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.

Under this setting, and for the right choice of loss function and "mixing" algorithm, it is possible for the learner to achieve a constant regret regardless of the number of prediction rounds.

In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS).

Under this setting, and for the right choice of loss function and "mixing" algorithm, it is possible for the learner to achieve a constant regret regardless of the number of prediction rounds.

We formalize and study the natural approach of designing convex surrogate loss functions via embeddings for problems such as classification or ranking.

In the surveying of subpopulations (e.g. by the US Census Bureau) one can improve noisy estimates (e.g.

Response to Reviewer 1: We appreciate your valuable & insightful comments and suggestions. Y es, it is an issue which is worth more discussion. It should be now clear that "compressed learning" is a popular Information Theory, 2013, among other papers written by prominent researchers. Thus, we hope our work will be useful both theoretically and practically. Also, thanks for suggesting to exploit the trade-off between number of bits, number of projections, and accuracy.