Class imbalance significantly degrades classification performance, yet its effects are rarely analyzed from a unified theoretical perspective. We propose a principled framework based on three fundamental scales: the imbalance coefficient $η$, the sample--dimension ratio $κ$, and the intrinsic separability $Δ$. Starting from the Gaussian Bayes classifier, we derive closed-form Bayes errors and show how imbalance shifts the discriminant boundary, yielding a deterioration slope that predicts four regimes: Normal, Mild, Extreme, and Catastrophic. Using a balanced high-dimensional genomic dataset, we vary only $η$ while keeping $κ$ and $Δ$ fixed. Across parametric and non-parametric models, empirical degradation closely follows theoretical predictions: minority Recall collapses once $\log(η)$ exceeds $Δ\sqrtκ$, Precision increases asymmetrically, and F1-score and PR-AUC decline in line with the predicted regimes. These results show that the triplet $(η,κ,Δ)$ provides a model-agnostic, geometrically grounded explanation of imbalance-induced deterioration.

Quantization compresses models to low bits for efficient inferences which has received increasing attentions. However, existing approaches focused on balanced datasets, while imbalanced data is pervasive in the real world. Therefore, in this study, we investigate the realistic problem, quantization on class-imbalanced data. We observe from the analytical results that quantizing imbalanced data tends to obtain a large error due to the differences between separate class distributions, which leads to a significant accuracy loss. To address this issue, we propose a novel quantization framework, Class Imbalanced Quantization (ClimbQ) that focuses on diminishing the inter-class heterogeneity for quantization error reduction. ClimbQ first scales the variance of each class distribution and then projects data through the new distributions to the same space for quantization. To guarantee the homogeneity of class variances after the ClimbQ process, we examine the quantized features and derive that the homogeneity satisfies when data size for each class is restricted (bounded). Accordingly, we design a Homogeneous Variance Loss (HomoVar Loss) which reweights the data losses of each class based on the bounded data sizes to satisfy the homogeneity of class variances. Extensive experiments on class-imbalanced and benchmark balanced datasets reveal that ClimbQ outperforms the state-of-the-art quantization techniques, especially on highly imbalanced data.

We investigate the issue of parameter estimation with nonuniform negative sampling for imbalanced data. We first prove that, with imbalanced data, the available information about unknown parameters is only tied to the relatively small number of positive instances, which justifies the usage of negative sampling. However, if the negative instances are subsampled to the same level of the positive cases, there is information loss. To maintain more information, we derive the asymptotic distribution of a general inverse probability weighted (IPW) estimator and obtain the optimal sampling probability that minimizes its variance. To further improve the estimation efficiency over the IPW method, we propose a likelihood-based estimator by correcting log odds for the sampled data and prove that the improved estimator has the smallest asymptotic variance among a large class of estimators. It is also more robust to pilot misspecification. We validate our approach on simulated data as well as a real click-through rate dataset with more than 0.3 trillion instances, collected over a period of a month. Both theoretical and empirical results demonstrate the effectiveness of our method.

Among the various types of cyberattacks, identifying zero-day attacks is problematic because they are unknown to security systems as their pattern and characteristics do not match known blacklisted attacks. There are many Machine Learning (ML) models designed to analyze and detect network attacks, especially using supervised models. However, these models are designed to classify samples (normal and attacks) based on the patterns they learn during the training phase, so they perform inefficiently on unseen attacks. This research addresses this issue by evaluating five different supervised models to assess their performance and execution time in predicting zero-day attacks and find out which model performs accurately and quickly. The goal is to improve the performance of these supervised models by not only proposing a framework that applies grid search, dimensionality reduction and oversampling methods to overcome the imbalance problem, but also comparing the effectiveness of oversampling on ml model metrics, in particular the accuracy. To emulate attack detection in real life, this research applies a highly imbalanced data set and only exposes the classifiers to zero-day attacks during the testing phase, so the models are not trained to flag the zero-day attacks. Our results show that Random Forest (RF) performs best under both oversampling and non-oversampling conditions, this increased effectiveness comes at the cost of longer processing times. Therefore, we selected XG Boost (XGB) as the top model due to its fast and highly accurate performance in detecting zero-day attacks.

Despite a realistic problem, quantization on class-imbalanced data has not been studied.

Thanks for the valuable comments and questions. 1) We understand the reviewer's concern that the ratio of Besides, there are various methods specially for data imbalance to alleviate the issues. Flawfinder and a commercial tool CXXX which we hide the name for legal concern. Static analyzers tend to miss most vulnerable functions and have high false positives, e.g., Cppcheck found 0 One important note is that [19] didn't To verify it, we tested trained models with different sizes of the combined dataset, i.e., 1/3, 2/3 As shown in Table 2, both accuracy and F1 increases as the data volume increases.

We demonstrate, theoretically and empirically, that class-imbalanced learning can significantly benefit in both semi-supervised and self-supervised manners.