In this paper, we study problem of estimating a sparse regression vector with
correct support in the presence of outlier samples. The inconsistency of
lasso-type methods is well known in this scenario. We propose a combinatorial
version of outlier-robust lasso which also identifies clean samples.
Subsequently, we use these clean samples to make a good estimation. We also
provide a novel invex relaxation for the combinatorial problem and provide
provable theoretical guarantees for this relaxation. Finally, we conduct
experiments to validate our theory and compare our results against standard
lasso.

本文研究了在存在离群样本的情况下，估计稀疏回归向量的正确支持问题。我们提出了一种组合离群鲁棒 lasso 的版本，该版本还可以识别清洁样本。随后，我们使用这些干净的样本进行很好的估计。我们还为组合问题提供了新颖的 invex 松弛，并为此松弛提供了可证明的理论保证。最后，我们进行实验以验证我们的理论，并将结果与标准 lasso 进行比较。

利用凸性进行稀疏线性模型的异常值鲁棒估计

Outlier-robust Estimation of a Sparse Linear Model Using Invexity

Reliable confidence estimation for deep neural classifiers is a challenging
yet fundamental requirement in high-stakes applications. Unfortunately, modern
deep neural networks are often overconfident for their erroneous predictions.
In this work, we exploit the easily available outlier samples, i.e., unlabeled
samples coming from non-target classes, for helping detect misclassification
errors. Particularly, we find that the well-known Outlier Exposure, which is
powerful in detecting out-of-distribution (OOD) samples from unknown classes,
does not provide any gain in identifying misclassification errors. Based on
these observations, we propose a novel method called OpenMix, which
incorporates open-world knowledge by learning to reject uncertain
pseudo-samples generated via outlier transformation. OpenMix significantly
improves confidence reliability under various scenarios, establishing a strong
and unified framework for detecting both misclassified samples from known
classes and OOD samples from unknown classes. The code is publicly available at
this https URL.

本研究提出了一种可靠的置信度估计方法以检测深度神经网络分类器的误分类，该方法通过利用异常样本、使用在非目标类中的无标签样本以协助检测误分类错误，并将开放世界知识结合到模型中，学习拒绝通过异常转换生成的不确定的伪样本，从而在各种场景下显著提高置信度可靠性。