We present a simple case study, demonstrating that Variational Information
Bottleneck (VIB) can improve a network's classification calibration as well as
its ability to detect out-of-distribution data. Without explicitly being
designed to do so, VIB gives two natural metrics for handling and quantifying
uncertainty.

通过简单的案例研究，我们展示了变分信息瓶颈（VIB）不仅可以提高神经网络的分类校准能力，还可以改善其检测未知数据的能力，并提供了两个量化和处理不确定性的自然度量。

变分信息瓶颈中的不确定性

Uncertainty in the Variational Information Bottleneck

In this work, we introduce the {\em average top-$k$} (\atk) loss as a new
aggregate loss for supervised learning, which is the average over the $k$
largest individual losses over a training dataset. We show that the \atk loss
is a natural generalization of the two widely used aggregate losses, namely the
average loss and the maximum loss, but can combine their advantages and
mitigate their drawbacks to better adapt to different data distributions.
Furthermore, it remains a convex function over all individual losses, which can
lead to convex optimization problems that can be solved effectively with
conventional gradient-based methods. We provide an intuitive interpretation of
the \atk loss based on its equivalent effect on the continuous individual loss
functions, suggesting that it can reduce the penalty on correctly classified
data. We further give a learning theory analysis of \matk learning on the
classification calibration of the \atk loss and the error bounds of \atk-SVM.
We demonstrate the applicability of minimum average top-$k$ learning for binary
classification and regression using synthetic and real datasets.

介绍了一种新的监督学习损失函数 —— 平均 top-k 损失，是平均训练集个别损失的 k 个最大值，能够克服平均损失和最大损失的缺陷，在不同数据分布上更好地适应。同时它是所有个别损失的凸函数，可以使用常规的梯度下降法解决凸优化问题，具有显著的理论和实际应用价值。

平均 Top-k 损失的学习

Learning with Average Top-k Loss

We study consistency properties of surrogate loss functions for general
multiclass learning problems, defined by a general multiclass loss matrix. We
extend the notion of classification calibration, which has been studied for
binary and multiclass 0-1 classification problems (and for certain other
specific learning problems), to the general multiclass setting, and derive
necessary and sufficient conditions for a surrogate loss to be calibrated with
respect to a loss matrix in this setting. We then introduce the notion of
convex calibration dimension of a multiclass loss matrix, which measures the
smallest `size' of a prediction space in which it is possible to design a
convex surrogate that is calibrated with respect to the loss matrix. We derive
both upper and lower bounds on this quantity, and use these results to analyze
various loss matrices. In particular, we apply our framework to study various
subset ranking losses, and use the convex calibration dimension as a tool to
show both the existence and non-existence of various types of convex calibrated
surrogates for these losses. Our results strengthen recent results of Duchi et
al. (2010) and Calauzenes et al. (2012) on the non-existence of certain types
of convex calibrated surrogates in subset ranking. We anticipate the convex
calibration dimension may prove to be a useful tool in the study and design of
surrogate losses for general multiclass learning problems.

研究多分类学习问题的替代损失函数的一致性属性，提出了分类校准和凸校准维度的概念和理论，并应用于分析各种损失矩阵和证明在子集排名下某些类型的凸校准替代损失不存在。