We show that established performance metrics in binary classification, such as Matthews' correlation coefficient (MCC), Cohen's $\kappa$, the F-score or the Jaccard similarity coefficient are not robust to class imbalance in the sense that if the proportion of the minority class tends to $0$, the true positive rate (TPR) of the Bayes classifier under these metrics {becomes very small or even tends to $0$}. Thus, in imbalanced classification problems, these metrics favour classifiers which ignore the minority class. To alleviate this issue we introduce robustified modifications of the MCC, of Cohen's $\kappa$ and of the F-score with an additional tuning parameter which allows to adapt the amount of robustness against class imbalance. As theoretical guarantee we show that the Bayes-optimal classifier for these robustified performance metrics, when expressed in terms of the density ratio $f_1/f_0$ of the class-conditional densities $f_i$, has a threshold parameter which is upper-bounded in terms of the tuning parameters. Therefore, even in strongly imbalanced settings, the TPR associated to this classifier will be bounded away from $0${, provided that $f_1/f_0$ exceeds this bound with positive probability under the positive class}. We numerically illustrate the behaviour of the various performance metrics and the effect of the tuning parameters in simulations as well as on a credit default data set. We also discuss connections to the receiver operating characteristic and precision-recall curves, which provide an alternative perspective on the proposed notion of robustness, and give recommendations on how to combine their usage with performance metrics.
Diabetes mellitus poses a significant health risk, as nearly 1 in 9 people are affected by it. Early detection can significantly lower this risk. Despite significant advancements in machine learning for identifying diabetic cases, results can still be influenced by the imbalanced nature of the data. To address this challenge, our study considered copula-based data augmentation, which preserves the dependency structure when generating data for the minority class and integrates it with machine learning (ML) techniques. We selected the Pima Indian dataset and generated data using A2 copula, then applied four machine learning algorithms: logistic regression, random forest, gradient boosting, and extreme gradient boosting. Our findings indicate that XGBoost combined with A2 copula oversampling achieved the best performance improving accuracy by 4.6%, precision by 15.6%, recall by 20.4%, F1-score by 18.2% and AUC by 25.5% compared to the standard SMOTE method. Furthermore, we statistically validated our results using the McNemar test. This research represents the first known use of A2 copulas for data augmentation and serves as an alternative to the SMOTE technique, highlighting the efficacy of copulas as a statistical method in machine learning applications.
Class imbalance remains a major challenge in machine learning, especially in multi-class problems with long-tailed distributions. Existing methods, such as data resampling, cost-sensitive techniques, and logistic loss modifications, though popular and often effective, lack solid theoretical foundations. As an example, we demonstrate that cost-sensitive methods are not Bayes-consistent. This paper introduces a novel theoretical framework for analyzing generalization in imbalanced classification. We then propose a new class-imbalanced margin loss function for both binary and multi-class settings, prove its strong $H$-consistency, and derive corresponding learning guarantees based on empirical loss and a new notion of class-sensitive Rademacher complexity. Leveraging these theoretical results, we devise novel and general learning algorithms, IMMAX (Imbalanced Margin Maximization), which incorporate confidence margins and are applicable to various hypothesis sets. While our focus is theoretical, we also present extensive empirical results demonstrating the effectiveness of our algorithms compared to existing baselines.
The classification of imbalanced data streams, which have unequal class distributions, is a key difficulty in machine learning, especially when dealing with multiple classes. While binary imbalanced data stream classification tasks have received considerable attention, only a few studies have focused on multi-class imbalanced data streams. Effectively managing the dynamic imbalance ratio is a key challenge in this domain. This study introduces a novel, robust, and resilient approach to address these challenges by integrating Locality Sensitive Hashing with Random Hyperplane Projections (LSH-RHP) into the Dynamic Ensemble Diversification (DynED) framework. To the best of our knowledge, we present the first application of LSH-RHP for undersampling in the context of imbalanced non-stationary data streams. The proposed method undersamples the majority classes by utilizing LSH-RHP, provides a balanced training set, and improves the ensemble's prediction performance. We conduct comprehensive experiments on 23 real-world and ten semi-synthetic datasets and compare LSH-DynED with 15 state-of-the-art methods. The results reveal that LSH-DynED outperforms other approaches in terms of both Kappa and mG-Mean effectiveness measures, demonstrating its capability in dealing with multi-class imbalanced non-stationary data streams. Notably, LSH-DynED performs well in large-scale, high-dimensional datasets with considerable class imbalances and demonstrates adaptation and robustness in real-world circumstances. To motivate our design, we review existing methods for imbalanced data streams, outline key challenges, and offer guidance for future work. For the reproducibility of our results, we have made our implementation available on GitHub.
Many classification tasks involve imbalanced data, in which a class is largely underrepresented. Several techniques consists in creating a rebalanced dataset on which a classifier is trained. In this paper, we study theoretically such a procedure, when the classifier is a Centered Random Forests (CRF). We establish a Central Limit Theorem (CLT) on the infinite CRF with explicit rates and exact constant. We then prove that the CRF trained on the rebalanced dataset exhibits a bias, which can be removed with appropriate techniques. Based on an importance sampling (IS) approach, the resulting debiased estimator, called IS-ICRF, satisfies a CLT centered at the prediction function value. For high imbalance settings, we prove that the IS-ICRF estimator enjoys a variance reduction compared to the ICRF trained on the original data. Therefore, our theoretical analysis highlights the benefits of training random forests on a rebalanced dataset (followed by a debiasing procedure) compared to using the original data. Our theoretical results, especially the variance rates and the variance reduction, appear to be valid for Breiman's random forests in our experiments.
This paper introduces a novel oversampling technique designed to improve classification performance on imbalanced datasets. The proposed method enhances the traditional SMOTE algorithm by incorporating convex combination and kernel-based weighting to generate synthetic samples that better represent the minority class. Through experiments on multiple real-world datasets, we demonstrate that the new technique outperforms existing methods in terms of F1-score, G-mean, and AUC, providing a robust solution for handling imbalanced datasets in classification tasks.
In an environment of increasingly volatile financial markets, the accurate estimation of risk remains a major challenge. Traditional econometric models, such as GARCH and its variants, are based on assumptions that are often too rigid to adapt to the complexity of the current market dynamics. To overcome these limitations, we propose a hybrid framework for Value-at-Risk (VaR) estimation, combining GARCH volatility models with deep reinforcement learning. Our approach incorporates directional market forecasting using the Double Deep Q-Network (DDQN) model, treating the task as an imbalanced classification problem. This architecture enables the dynamic adjustment of risk-level forecasts according to market conditions. Empirical validation on daily Eurostoxx 50 data covering periods of crisis and high volatility shows a significant improvement in the accuracy of VaR estimates, as well as a reduction in the number of breaches and also in capital requirements, while respecting regulatory risk thresholds. The ability of the model to adjust risk levels in real time reinforces its relevance to modern and proactive risk management.
The biomedical field is beginning to explore the use of quantum machine learning (QML) for tasks traditionally handled by classical machine learning, especially in predicting ADME (absorption, distribution, metabolism, and excretion) properties, which are essential in drug evaluation. However, ADME tasks pose unique challenges for existing quantum computing systems (QCS) frameworks, as they involve both classification with unbalanced dataset and regression problems. These dual requirements make it necessary to adapt and refine current QCS frameworks to effectively address the complexities of ADME predictions. We propose a novel training-free scoring mechanism to evaluate QML circuit performance on imbalanced classification and regression tasks. Our mechanism demonstrates significant correlation between scoring metrics and test performance on imbalanced classification tasks. Additionally, we develop methods to quantify continuous similarity relationships between quantum states, enabling performance prediction for regression tasks. This represents the first comprehensive approach to searching and evaluating QCS circuits specifically for regression applications. Validation on representative ADME tasks-one imbalanced classification and one regression-demonstrates moderate positive correlation between our scoring metrics and circuit performance, significantly outperforming baseline scoring methods that show negligible correlation.
Support vector machine (SVM) is a powerful machine learning algorithm to handle classification tasks. However, the classical SVM is developed for binary problems with the assumption of balanced datasets. Obviously, the multi-class imbalanced classification problems are more complex. In this paper, we propose an improved SVM via Differential Evolution (i-SVM-DE) method to deal with it. An improved SVM (i-SVM) model is proposed to handle the data imbalance by combining cost sensitive technique and separation margin modification in the constraints, which formalize a parameter optimization problem. By using one-versus-one (OVO) scheme, a multi-class problem is decomposed into a number of binary subproblems. A large optimization problem is formalized through concatenating the parameters in the binary subproblems. To find the optimal model effectively and learn the support vectors for each class simultaneously, an improved differential evolution (DE) algorithm is applied to solve this large optimization problem. Instead of the validation set, we propose the fitness functions to evaluate the learned model and obtain the optimal parameters in the search process of DE. A series of experiments are carried out to verify the benefits of our proposed method. The results indicate that i-SVM-DE is statistically superior by comparing with the other baseline methods.
Data augmentation is an important technique in training deep neural networks as it enhances their ability to generalize and remain robust. While data augmentation is commonly used to expand the sample size and act as a consistency regularization term, there is a lack of research on the relationship between them. To address this gap, this paper introduces a more comprehensive mathematical framework for data augmentation. Through this framework, we establish that the expected risk of the shifted population is the sum of the original population risk and a gap term, which can be interpreted as a consistency regularization term. The paper also provides a theoretical understanding of this gap, highlighting its negative effects on the early stages of training. We also propose a method to mitigate these effects. To validate our approach, we conducted experiments using same data augmentation techniques and computing resources under several scenarios, including standard training, out-of-distribution, and imbalanced classification. The results demonstrate that our methods surpass compared methods under all scenarios in terms of generalization ability and convergence stability. We provide our code implementation at the following link: https://github.com/ydlsfhll/ASPR.
Classification with imbalanced data is a common challenge in data analysis, where certain classes (minority classes) account for a small fraction of the training data compared with other classes (majority classes). Classical statistical theory based on large-sample asymptotics and finite-sample corrections is often ineffective for high-dimensional data, leaving many overfitting phenomena in empirical machine learning unexplained. In this paper, we develop a statistical theory for high-dimensional imbalanced classification by investigating support vector machines and logistic regression. We find that dimensionality induces truncation or skewing effects on the logit distribution, which we characterize via a variational problem under high-dimensional asymptotics. In particular, for linearly separable data generated from a two-component Gaussian mixture model, the logits from each class follow a normal distribution $\mathsf{N}(0,1)$ on the testing set, but asymptotically follow a rectified normal distribution $\max\{\kappa, \mathsf{N}(0,1)\}$ on the training set -- which is a pervasive phenomenon we verified on tabular data, image data, and text data. This phenomenon explains why the minority class is more severely affected by overfitting. Further, we show that margin rebalancing, which incorporates class sizes into the loss function, is crucial for mitigating the accuracy drop for the minority class. Our theory also provides insights into the effects of overfitting on calibration and other uncertain quantification measures.
Graph neural networks are gaining attention in fifth-generation (5G) core network digital twins, which are data-driven complex systems with numerous components. Analyzing these data can be challenging due to rare failure types, leading to imbalanced classification in multiclass settings. Digital twins of 5G networks increasingly employ graph classification as the main method for identifying failure types. However, the skewed distribution of failure occurrences is a significant class-imbalance problem that prevents practical graph data mining. Previous studies have not sufficiently addressed this complex problem. This paper, proposes class-Fourier GNN (CF-GNN) that introduces a class-oriented spectral filtering mechanism to ensure precise classification by estimating a unique spectral filter for each class. This work employs eigenvalue and eigenvector spectral filtering to capture and adapt to variations in minority classes, ensuring accurate class-specific feature discrimination, and adept at graph representation learning for complex local structures among neighbors in an end-to-end setting. The extensive experiments demonstrate that the proposed CF-GNN could help create new techniques for enhancing classifiers and investigate the characteristics of the multiclass imbalanced data in a network digital twin system.
Despite extensive research spanning several decades, class imbalance is still considered a profound difficulty for both machine learning and deep learning models. While data oversampling is the foremost technique to address this issue, traditional sampling techniques are often decoupled from the training phase of the predictive model, resulting in suboptimal representations. To address this, we propose a novel learning framework that can generate synthetic data instances in a data-driven manner. The proposed framework formulates the oversampling process as a composition of discrete decision criteria, thereby enhancing the representation power of the model's learning process. Extensive experiments on the imbalanced classification task demonstrate the superiority of our framework over state-of-the-art algorithms.
Ensemble technique and under-sampling technique are both effective tools used for imbalanced dataset classification problems. In this paper, a novel ensemble method combining the advantages of both ensemble learning for biasing classifiers and a new under-sampling method is proposed. The under-sampling method is named Binary PSO instance selection; it gathers with ensemble classifiers to find the most suitable length and combination of the majority class samples to build a new dataset with minority class samples. The proposed method adopts multi-objective strategy, and contribution of this method is a notable improvement of the performances of imbalanced classification, and in the meantime guaranteeing a best integrity possible for the original dataset. We experimented the proposed method and compared its performance of processing imbalanced datasets with several other conventional basic ensemble methods. Experiment is also conducted on these imbalanced datasets using an improved version where ensemble classifiers are wrapped in the Binary PSO instance selection. According to experimental results, our proposed methods outperform single ensemble methods, state-of-the-art under-sampling methods, and also combinations of these methods with the traditional PSO instance selection algorithm.
Skin cancer is the most common type of cancer in the world, accounting for approximately 30% of all diagnosed tumors. Early diagnosis reduces mortality rates and prevents disfiguring effects in different body regions. In recent years, machine learning techniques, particularly deep learning, have shown promising results in this task, presenting studies that have demonstrated that combining a patient's clinical information with images of the lesion is crucial for improving the classification of skin lesions. Despite that, meaningful use of clinical information with multiple images is mandatory, requiring further investigation. Thus, this project aims to contribute to developing multimodal machine learning-based models to cope with the skin lesion classification task employing a lightweight transformer model. As a main hypothesis, models can take multiple images from different sources as input, along with clinical information from the patient's history, leading to a more reliable diagnosis. Our model deals with the not-trivial task of combining images and clinical information (from anamneses) concerning the skin lesions in a lightweight transformer architecture that does not demand high computation resources but still presents competitive classification results.
We consider the problem of transfer learning in outlier detection where target abnormal data is rare. While transfer learning has been considered extensively in traditional balanced classification, the problem of transfer in outlier detection and more generally in imbalanced classification settings has received less attention. We propose a general meta-algorithm which is shown theoretically to yield strong guarantees w.r.t. to a range of changes in abnormal distribution, and at the same time amenable to practical implementation. We then investigate different instantiations of this general meta-algorithm, e.g., based on multi-layer neural networks, and show empirically that they outperform natural extensions of transfer methods for traditional balanced classification settings (which are the only solutions available at the moment).
Class imbalance poses a significant challenge in machine learning (ML), often leading to biased models favouring the majority class. In this paper, we propose GAT-RWOS, a novel graph-based oversampling method that combines the strengths of Graph Attention Networks (GATs) and random walk-based oversampling. GAT-RWOS leverages the attention mechanism of GATs to guide the random walk process, focusing on the most informative neighbourhoods for each minority node. By performing attention-guided random walks and interpolating features along the traversed paths, GAT-RWOS generates synthetic minority samples that expand class boundaries while preserving the original data distribution. Extensive experiments on a diverse set of imbalanced datasets demonstrate the effectiveness of GAT-RWOS in improving classification performance, outperforming state-of-the-art oversampling techniques. The proposed method has the potential to significantly improve the performance of ML models on imbalanced datasets and contribute to the development of more reliable classification systems.
Handling imbalance in class distribution when building a classifier over tabular data has been a problem of long-standing interest. One popular approach is augmenting the training dataset with synthetically generated data. While classical augmentation techniques were limited to linear interpolation of existing minority class examples, recently higher capacity deep generative models are providing greater promise. However, handling of imbalance in class distribution when building a deep generative model is also a challenging problem, that has not been studied as extensively as imbalanced classifier model training. We show that state-of-the-art deep generative models yield significantly lower-quality minority examples than majority examples. %In this paper, we start with the observation that imbalanced data training of generative models trained imbalanced dataset which under-represent the minority class. We propose a novel technique of converting the binary class labels to ternary class labels by introducing a class for the region where minority and majority distributions overlap. We show that just this pre-processing of the training set, significantly improves the quality of data generated spanning several state-of-the-art diffusion and GAN-based models. While training the classifier using synthetic data, we remove the overlap class from the training data and justify the reasons behind the enhanced accuracy. We perform extensive experiments on four real-life datasets, five different classifiers, and five generative models demonstrating that our method enhances not only the synthesizer performance of state-of-the-art models but also the classifier performance.
Binary classification tasks with imbalanced classes pose significant challenges in machine learning. Traditional classifiers often struggle to accurately capture the characteristics of the minority class, resulting in biased models with subpar predictive performance. In this paper, we introduce a novel approach to tackle this issue by leveraging Universum points to support the minority class within quadratic twin support vector machine models. Unlike traditional classifiers, our models utilize quadratic surfaces instead of hyperplanes for binary classification, providing greater flexibility in modeling complex decision boundaries. By incorporating Universum points, our approach enhances classification accuracy and generalization performance on imbalanced datasets. We generated four artificial datasets to demonstrate the flexibility of the proposed methods. Additionally, we validated the effectiveness of our approach through empirical evaluations on benchmark datasets, showing superior performance compared to conventional classifiers and existing methods for imbalanced classification.
Imbalanced data distributions are prevalent in real-world scenarios, posing significant challenges in both imbalanced classification and imbalanced regression tasks. They often cause deep learning models to overfit in areas of high sample density (many-shot regions) while underperforming in areas of low sample density (few-shot regions). This characteristic restricts the utility of deep learning models in various sectors, notably healthcare, where areas with few-shot data hold greater clinical relevance. While recent studies have shown the benefits of incorporating distribution information in imbalanced classification tasks, such strategies are rarely explored in imbalanced regression. In this paper, we address this issue by introducing a novel loss function, termed Dist Loss, designed to minimize the distribution distance between the model's predictions and the target labels in a differentiable manner, effectively integrating distribution information into model training. Dist Loss enables deep learning models to regularize their output distribution during training, effectively enhancing their focus on few-shot regions. We have conducted extensive experiments across three datasets spanning computer vision and healthcare: IMDB-WIKI-DIR, AgeDB-DIR, and ECG-Ka-DIR. The results demonstrate that Dist Loss effectively mitigates the negative impact of imbalanced data distribution on model performance, achieving state-of-the-art results in sparse data regions. Furthermore, Dist Loss is easy to integrate, complementing existing methods.