In this paper we revisit the classical problem of classification, but impose
privacy constraints. Under such constraints, the raw data
$(X_1,Y_1),\ldots,(X_n,Y_n)$ cannot be directly observed, and all classifiers
are functions of the randomised outcome of a suitable local differential
privacy mechanism. The statistician is free to choose the form of this privacy
mechanism, and here we add Laplace distributed noise to a discretisation of the
location of each feature vector $X_i$ and to its label $Y_i$. The
classification rule is the privatized version of the well-studied partitioning
classification rule. In addition to the standard Lipschitz and margin
conditions, a novel characteristic is introduced, by which the exact rate of
convergence of the classification error probability is calculated, both for
non-private and private data.

在本文中，我们重新审视了分类的经典问题，但施加了隐私约束。在此约束下，无法直接观察原始数据（X1，Y1），…，（Xn，Yn），并且所有的分类器都是合适的本地差分隐私机制的随机结果的函数。统计学家可以自由选择这种隐私机制的形式，在这里，我们向每个特征向量 Xi 的位置和其标签 Yi 的离散化添加了拉普拉斯分布的噪声。分类规则是经过隐私保护的版本的良好研究分区分类规则。除了标准的 Lipschitz 和边距条件之外，还引入了一种新的特征，通过该特征可以计算出分类误差概率的精确收敛速率，无论是针对非私有数据还是私有数据。

非私有和私有数据的速率最优分类

On rate-optimal classification from non-private and from private data

Estimating the 3DoF rotation from a single RGB image is an important yet
challenging problem. Probabilistic rotation regression has raised more and more
attention with the benefit of expressing uncertainty information along with the
prediction. Though modeling noise using Gaussian-resembling Bingham
distribution and matrix Fisher distribution is natural, they are shown to be
sensitive to outliers for the nature of quadratic punishment to deviations. In
this paper, we draw inspiration from multivariate Laplace distribution and
propose a novel Rotation Laplace distribution on SO(3). Rotation Laplace
distribution is robust to the disturbance of outliers and enforces much
gradient to the low-error region, resulting in a better convergence. Our
extensive experiments show that our proposed distribution achieves
state-of-the-art performance for rotation regression tasks over both
probabilistic and non-probabilistic baselines. Our project page is at
this https URL

本文提出了一种基于 Laplace 分布的 Rotation Laplace 分布，用于解决单 RGB 图像 3DoF 旋转估计的问题，其具有鲁棒性和更好的收敛效果，并在概率和非概率基线上实现了最先进的旋转回归任务表现。

一个在 SO (3) 上受拉普拉斯启发的概率旋转估计分布

A Laplace-inspired Distribution on SO(3) for Probabilistic Rotation  Estimation

In this paper, we exploit the properties of mean absolute error (MAE) as a
loss function for the deep neural network (DNN) based vector-to-vector
regression. The goal of this work is two-fold: (i) presenting performance
bounds of MAE, and (ii) demonstrating new properties of MAE that make it more
appropriate than mean squared error (MSE) as a loss function for DNN based
vector-to-vector regression. First, we show that a generalized upper-bound for
DNN-based vector- to-vector regression can be ensured by leveraging the known
Lipschitz continuity property of MAE. Next, we derive a new generalized upper
bound in the presence of additive noise. Finally, in contrast to conventional
MSE commonly adopted to approximate Gaussian errors for regression, we show
that MAE can be interpreted as an error modeled by Laplacian distribution.
Speech enhancement experiments are conducted to corroborate our proposed
theorems and validate the performance advantages of MAE over MSE for DNN based
regression.

本文探究均方误差作为深度神经网络回归模型的损失函数的性质，提出了均方误差的新特性使其成为更适合于 DNN 的回归损失函数，并阐述了 MAE 作为拉普拉斯分布错误的模型的优越性以及实现 MAE 比 MSE 更好地拟合深度神经网络回归的性能优势。