Shrinkage can effectively improve the condition number and accuracy of
covariance matrix estimation, especially for low-sample-support applications
with the number of training samples smaller than the dimensionality. This paper
investigates parameter choice for linear shrinkage estimators. We propose
data-driven, leave-one-out cross-validation (LOOCV) methods for automatically
choosing the shrinkage coefficients, aiming to minimize the Frobenius norm of
the estimation error. A quadratic loss is used as the prediction error for
LOOCV. The resulting solutions can be found analytically or by solving
optimization problems of small sizes and thus have low complexities. Our
proposed methods are compared with various existing techniques. We show that
the LOOCV method achieves near-oracle performance for shrinkage designs using
sample covariance matrix (SCM) and several typical shrinkage targets.
Furthermore, the LOOCV method provides low-complexity solutions for estimators
that use general shrinkage targets, multiple targets, and/or ordinary least
squares (OLS)-based covariance matrix estimation. We also show applications of
our proposed techniques to several different problems in array signal
processing.

本文研究线性收缩估计器的参数选择，并提出了数据驱动的交叉验证方法，用于自动选择收缩系数，以最小化估计误差的弗罗贝尼乌斯范数。该方法不仅适用于使用样本协方差矩阵和多种典型收缩目标的收缩设计，还可用于使用一般收缩目标，多个目标和 / 或基于最小二乘法的协方差矩阵估计器的方案，并在数种不同的阵列信号处理问题中展示了应用。

低复杂度交叉验证线性收缩协方差矩阵估计

Linear Shrinkage Estimation of Covariance Matrices Using Low-Complexity  Cross-Validation

Differential privacy is becoming a gold standard for privacy research; it
offers a guaranteed bound on loss of privacy due to release of query results,
even under worst-case assumptions. The theory of differential privacy is an
active research area, and there are now differentially private algorithms for a
wide range of interesting problems.
However, the question of when differential privacy works in practice has
received relatively little attention. In particular, there is still no rigorous
method for choosing the key parameter $\epsilon$, which controls the crucial
tradeoff between the strength of the privacy guarantee and the accuracy of the
published results.
In this paper, we examine the role that these parameters play in concrete
applications, identifying the key questions that must be addressed when
choosing specific values. This choice requires balancing the interests of two
different parties: the data analyst and the prospective participant, who must
decide whether to allow their data to be included in the analysis. We propose a
simple model that expresses this balance as formulas over a handful of
parameters, and we use our model to choose $\epsilon$ on a series of simple
statistical studies. We also explore a surprising insight: in some
circumstances, a differentially private study can be more accurate than a
non-private study for the same cost, under our model. Finally, we discuss the
simplifying assumptions in our model and outline a research agenda for possible
refinements.

本文从实践角度讨论差分隐私，提出一个基于公式的简单模型来平衡隐私保护和结果准确性之间的权衡，并使用该模型来选择关键参数 epsilon。研究表明，在一些情况下，差分隐私研究可以比非私密研究更加准确。