The Dynamic Chain Event Graph (DCEG) is able to depict many classes of
discrete random processes exhibiting asymmetries in their developments and
context-specific conditional probabilities structures. However, paradoxically,
this very generality has so far frustrated its wide application. So in this
paper we develop an object-oriented method to fully analyse a particularly
useful and feasibly implementable new subclass of these graphical models called
the N Time-Slice DCEG (NT-DCEG). After demonstrating a close relationship
between an NT-DCEG and a specific class of Markov processes, we discuss how
graphical modellers can exploit this connection to gain a deep understanding of
their processes. We also show how to read from the topology of this graph
context-specific independence statements that can then be checked by domain
experts. Our methods are illustrated throughout using examples of dynamic
multivariate processes describing inmate radicalisation in a prison.

本文介绍了一种名为 NT-DCEG 的图形模型，并将其与马尔可夫过程进行了比较；我们讨论了如何利用图形模型中的拓扑关系来获得深入的理解，并通过描述犯人激进化的案例说明了其应用。

一个 N 时间步长的动态链事件图

An N Time-Slice Dynamic Chain Event Graph

Estimation of structure, such as in variable selection, graphical modelling
or cluster analysis is notoriously difficult, especially for high-dimensional
data. We introduce stability selection. It is based on subsampling in
combination with (high-dimensional) selection algorithms. As such, the method
is extremely general and has a very wide range of applicability. Stability
selection provides finite sample control for some error rates of false
discoveries and hence a transparent principle to choose a proper amount of
regularisation for structure estimation. Variable selection and structure
estimation improve markedly for a range of selection methods if stability
selection is applied. We prove for randomised Lasso that stability selection
will be variable selection consistent even if the necessary conditions needed
for consistency of the original Lasso method are violated. We demonstrate
stability selection for variable selection and Gaussian graphical modelling,
using real and simulated data.

介绍一种名为稳定性选择的高维数据结构估计方法，结合子抽样和选择算法，提供透明的原则以选择适当的正则化量来改善结构估计的可变性选择和图形建模。

稳定性选择

Stability Selection

In graphical modelling, a bi-directed graph encodes marginal independences
among random variables that are identified with the vertices of the graph. We
show how to transform a bi-directed graph into a maximal ancestral graph that
(i) represents the same independence structure as the original bi-directed
graph, and (ii) minimizes the number of arrowheads among all ancestral graphs
satisfying (i). Here the number of arrowheads of an ancestral graph is the
number of directed edges plus twice the number of bi-directed edges. In
Gaussian models, this construction can be used for more efficient iterative
maximization of the likelihood function and to determine when maximum
likelihood estimates are equal to empirical counterparts.

介绍了如何将双向图转化为最大祖先图，以提高高斯模型中的极大似然函数迭代求解效率及找出最大似然估计等于经验估计的情况。