resampling techniques and classification algorithms with their default hyperparameters. Our experimental results show that a Bayesian optimization approach outperforms the other approaches for CASH in this application domain. Show less
de Jesus de Araujo Rios, T.; Stein, B., van; Bäck, T.H.W.; Sendhoff, B.; Menzel, S. 2021
Point cloud autoencoders were recently introduced as powerful models for data compression. They learn a lowdimensional set of variables that are suitable as design parameters for shape generation... Show morePoint cloud autoencoders were recently introduced as powerful models for data compression. They learn a lowdimensional set of variables that are suitable as design parameters for shape generation and optimization problems. In engineering tasks, 3D point clouds are often derived from fine polygon meshes, which are the most suitable representations for physics simulation, e.g., computational fluid dynamics (CFD). Yet, the reconstruction of high-quality meshes from autoencoder-based point clouds is challenging, often requiring supervised and manual work, which is prohibitive during the optimization. Target shape matching optimization using existing mesh prototypes overcomes the difficulties of recovering shape information from the point coordinates. However, for autoencoders trained on data sets comprising shapes with high degree of dissimilarity, there is not a single mesh prototype that can fit any autoencoder-based point cloud, and the selection of a set of prototypes is nontrivial. In the present paper we propose a method for optimizing a selection of prototypical meshes to match the maximum number of shapes in the autoencoder output space as possible, which is achieved by linking the advantages of the latent space representation of an autoencoder and the state-of-the-art free form deformation (FFD) method. Furthermore, we approached the balance between costs (number of mesh prototypes) and number of covered shapes by varying the number of prototypes and the dimensionality of the autoencoder latent space, showing that higher-dimensional latent spaces encode finer geometric changes, requiring more sophisticated FFD setups. Show less
Although over 90 oversampling approaches have been developed in the imbalance learning domain, most of the empirical study and application work are still based on the “classical” resampling... Show moreAlthough over 90 oversampling approaches have been developed in the imbalance learning domain, most of the empirical study and application work are still based on the “classical” resampling techniques. In this paper, several experiments on 19 benchmark datasets are set up to study the efficiency of six powerful oversampling approaches, including both “classical” and new ones. According to our experimental results, oversampling techniques that consider the minority class distribution (new ones) perform better in most cases and RACOG gives the best performance among the six reviewed approaches. We further validate our conclusion on our real-world inspired vehicle datasets and also find applying oversampling techniques can improve the performance by around 10%. In addition, seven data complexity measures are considered for the initial purpose of investigating the relationship between data complexity measures and the choice of resampling techniques. Although no obvious relationship can be abstracted in our experiments, we find F1v value, a measure for evaluating the overlap which most researchers ignore, has a strong negative correlation with the potential AUC value (after resampling). Show less
Although the anomaly detection problem can be considered as an extreme case of class imbalance problem, very few studies consider improving class imbalance classification with anomaly detection... Show moreAlthough the anomaly detection problem can be considered as an extreme case of class imbalance problem, very few studies consider improving class imbalance classification with anomaly detection ideas. Most data-level approaches in the imbalanced learning domain aim to introduce more information to the original dataset by generating synthetic samples. However, in this paper, we gain additional information in another way, by introducing additional attributes. We propose to introduce the outlier score and four types of samples (safe, borderline, rare, outlier) as additional attributes in order to gain more information on the data characteristics and improve the classification performance. According to our experimental results, introducing additional attributes can improve the imbalanced classification performance in most cases (6 out of 7 datasets). Further study shows that this performance improvement is mainly contributed by a more accurate classification in the overlapping region of the two classes (majority and minority classes). The proposed idea of introducing additional attributes is simple to implement and can be combined with resampling techniques and other algorithmic-level approaches in the imbalanced learning domain. Show less
Rios, T.; Wollstadt, P.; Stein, B. van; Bäck, T.H.W.; Xu, Z.; Sendhoff, B.; Menzel, S. 2019
Geometric Deep Learning (GDL) methods have recently gained interest as powerful, high-dimensional models for approaching various geometry processing tasks. However, training deep neural network... Show moreGeometric Deep Learning (GDL) methods have recently gained interest as powerful, high-dimensional models for approaching various geometry processing tasks. However, training deep neural network models on geometric input requires considerable computational effort. Even more so, if one considers typical problem sizes found in application domains such as engineering tasks, where geometric data are often orders of magnitude larger than the inputs currently considered in GDL literature. Hence, an assessment of the scalability of the training task is necessary, where model and data set parameters can be mapped to the computational demand during training. The present paper therefore studies the effects of data set size and the number of free model parameters on the computational effort of training a Point Cloud Autoencoder (PC-AE). We further review pre-processing techniques to obtain efficient representations of high-dimensional inputs to the PC-AE and investigate the effects of these techniques on the information abstracted by the trained model. We perform these experiments on synthetic geometric data inspired by engineering applications using computing hardware with particularly recent graphics processing units (GPUs) with high memory specifications. The present study thus provides a comprehensive evaluation of how to scale geometric deep learning architectures to high-dimensional inputs to allow for an application of state-of-the-art deep learning methods in real-world tasks. Show less
Rios, T.; Sendhoff, B.; Menzel, S.; Bäck, T.H.W.; Stein, B. van 2019
A crucial step for optimizing a system is to formulate the objective function, and part of it concerns the selection of the design parameters. One of the major goals is to achieve a fair trade-off... Show moreA crucial step for optimizing a system is to formulate the objective function, and part of it concerns the selection of the design parameters. One of the major goals is to achieve a fair trade-off between exploring feasible solutions in the design space and maintaining admissible computational effort. In order to achieve such balance in optimization problems with Computer Aided Engineering (CAE) models, the conventional constructive geometric representations are substituted by deformation methods, e.g. free form deformation, where the position of a few control points might be capable of handling large scale shape modifications. In light of the recent developments in the field of geometric deep learning, autoencoders have risen as a promising alternative for efficiently condensing high-dimensional models into compact representations. In this paper, we present a novel perspective on geometric deep learning models by exploring the applicability of the latent space of a point cloud autoencoder in shape optimization problems with evolutionary algorithms. Focusing on engineering applications, a target shape matching optimization is used as a surrogate to the computationally expensive CAE simulations required in engineering optimizations. Through the quality assessment of the solutions achieved in the optimization and further aspects, such as shape feasibility, point cloud autoencoders showed to be consistent and suitable geometric representations for such problems, adding a new perspective on the approaches for handling high-dimensional models to optimization tasks. Show less
Although the class-imbalance classification problem has caught a huge amount of attention, hyperparameter optimisation has not been studied in detail in this field. Both classification algorithms... Show moreAlthough the class-imbalance classification problem has caught a huge amount of attention, hyperparameter optimisation has not been studied in detail in this field. Both classification algorithms and resampling techniques involve some hyperparameters that can be tuned. This paper sets up several experiments and draws the conclusion that, compared to using default hyperparameters, applying hyperparameter optimisation for both classification algorithms and resampling approaches can produce the best results for classifying the imbalanced datasets. Moreover, this paper shows that data complexity, especially the overlap between classes, has a big impact on the potential improvement that can be achieved through hyperparameter optimisation. Results of our experiments also indicate that using resampling techniques cannot improve the performance for some complex datasets, which further emphasizes the importance of analyzing data complexity before dealing with imbalanced datasets. Show less
