Standardized benchmarks like RobustBench are crucial for evaluating adversarial robustness. However, the increasing dominance of models trained on massive synthetic datasets (orders of magnitude larger than original training sets) raises questions about reported performance gains. This work identifies and investigates a potential inflation factor: high feature-level similarity between large-scale synthetic training data and benchmark test sets. We argue this similarity is an inherent characteristic arising from the probabilistic generation process of these large datasets, which naturally produces examples highly similar to test instances in feature space. This creates what we term an “Implicit Information Advantage,” where models effectively train on near-duplicates of test instances. Through comprehensive empirical analysis, we demonstrate that: (1) Synthetic datasets exhibit significantly higher similarity to the test set compared to the original training data. (2) A direct correlation exists between this similarity and robustness outcomes, with test images benefiting most having the highest similarity scores. (3) Strikingly, ablation studies show that training on just a small fraction (e.g., 1%) of the most similar synthetic examples can yield robustness comparable to using the full massive dataset. These findings suggest current benchmarks may overestimate true robust generalization due to this similarity artifact. We call for revised evaluation protocols and greater transparency to ensure benchmarks accurately measure true generalization. Code and data can be found in https://github.com/fzjcdt/RethinkingRobustBench.

AdaBoost approaches have been used for multi-class imbalance classification with an imbalance ratio measured on class sizes. However, such ratio would assign each training sample of the same class with the same weight, thus failing to reflect the data distribution within a class. We propose to incorporate the density information of training samples into the class imbalance ratio so that samples of the same class could have different weights. As one could use the entire training set to calculate the imbalance and density factors, the weight of a training sample resulting from the two factors remains static throughout the training epochs. However, static weights could not reflect the up-to-date training status of base learners. To deal with this, we propose to design an adaptive weighting mechanism by making use of up-to-date training status to further alleviate the multi-class imbalance issue. Ultimately, we incorporate the class imbalance ratio, the density-based factor, and the adaptive weighting mechanism into a single variable, based on which the adaptive weights of all training samples are computed. Experimental studies are carried out to investigate the effectiveness of the proposed approach and each of the three components in dealing with multi-class imbalance classification problem.

In a streaming environment, the characteristics of the data themselves and their relationship with the labels are likely to experience changes as time goes on. Most drift detection methods for supervised data streams are performance-based, that is, they detect changes only after the classication accuracy deteriorates. This may not be sufcient in many application areas where the reason behind a drift is also important. Another category of drift detectors are data distribution-based detectors. Although they can detect some drifts within the input space, changes affecting only the labelling mechanism cannot be identied. Furthermore, little work is available on drift detection for high-dimensional supervised data streams. In this paper we propose an advanced Hierarchical Reduced-space Drift Detection Framework for Supervised Data Streams (HRDS) which captures drifts regardless of their effects on classication performance. This framework suggests monitoring both marginal and class-conditional distributions within a lower-dimensional space specically relevant to the assigned classication task. Experimental comparisons have demonstrated that the proposed HRDS not only achieves high-quality performance on high-dimensional data streams, but also outperforms its competitors in terms of detection recall, precision and F-measure across a wide range of different concept drift types including subtle drifts.

Surrogate-assisted evolutionary algorithms (SAEAs), which use efficient surrogate models or meta-models to approximate the fitness function in evolutionary algorithms (EAs), are effective and popular methods for solving computationally expensive optimization problems. During the past decades, a number of SAEAs have been proposed by combining different surrogate models and EAs. This paper dedicates to providing a more systematical review and comprehensive empirical study of surrogate models used in single-objective SAEAs. A new taxonomy of surrogate models in SAEAs for single-objective optimization is introduced in this paper. Surrogate models are classified into two major categories: absolute fitness models, which directly approximate the fitness function values of candidate solutions, and relative fitness models, which estimates the relative rank or preference of candidates rather than their fitness values. Then, the characteristics of different models are analyzed and compared by conducting a series of experiments in terms of time complexity (execution time), model accuracy, parameter influence, and the overall performance when used in EAs. The empirical results are helpful for researchers to select suitable surrogate models when designing SAEAs. Open research questions and future work are discussed at the end of the paper.

Imbalanced datasets may negatively impact the predictive performance of most classical classification algorithms. This problem, commonly found in real-world, is known in machine learning domain as imbalanced learning. Most techniques proposed to deal with imbalanced learning have been proposed and applied only to binary classification. When applied to multiclass tasks, their efficiency usually decreases and negative side effects may appear. This paper addresses these limitations by presenting a novel adaptive approach, E-MOSAIC (Ensemble of Classifiers based on MultiObjective Genetic Sampling for Imbalanced Classification). E-MOSAIC evolves a selection of samples extracted from training dataset, which are treated as individuals of a MOEA. The multiobjective process looks for the best combinations of instances capable of producing classifiers with high predictive accuracy in all classes. E-MOSAIC also incorporates two mechanisms to promote the diversity of these classifiers, which are combined into an ensemble specifically designed for imbalanced learning. Experiments using twenty imbalanced multi-class datasets were carried out. In these experiments, the predictive performance of E-MOSAIC is compared with state-of-the-art methods, including methods based on presampling, active-learning, cost-sensitive, and boosting. According to the experimental results, the proposed method obtained the best predictive performance for the multiclass accuracy measures mAUC and G-mean.

Sparse Bayesian learning is a state-of-the-art supervised learning algorithm that can choose a subset of relevant samples from the input data and make reliable probabilistic predictions. However, in the presence of high-dimensional data with irrelevant features, traditional sparse Bayesian classifiers suffer from performance degradation and low efficiency due to the incapability of eliminating irrelevant features. To tackle this problem, we propose a novel sparse Bayesian embedded feature selection algorithm that adopts truncated Gaussian distributions as both sample and feature priors. The proposed algorithm, called probabilistic feature selection and classification vector machine (PFCVM LP ) is able to simultaneously select relevant features and samples for classification tasks. In order to derive the analytical solutions, Laplace approximation is applied to compute approximate posteriors and marginal likelihoods. Finally, parameters and hyperparameters are optimized by the type-II maximum likelihood method. Experiments on three datasets validate the performance of PFCVM LP along two dimensions: classification performance and effectiveness for feature selection. Finally, we analyze the generalization performance and derive a generalization error bound for PFCVM LP . By tightening the bound, the importance of feature selection is demonstrated.

Semi-supervised learning (SSL) concerns the problem of how to improve classifiers’ performance through making use of prior knowledge from unlabeled data. Many SSL methods have been developed to integrate unlabeled data into the classifiers based on either the manifold or cluster assumption in recent years. In particular, the graph-based approaches, following the manifold assumption, have achieved a promising performance in many real-world applications. However, most of them work well on small-scale data sets only and lack probabilistic outputs. In this paper, a scalable graph-based SSL framework through sparse Bayesian model is proposed by defining a graph-based sparse prior. Based on the traditional Bayesian inference technique, a sparse Bayesian SSL algorithm (SBS$^2$L) is obtained, which can remove the irrelevant unlabeled samples and make probabilistic prediction for out-of-sample data. Moreover, in order to scale SBS$^2$L to large-scale data sets, an incremental SBS$^2$L (ISBS$^2$L) is derived. The key idea of ISBS$^2$L is employing an incremental strategy and sequentially selecting parts of unlabeled samples that contribute to the learning instead of using all available unlabeled samples directly. ISBS$^2$L has lower time and space complexities than previous SSL algorithms with the use of all unlabeled samples. Extensive experiments on various data sets verify that our algorithms can achieve comparable classification effectiveness and efficiency with much better scalability. Finally, the generalization error bound is derived based on robustness analysis.

Time series forecasting for streaming data plays an important role in many real applications, ranging from IoT systems, cyber-networks, to industrial systems and healthcare. However the real data is often complicated with anomalies and change points, which can lead the learned models deviating from the underlying patterns of the time series, especially in the context of online learning mode. In this paper we present an adaptive gradient learning method for recurrent neural networks (RNN) to forecast streaming time series in the presence of anomalies and change points. We explore the local features of time series to automatically weight the gradients of the loss of the newly available observations with distributional properties of the data in real time. We perform extensive experimental analysis on both synthetic and real datasets to evaluate the performance of the proposed method.

Class evolution, the phenomenon of class emergence and disappearance, is an important research topic for data stream mining. All previous studies implicitly regard class evolution as a transient change, which is not true for many real-world problems. This paper concerns the scenario where classes emerge or disappear gradually. A class-based ensemble approach, namely Class-Based ensemble for Class Evolution (CBCE), is proposed. By maintaining a base learner for each class and dynamically updating the base learners with new data, CBCE can rapidly adjust to class evolution. A novel under-sampling method for the base learners is also proposed to handle the dynamic class-imbalance problem caused by the gradual evolution of classes. Empirical studies demonstrate the effectiveness of CBCE in various class evolution scenarios in comparison to existing class evolution adaptation methods.

The classification of patterns into naturally ordered labels is referred to as ordinal regression or ordinal classification. Usually, this classification setting is by nature highly imbalanced, because there are classes in the problem that are a priori more probable than others. Although standard over-sampling methods can improve the classification of minority classes in ordinal classification, they tend to introduce severe errors in terms of the ordinal label scale, given that they do not take the ordering into account. A specific ordinal over-sampling method is developed in this paper for the first time in order to improve the performance of machine learning classifiers. The method proposed includes ordinal information by approaching over-sampling from a graph-based perspective. The results presented in this paper show the good synergy of a popular ordinal regression method (a reformulation of support vector machines) with the graph-based proposed algorithms, and the possibility of improving both the classification and the ordering of minority classes. A cost-sensitive version of the ordinal regression method is also introduced and compared with the over-sampling proposals, showing in general lower performance for minority classes.

Online class imbalance learning is a new learning problem that combines the challenges of both online learning and class imbalance learning. It deals with data streams having very skewed class distributions. This type of problems commonly exists in real-world applications, such as fault diagnosis of real-time control monitoring systems and intrusion detection in computer networks. In our earlier work, we defined class imbalance online, and proposed two learning algorithms OOB and UOB that build an ensemble model overcoming class imbalance in real time through resampling and time-decayed metrics. In this paper, we further improve the resampling strategy inside OOB and UOB, and look into their performance in both static and dynamic data streams. We give the first comprehensive analysis of class imbalance in data streams, in terms of data distributions, imbalance rates and changes in class imbalance status. We find that UOB is better at recognizing minority-class examples in static data streams, and OOB is more robust against dynamic changes in class imbalance status. The data distribution is a major factor affecting their performance. Based on the insight gained, we then propose two new ensemble methods that maintain both OOB and UOB with adaptive weights for final predictions, called WEOB1 and WEOB2. They are shown to possess the strength of OOB and UOB with good accuracy and robustness.

Since the 1970s the goal of generating programs in an automatic way (i.e., Automatic Programming) has been sought. A user would just define what he expects from the program (i.e., the requirements), and it should be automatically generated by the computer without the help of any programmer. Unfortunately, this task is much harder than expected. Although transformation methods are usually employed to address this problem, they cannot be employed if the gap between the specification and the actual implementation is too wide. In this paper we introduce a novel conceptual framework for evolving programs from their specification. We use genetic programming to evolve the programs, and at the same time we exploit the specification to co-evolve sets of unit tests. Programs are rewarded by how many tests they do not fail, whereas the unit tests are rewarded by how many programs they make to fail. We present and analyse seven different problems on which this novel technique is successfully applied.

Computing unique input output (UIO) sequences is a fundamental and hard problem in conformance testing of finite state machines (FSM). Previous experimental research has shown that evolutionary algorithms (EAs) can be applied successfully to find UIOs for some FSMs. However, before EAs can be recommended as a practical technique for computing UIOs, it is necessary to better understand the potential and limitations of these algorithms on this problem. In particular, more research is needed in determining for what instance classes of the problem EAs are feasible, and for what instance classes EAs are provably better than random search strategies. This paper presents rigorous theoretical and numerical analyses of the runtime of the (1 + 1) EA and random search on several selected instance classes of this problem. The theoretical analysis shows firstly, that there are instance classes where the EA is efficient, while random testing fails completely. Secondly, an instance class that is difficult for both random testing and the EA is presented. Finally, a parametrised instance class with tunable difficulty is presented. The numerical study estimates the constants in the asymptotic expressions obtained in the theoretical analysis, and the variability of the runtime. The numerical results fit well with the theoretical results, even for small problem instance sizes. Together, these results provide a first theoretical characterisation of the potential and limitations of the (1 + 1) EA on the problem of computing UIOs.

Population-based Algorithm Portfolios (PAP) is an appealing framework for integrating different Evolutionary Algorithms (EAs) to solve challenging numerical optimization problems. Particularly, PAP has shown significant advantages to single EAs when a number of problems need to be solved simultaneously. Previous investigation on PAP reveals that choosing appropriate constituent algorithms is crucial to the success of PAP. However, no method has been developed for this purpose. In this paper, an extended version of PAP, namely PAP based on Estimated Performance Matrix (EPM-PAP) is proposed. EPM-PAP is equipped with a novel constituent algorithms selection module, which is based on the EPM of each candidate EAs. Empirical studies demonstrate that the EPM-based selection method can successfully identify appropriate constituent EAs, and thus EPM-PAP outperformed all single EAs considered in this work.

Imbalanced learning problems contain an unequal distribution of data samples among different classes and pose a challenge to any classifier as it becomes hard to learn the minority class samples. Synthetic oversampling methods address this problem by generating the synthetic minority class samples to balance the distribution between the samples of the majority and minority classes. This paper identifies that most of the existing oversampling methods may generate the wrong synthetic minority samples in some scenarios and make learning tasks harder. To this end, a new method, called Majority Weighted Minority Oversampling TEchnique (MWMOTE), is presented for efficiently handling imbalanced learning problems. MWMOTE first identifies the hard-to-learn informative minority class samples and assigns them weights according to their euclidean distance from the nearest majority class samples. It then generates the synthetic samples from the weighted informative minority class samples using a clustering approach. This is done in such a way that all the generated samples lie inside some minority class cluster. MWMOTE has been evaluated extensively on four artificial and 20 real-world data sets. The simulation results show that our method is better than or comparable with some other existing methods in terms of various assessment metrics, such as geometric mean (G-mean) and area under the receiver operating curve (ROC), usually known as area under curve (AUC).

Pipe breaks in urban water distribution network lead to significant economical and social costs, putting the service quality as well as the profit of water utilities at risk. To cope with such a situation, scheduled preventive maintenance is desired, which aims to predict and fix potential break pipes proactively. Physical models developed for understanding and predicting the failure of pipes are usually expensive, thus can only be used on a limited number of trunk pipes. As an alternative, statistical models that try to predict pipe breaks based on historical data are far less expensive, and therefore have attracted a lot of interests from water utilities recently. In this paper, we report a novel data mining prediction system that has been built for a water utility in a big Chinese city. Various aspects of how to build such a system are described, including problem formulation, data cleaning, model construction, as well as evaluating the importance of attributes according to the requirements of end users in water utilities. Satisfactory results have been achieved by our prediction system. For example, with the system trained on the available dataset at the end of 2010, the water utility would avoid 50% of pipe breaks in 2011 by examining only 6.98% of its pipes in advance. During the construction of the system, we find that the extremely skew distribution of break and non-break pipes, interestingly, is not an obstacle. This lesson could serve as a practical reference for both academical studies on imbalanced learning as well as future explorations on pipe failure prediction problems.

We present novel, efficient, model based kernels for time series data rooted in the reservoir computation framework. The kernels are implemented by fitting reservoir models sharing the same fixed deterministically constructed state transition part to individual time series. The proposed kernels can naturally handle time series of different length without the need to specify a parametric model class for the time series. Compared with most time series kernels, our kernels are computationally efficient. We show how the model distances used in the kernel can be calculated analytically or efficiently estimated. The experimental results on synthetic and benchmark time series classification tasks confirm the efficiency of the proposed kernel in terms of both generalization accuracy and computational speed. This paper also investigates on-line reservoir kernel construction for extremely long time series.

In class imbalance learning problems, how to better recognize examples from the minority class is the key focus, since it is usually more important and expensive than the majority class. Quite a few ensemble solutions have been proposed in the literature with varying degrees of success. It is generally believed that diversity in an ensemble could help to improve the performance of class imbalance learning. However, no study has actually investigated diversity in depth in terms of its definitions and effects in the context of class imbalance learning. It is unclear whether diversity will have a similar or different impact on the performance of minority and majority classes. In this paper, we aim to gain a deeper understanding of if and when ensemble diversity has a positive impact on the classification of imbalanced data sets. First, we explain when and why diversity measured by Q-statistic can bring improved overall accuracy based on two classification patterns proposed by Kuncheva et al. We define and give insights into good and bad patterns in imbalanced scenarios. Then, the pattern analysis is extended to single-class performance measures, including recall, precision, and F-measure, which are widely used in class imbalance learning. Six different situations of diversity's impact on these measures are obtained through theoretical analysis. Finally, to further understand how diversity affects the single class performance and overall performance in class imbalance problems, we carry out extensive experimental studies on both artificial data sets and real-world benchmarks with highly skewed class distributions. We find strong correlations between diversity and discussed performance measures. Diversity shows a positive impact on the minority class in general. It is also beneficial to the overall performance in terms of AUC and G-mean.

Online learning algorithms often have to operate in the presence of concept drifts. A recent study revealed that different diversity levels in an ensemble of learning machines are required in order to maintain high generalization on both old and new concepts. Inspired by this study and based on a further study of diversity with different strategies to deal with drifts, we propose a new online ensemble learning approach called Diversity for Dealing with Drifts (DDD). DDD maintains ensembles with different diversity levels and is able to attain better accuracy than other approaches. Furthermore, it is very robust, outperforming other drift handling approaches in terms of accuracy when there are false positive drift detections. In all the experimental comparisons we have carried out, DDD always performed at least as well as other drift handling approaches under various conditions, with very few exceptions.

Negative Correlation Learning (NCL) [CHECK END OF SENTENCE], [CHECK END OF SENTENCE] is a neural network ensemble learning algorithm which introduces a correlation penalty term to the cost function of each individual network so that each neural network minimizes its mean-square-error (MSE) together with the correlation. This paper describes NCL in detail and observes that the NCL corresponds to training the entire ensemble as a single learning machine that only minimizes the MSE without regularization. This insight explains that NCL is prone to overfitting the noise in the training set. The paper analyzes this problem and proposes the multiobjective regularized negative correlation learning (MRNCL) algorithm which incorporates an additional regularization term for the ensemble and uses the evolutionary multiobjective algorithm to design ensembles. In MRNCL, we define the crossover and mutation operators and adopt nondominated sorting algorithm with fitness sharing and rank-based fitness assignment. The experiments on synthetic data as well as real-world data sets demonstrate that MRNCL achieves better performance than NCL, especially when the noise level is nontrivial in the data set. In the experimental discussion, we give three reasons why our algorithm outperforms others.

Online learning algorithms often have to operate in the presence of concept drift (i.e., the concepts to be learned can change with time). This paper presents a new categorization for concept drift, separating drifts according to different criteria into mutually exclusive and nonheterogeneous categories. Moreover, although ensembles of learning machines have been used to learn in the presence of concept drift, there has been no deep study of why they can be helpful for that and which of their features can contribute or not for that. As diversity is one of these features, we present a diversity analysis in the presence of different types of drifts. We show that, before the drift, ensembles with less diversity obtain lower test errors. On the other hand, it is a good strategy to maintain highly diverse ensembles to obtain lower test errors shortly after the drift independent on the type of drift, even though high diversity is more important for more severe drifts. Longer after the drift, high diversity becomes less important. Diversity by itself can help to reduce the initial increase in error caused by a drift, but does not provide the faster recovery from drifts in long-term.

Many real-world applications have problems when learning from imbalanced data sets, such as medical diagnosis, fraud detection, and text classification. Very few minority class instances cannot provide sufficient information and result in performance degrading greatly. As a good way to improve the classification performance of weak learner, some ensemble-based algorithms have been proposed to solve class imbalance problem. However, it is still not clear that how diversity affects classification performance especially on minority classes, since diversity is one influential factor of ensemble. This paper explores the impact of diversity on each class and overall performance. As the other influential factor, accuracy is also discussed because of the trade-off between diversity and accuracy. Firstly, three popular re-sampling methods are combined into our ensemble model and evaluated for diversity analysis, which includes under-sampling, over-sampling, and SMOTE - a data generation algorithm. Secondly, we experiment not only on two-class tasks, but also those with multiple classes. Thirdly, we improve SMOTE in a novel way for solving multi-class data sets in ensemble model - SMOTEBagging.

An ensemble is a group of learners that work together as a committee to solve a problem. The existing ensemble learning algorithms often generate unnecessarily large ensembles, which consume extra computational resource and may degrade the generalization performance. Ensemble pruning algorithms aim to find a good subset of ensemble members to constitute a small ensemble, which saves the computational resource and performs as well as, or better than, the unpruned ensemble. This paper introduces a probabilistic ensemble pruning algorithm by choosing a set of ldquosparserdquo combination weights, most of which are zeros, to prune the ensemble. In order to obtain the set of sparse combination weights and satisfy the nonnegative constraint of the combination weights, a left-truncated, nonnegative, Gaussian prior is adopted over every combination weight. Expectation propagation (EP) algorithm is employed to approximate the posterior estimation of the weight vector. The leave-one-out (LOO) error can be obtained as a by-product in the training of EP without extra computation and is a good indication for the generalization error. Therefore, the LOO error is used together with the Bayesian evidence for model selection in this algorithm. An empirical study on several regression and classification benchmark data sets shows that our algorithm utilizes far less component learners but performs as well as, or better than, the unpruned ensemble. Our results are very competitive compared with other ensemble pruning algorithms.

UCS is a supervised learning classifier system that was introduced in 2003 for classification in data mining tasks. The representation of a rule in UCS as a univariate classification rule is straightforward for a human to understand. However, the system may require a large number of rules to cover the input space. Artificial neural networks (NNs), on the other hand, normally provide a more compact representation. However, it is not a straightforward task to understand the network. In this paper, we propose a novel way to incorporate NNs into UCS. The approach offers a good compromise between compactness, expressiveness, and accuracy. By using a simple artificial NN as the classifier's action, we obtain a more compact population size, better generalization, and the same or better accuracy while maintaining a reasonable level of expressiveness. We also apply negative correlation learning (NCL) during the training of the resultant NN ensemble. NCL is shown to improve the generalization of the ensemble.

This paper proposes a general boosting framework for combining multiple kernel models in the context of both classification and regression problems. Our main approach is built on the idea of gradient boosting together with a new regularization scheme and aims at reducing the cubic complexity of training kernel models. We focus mainly on using the proposed boosting framework to combine kernel ridge regression (KRR) models for regression tasks. Numerical experiments on four large-scale data sets have shown that boosting multiple small KRR models is superior to training a single large KRR model on both improving generalization performance and reducing computational requirements.

Research on potential interactions between connectionist learning systems, i.e., artificial neural networks (ANNs), and evolutionary search procedures, like genetic algorithms (GAs), has attracted a lot of attention recently. Evolutionary ANNs (EANNs) can be considered as the combination of ANNs and evolutionary search procedures. This article first distinguishes among three kinds of evolution in EANNs, i.e., the evolution of connection weights, of architectures, and of learning rules. Then it reviews each kind of evolution in detail and analyzes critical issues related to different evolutions. the review shows that although a lot of work has been done on the evolution of connection weights and architectures, few attempts have been made to understand the evolution of learning rules. Interactions among different evolutions are seldom mentioned in current research. However, the evolution of learning rules and its interactions with other kinds of evolution, play a vital role in EANNs. Finally, this article briefly describes a general framework for EANNs, which not only includes the aforementioned three kinds of evolution, but also considers interactions among them. © 1993 John Wiley & Sons, Inc.