There is growing body of learning problems for which it is natural to
organize the parameters into matrix, so as to appropriately regularize the
parameters under some matrix norm (in order to impose some more sophisticated
prior knowledge). This work describes and analyzes a systematic method for
constructing such matrix-based, regularization methods. In particular, we focus
on how the underlying statistical properties of a given problem can help us
decide which regularization function is appropriate.
Our methodology is based on the known duality fact: that a function is
strongly convex with respect to some norm if and only if its conjugate function
is strongly smooth with respect to the dual norm. This result has already been
found to be a key component in deriving and analyzing several learning
algorithms. We demonstrate the potential of this framework by deriving novel
generalization and regret bounds for multi-task learning, multi-class learning,
and kernel learning.

本文研究了一种将参数组织成矩阵的学习方式，采用矩阵范数来适当地规范参数以实现更复杂的先验知识。基于已知的对偶事实，即函数相对于某些范数是强凸的，当且仅当其共轭函数相对于对偶范数是强平滑的，我们的方法是基于统计学性质来确定合适的正则化函数。通过将这个框架应用于多任务学习、多类学习和核学习中，并推导出新的广义化和失误上限，我们展示了这个方法的潜力。

学习矩阵的正则化技术

Regularization Techniques for Learning with Matrices

Respondent-Driven Sampling (RDS) employs a variant of a link-tracing network
sampling strategy to collect data from hard-to-reach populations. By tracing
the links in the underlying social network, the process exploits the social
structure to expand the sample and reduce its dependence on the initial
(convenience) sample.
The primary goal of RDS is typically to estimate population averages in the
hard-to-reach population. The current estimates make strong assumptions in
order to treat the data as a probability sample. In particular, we evaluate
three critical sensitivities of the estimators: to bias induced by the initial
sample, to uncontrollable features of respondent behavior, and to the
without-replacement structure of sampling.
This paper sounds a cautionary note for the users of RDS. While current RDS
methodology is powerful and clever, the favorable statistical properties
claimed for the current estimates are shown to be heavily dependent on often
unrealistic assumptions.

该研究警告使用 Respondent-Driven Sampling 抽样方法时，当前估计方法依赖于常常不切实际的假设，其统计学特性可能被高估。

受访者驱动抽样：现有方法的评估

Respondent-Driven Sampling: An Assessment of Current Methodology

We use complex network concepts to analyze statistical properties of urban
public transport networks (PTN). To this end, we present a comprehensive survey
of the statistical properties of PTNs based on the data of fourteen cities of
so far unexplored network size. Especially helpful in our analysis are
different network representations. Within a comprehensive approach we calculate
PTN characteristics in all of these representations and perform a comparative
analysis. The standard network characteristics obtained in this way often
correspond to features that are of practical importance to a passenger using
public traffic in a given city. Specific features are addressed that are unique
to PTNs and networks with similar transport functions (such as networks of
neurons, cables, pipes, vessels embedded in 2D or 3D space). Based on the
empirical survey, we propose a model that albeit being simple enough is capable
of reproducing many of the identified PTN properties. A central ingredient of
this model is a growth dynamics in terms of routes represented by self-avoiding
walks.

本研究使用复杂网络概念分析了城市公共交通网络的统计特性，提出了一个简单的增长动态模型以重现它们的特性。