Staged trees are probabilistic graphical models capable of representing any
class of non-symmetric independence via a coloring of its vertices. Several
structural learning routines have been defined and implemented to learn staged
trees from data, under the frequentist or Bayesian paradigm. They assume a data
set has been observed fully and, in practice, observations with missing entries
are either dropped or imputed before learning the model. Here, we introduce the
first algorithms for staged trees that handle missingness within the learning
of the model. To this end, we characterize the likelihood of staged tree models
in the presence of missing data and discuss pseudo-likelihoods that approximate
it. A structural expectation-maximization algorithm estimating the model
directly from the full likelihood is also implemented and evaluated. A
computational experiment showcases the performance of the novel learning
algorithms, demonstrating that it is feasible to account for different
missingness patterns when learning staged trees.

该研究介绍了处理缺失数据的阶梯树学习算法，通过模型的全似然性能直接估计模型，证明了在学习阶梯树时考虑不同的缺失模式是可行的。

从不完整数据中学习分阶段树

Learning Staged Trees from Incomplete Data

Recent sequential pattern mining methods have used the minimum description
length (MDL) principle to define an encoding scheme which describes an
algorithm for mining the most compressing patterns in a database. We present a
novel subsequence interleaving model based on a probabilistic model of the
sequence database, which allows us to search for the most compressing set of
patterns without designing a specific encoding scheme. Our proposed algorithm
is able to efficiently mine the most relevant sequential patterns and rank them
using an associated measure of interestingness. The efficient inference in our
model is a direct result of our use of a structural expectation-maximization
framework, in which the expectation-step takes the form of a submodular
optimization problem subject to a coverage constraint. We show on both
synthetic and real world datasets that our model mines a set of sequential
patterns with low spuriousness and redundancy, high interpretability and
usefulness in real-world applications. Furthermore, we demonstrate that the
quality of the patterns from our approach is comparable to, if not better than,
existing state of the art sequential pattern mining algorithms.

本文提出一种基于概率模型的新型子序列交织模型，利用 MDL 原则定义了一种编码方案，能够高效地挖掘最相关的顺序模式，并使用相关的趣味性度量对其进行排序，同时使用结构化的期望最大化框架进行有效的推断。实验结果表明该模型挖掘出的模式具有低的错误率和冗余性，并具有实际应用中的高解释性和实用性。