2022-12-01
Label Shift has been widely believed to be harmful to the generalization performance of machine learning models. Researchers have proposed many approaches to mitigate the impact of the label shift, e.g., balancing the training data. However, these methods often consider the underparametrized regime, where the sample size is much larger than the data dimension. The research under the overparametrized regime is very limited. To bridge this gap, we propose a new asymptotic analysis of the Fisher Linear Discriminant classifier for binary classification with label shift. Specifically, we prove that there exists a phase transition phenomenon: Under certain overparametrized regime, the classifier trained using imbalanced data outperforms the counterpart with reduced balanced data. Moreover, we investigate the impact of regularization to the label shift: The aforementioned phase transition vanishes as the regularization becomes strong.
translated by 谷歌翻译

2022-06-07

translated by 谷歌翻译

2019-06-05
We introduce a tunable loss function called $\alpha$-loss, parameterized by $\alpha \in (0,\infty]$, which interpolates between the exponential loss ($\alpha = 1/2$), the log-loss ($\alpha = 1$), and the 0-1 loss ($\alpha = \infty$), for the machine learning setting of classification. Theoretically, we illustrate a fundamental connection between $\alpha$-loss and Arimoto conditional entropy, verify the classification-calibration of $\alpha$-loss in order to demonstrate asymptotic optimality via Rademacher complexity generalization techniques, and build-upon a notion called strictly local quasi-convexity in order to quantitatively characterize the optimization landscape of $\alpha$-loss. Practically, we perform class imbalance, robustness, and classification experiments on benchmark image datasets using convolutional-neural-networks. Our main practical conclusion is that certain tasks may benefit from tuning $\alpha$-loss away from log-loss ($\alpha = 1$), and to this end we provide simple heuristics for the practitioner. In particular, navigating the $\alpha$ hyperparameter can readily provide superior model robustness to label flips ($\alpha > 1$) and sensitivity to imbalanced classes ($\alpha < 1$).
translated by 谷歌翻译

2021-08-05

translated by 谷歌翻译

2020-11-10
Classical asymptotic theory for statistical inference usually involves calibrating a statistic by fixing the dimension $d$ while letting the sample size $n$ increase to infinity. Recently, much effort has been dedicated towards understanding how these methods behave in high-dimensional settings, where $d$ and $n$ both increase to infinity together. This often leads to different inference procedures, depending on the assumptions about the dimensionality, leaving the practitioner in a bind: given a dataset with 100 samples in 20 dimensions, should they calibrate by assuming $n \gg d$, or $d/n \approx 0.2$? This paper considers the goal of dimension-agnostic inference; developing methods whose validity does not depend on any assumption on $d$ versus $n$. We introduce an approach that uses variational representations of existing test statistics along with sample splitting and self-normalization to produce a new test statistic with a Gaussian limiting distribution, regardless of how $d$ scales with $n$. The resulting statistic can be viewed as a careful modification of degenerate U-statistics, dropping diagonal blocks and retaining off-diagonal blocks. We exemplify our technique for some classical problems including one-sample mean and covariance testing, and show that our tests have minimax rate-optimal power against appropriate local alternatives. In most settings, our cross U-statistic matches the high-dimensional power of the corresponding (degenerate) U-statistic up to a $\sqrt{2}$ factor.
translated by 谷歌翻译

2021-03-02

translated by 谷歌翻译

translated by 谷歌翻译

2021-12-02

translated by 谷歌翻译

2022-11-28
While it has long been empirically observed that adversarial robustness may be at odds with standard accuracy and may have further disparate impacts on different classes, it remains an open question to what extent such observations hold and how the class imbalance plays a role within. In this paper, we attempt to understand this question of accuracy disparity by taking a closer look at linear classifiers under a Gaussian mixture model. We decompose the impact of adversarial robustness into two parts: an inherent effect that will degrade the standard accuracy on all classes, and the other caused by the class imbalance ratio, which will increase the accuracy disparity compared to standard training. Furthermore, we also extend our model to the general family of stable distributions. We demonstrate that while the constraint of adversarial robustness consistently degrades the standard accuracy in the balanced class setting, the class imbalance ratio plays a fundamentally different role in accuracy disparity compared to the Gaussian case, due to the heavy tail of the stable distribution. We additionally perform experiments on both synthetic and real-world datasets. The empirical results not only corroborate our theoretical findings, but also suggest that the implications may extend to nonlinear models over real-world datasets.
translated by 谷歌翻译

2021-06-07

translated by 谷歌翻译

2022-12-01
It is widely believed that given the same labeling budget, active learning algorithms like uncertainty sampling achieve better predictive performance than passive learning (i.e. uniform sampling), albeit at a higher computational cost. Recent empirical evidence suggests that this added cost might be in vain, as uncertainty sampling can sometimes perform even worse than passive learning. While existing works offer different explanations in the low-dimensional regime, this paper shows that the underlying mechanism is entirely different in high dimensions: we prove for logistic regression that passive learning outperforms uncertainty sampling even for noiseless data and when using the uncertainty of the Bayes optimal classifier. Insights from our proof indicate that this high-dimensional phenomenon is exacerbated when the separation between the classes is small. We corroborate this intuition with experiments on 20 high-dimensional datasets spanning a diverse range of applications, from finance and histology to chemistry and computer vision.
translated by 谷歌翻译

translated by 谷歌翻译

2020-07-27

translated by 谷歌翻译
${authors} 分类：${tags}
${pubdate}${abstract_cn}
translated by 谷歌翻译