Let $\Gamma_n$ be an $n\times n$ Haar-invariant orthogonal matrix. Let $ Z_n$
be the $p\times q$ upper-left submatrix of $\Gamma_n,$ where $p=p_n$ and
$q=q_n$ are two positive integers. Let $G_n$ be a $p\times q$ matrix whose $pq$
entries are independent standard normals. In this paper we consider the
distance between $\sqrt{n} Z_n$ and $ G_n$ in terms of the total variation
distance, the Kullback-Leibler distance, the Hellinger distance and the
Euclidean distance. We prove that each of the first three distances goes to
zero as long as $pq/n$ goes to zero, and not so this rate is sharp in the sense
that each distance does not go to zero if $(p, q)$ sits on the curve $pq=\sigma
n$, where $\sigma$ is a constant. However, it is different for the Euclidean
distance, which goes to zero provided $pq^2/n$ goes to zero, and not so if
$(p,q)$ sits on the curve $pq^2=\sigma n.$ A previous work by Jiang
\cite{Jiang06} shows that the total variation distance goes to zero if both
$p/\sqrt{n}$ and $q/\sqrt{n}$ go to zero, and it is not true provided
$p=c\sqrt{n}$ and $q=d\sqrt{n}$ with $c$ and $d$ being constants. One of the
above results confirms a conjecture that the total variation distance goes to
zero as long as $pq/n\to 0$ and the distance does not go to zero if $pq=\sigma
n$ for some constant $\sigma$.

本文探讨了计算方阵距离的不同方法，并证明了在一定条件下，前三种距离都会趋近于零，而欧几里得距离只有在另一条件下才会趋近于零。

随机正交矩阵与独立正态分布之间的距离

Distances between Random Orthogonal Matrices and Independent Normals

The cost function used to train a generative model should fit the purpose of
the model. If the model is intended for tasks such as generating perceptually
correct samples, it is beneficial to maximise the likelihood of a sample drawn
from the model, Q, coming from the same distribution as the training data, P.
This is equivalent to minimising the Kullback-Leibler (KL) distance, KL[Q||P].
However, if the model is intended for tasks such as retrieval or classification
it is beneficial to maximise the likelihood that a sample drawn from the
training data is captured by the model, equivalent to minimising KL[P||Q]. The
cost function used in adversarial training optimises the Jensen-Shannon entropy
which can be seen as an even interpolation between KL[Q||P] and KL[P||Q]. Here,
we propose an alternative adversarial cost function which allows easy tuning of
the model for either task. Our task specific cost function is evaluated on a
dataset of hand-written characters in the following tasks: Generation,
retrieval and one-shot learning.

研究讨论了生成模型的成本函数对于不同任务的优化策略，并提出了一种新的对抗成本函数，可以在手写字符的生成、检索和一次性学习任务中进行评估。

任务特定对抗代价函数

Task Specific Adversarial Cost Function

This paper introduces a novel approach that enables a number of cognitive
radio devices that are observing the availability pattern of a number of
primary users(PUs), to cooperate and use \emph{Bayesian nonparametric}
techniques to estimate the distributions of the PUs' activity pattern, assumed
to be completely unknown. In the proposed model, each cognitive node may have
its own individual view on each PU's distribution, and, hence, seeks to find
partners having a correlated perception. To address this problem, a coalitional
game is formulated between the cognitive devices and an algorithm for
cooperative coalition formation is proposed. It is shown that the proposed
coalition formation algorithm allows the cognitive nodes that are experiencing
a similar behavior from some PUs to self-organize into disjoint, independent
coalitions. Inside each coalition, the cooperative cognitive nodes use a
combination of Bayesian nonparametric models such as the Dirichlet process and
statistical goodness of fit techniques in order to improve the accuracy of the
estimated PUs' activity distributions. Simulation results show that the
proposed algorithm significantly improves the estimates of the PUs'
distributions and yields a performance advantage, in terms of reduction of the
average achieved Kullback-Leibler distance between the real and the estimated
distributions, reaching up to 36.5% relative the non-cooperative estimates. The
results also show that the proposed algorithm enables the cognitive nodes to
adapt their cooperative decisions when the actual PUs' distributions change due
to, for example, PU mobility.

本文提出了一种新的方法，旨在使多个认知无线电设备协作、使用贝叶斯非参数技术来估计原始用户的活动分布，进而通过形成联盟来优化算法性能，并得到了较高的准确性和性能优越性。

一种基于合作贝叶斯非参数框架的认知无线电网络主用户活动监测方法

A Cooperative Bayesian Nonparametric Framework for Primary User Activity  Monitoring in Cognitive Radio Network

We discuss some methods to quantitatively investigate the properties of
correlation matrices. Correlation matrices play an important role in portfolio
optimization and in several other quantitative descriptions of asset price
dynamics in financial markets. Specifically, we discuss how to define and
obtain hierarchical trees, correlation based trees and networks from a
correlation matrix. The hierarchical clustering and other procedures performed
on the correlation matrix to detect statistically reliable aspects of the
correlation matrix are seen as filtering procedures of the correlation matrix.
We also discuss a method to associate a hierarchically nested factor model to a
hierarchical tree obtained from a correlation matrix. The information retained
in filtering procedures and its stability with respect to statistical
fluctuations is quantified by using the Kullback-Leibler distance.

本文研究了量化研究相关矩阵性质的方法，并介绍了如何从相关矩阵中定义和获得层次树和基于相关性的树和网络。通过对相关矩阵执行分层聚类和其他程序来检测相关矩阵的可靠方面，并且还讨论了将嵌套因子模型与从相关矩阵获得的分层树相关联的方法。通过使用 Kullback-Leibler 距离量化过滤过程中保留的信息及其稳定性。