Two key tasks in high-dimensional regularized regression are tuning the
regularization strength for good predictions and estimating the out-of-sample
risk. It is known that the standard approach -- $k$-fold cross-validation -- is
inconsistent in modern high-dimensional settings. While leave-one-out and
generalized cross-validation remain consistent in some high-dimensional cases,
they become inconsistent when samples are dependent or contain heavy-tailed
covariates. To model structured sample dependence and heavy tails, we use
right-rotationally invariant covariate distributions - a crucial concept from
compressed sensing. In the common modern proportional asymptotics regime where
the number of features and samples grow comparably, we introduce a new
framework, ROTI-GCV, for reliably performing cross-validation. Along the way,
we propose new estimators for the signal-to-noise ratio and noise variance
under these challenging conditions. We conduct extensive experiments that
demonstrate the power of our approach and its superiority over existing
methods.

在高维正则化回归中，我们使用旋转不变协变分布来建模结构化的样本依赖性和重尾现象，并引入了一种可靠执行交叉验证的新框架 ROTI-GCV，同时提出了在这些具有挑战性的条件下对信噪比和噪声方差进行估计的新估计器。通过广泛的实验，我们展示了我们方法的强大性以及其相较于现有方法的优越性。

ROTI-GCV：适用于右旋转不变数据的广义交叉验证

ROTI-GCV: Generalized Cross-Validation for right-ROTationally Invariant  Data

We propose a numerical accountant for evaluating the tight
$(\varepsilon,\delta)$-privacy loss for algorithms with discrete one
dimensional output. The method is based on the privacy loss distribution
formalism and it uses the recently introduced fast Fourier transform based
accounting technique. We carry out an error analysis of the method in terms of
moment bounds of the privacy loss distribution which leads to rigorous lower
and upper bounds for the true $(\varepsilon,\delta)$-values. As an application,
we present a novel approach to accurate privacy accounting of the subsampled
Gaussian mechanism. This completes the previously proposed analysis by giving
strict lower and upper bounds for the privacy parameters. We demonstrate the
performance of the accountant on the binomial mechanism and show that our
approach allows decreasing noise variance up to 75 percent at equal privacy
compared to existing bounds in the literature. We also illustrate how to
compute tight bounds for the exponential mechanism applied to counting queries.

提出一种基于隐私损失分布的数值账本方法，用于准确隐私计算，尤其是对子采样高斯机制的严格上下界隐私参数的计算，并给出幂系数约束下的隐私损失分布的误差分析，应用于计数查询的指数机制的计算也满足严格下界隐私参数。

使用 FFT 的离散值机制和子采样高斯机制的严格差分隐私

Tight Differential Privacy for Discrete-Valued Mechanisms and for the  Subsampled Gaussian Mechanism Using FFT

We propose a novel deep network architecture for image\\ denoising based on a
Gaussian Conditional Random Field (GCRF) model. In contrast to the existing
discriminative denoising methods that train a separate model for each noise
level, the proposed deep network explicitly models the input noise variance and
hence is capable of handling a range of noise levels. Our deep network, which
we refer to as deep GCRF network, consists of two sub-networks: (i) a parameter
generation network that generates the pairwise potential parameters based on
the noisy input image, and (ii) an inference network whose layers perform the
computations involved in an iterative GCRF inference procedure.\ We train the
entire deep GCRF network (both parameter generation and inference networks)
discriminatively in an end-to-end fashion by maximizing the peak
signal-to-noise ratio measure. Experiments on Berkeley segmentation and
PASCALVOC datasets show that the proposed deep GCRF network outperforms
state-of-the-art image denoising approaches for several noise levels.

本文提出一种基于高斯条件随机场模型的图像去噪新颖网络架构，通过显式建模输入噪声方差，可处理多种噪声级别，分为参数生成和推断两大子网，并最终通过对峰值信噪比的最大化来进行端到端的判别式训练，实验证明，该模型在处理多种噪声级别的图像去噪任务中胜过现有的最优方法。