Hawkes processes are a special class of temporal point processes which
exhibit a natural notion of causality, as occurrence of events in the past may
increase the probability of events in the future. Discovery of the underlying
influence network among the dimensions of multi-dimensional temporal processes
is of high importance in disciplines where a high-frequency data is to model,
e.g. in financial data or in seismological data. This paper approaches the
problem of learning Granger-causal network in multi-dimensional Hawkes
processes. We formulate this problem as a model selection task in which we
follow the minimum description length (MDL) principle. Moreover, we propose a
general algorithm for MDL-based inference using a Monte-Carlo method and we use
it for our causal discovery problem. We compare our algorithm with the
state-of-the-art baseline methods on synthetic and real-world financial data.
The synthetic experiments demonstrate superiority of our method incausal graph
discovery compared to the baseline methods with respect to the size of the
data. The results of experiments with the G-7 bonds price data are consistent
with the experts knowledge.

本文提出了用 MDL 算法推导多维 Hawkes 过程网络的因果关系，同时在金融数据实验中表现出优异性能。

利用最小描述长度方法推导 Hawkes 过程中的因果关系

Causal Discovery in Hawkes Processes by Minimum Description Length

An ideal outcome of pattern mining is a small set of informative patterns,
containing no redundancy or noise, that identifies the key structure of the
data at hand. Standard frequent pattern miners do not achieve this goal, as due
to the pattern explosion typically very large numbers of highly redundant
patterns are returned.
We pursue the ideal for sequential data, by employing a pattern set mining
approach-an approach where, instead of ranking patterns individually, we
consider results as a whole. Pattern set mining has been successfully applied
to transactional data, but has been surprisingly under studied for sequential
data.
In this paper, we employ the MDL principle to identify the set of sequential
patterns that summarises the data best. In particular, we formalise how to
encode sequential data using sets of serial episodes, and use the encoded
length as a quality score. As search strategy, we propose two approaches: the
first algorithm selects a good pattern set from a large candidate set, while
the second is a parameter-free any-time algorithm that mines pattern sets
directly from the data. Experimentation on synthetic and real data demonstrates
we efficiently discover small sets of informative patterns.

本文介绍了一种针对序列数据的模式集挖掘方法，使用 MDL 原则编码序列数据，通过权重编码序列中的序列事件集以确定模式质量，通过两种算法进行模式挖掘，证明能够有效发现具有信息量的小模式集。

长短参半：用序列事件摘要串行情节

The Long and the Short of It: Summarising Event Sequences with Serial  Episodes

We address the problem of automatically acquiring case-frame patterns from
large corpus data. In particular, we view this problem as the problem of
estimating a (conditional) distribution over a partition of words, and propose
a new generalization method based on the MDL (Minimum Description Length)
principle. In order to assist with the efficiency, our method makes use of an
existing thesaurus and restricts its attention on those partitions that are
present as `cuts' in the thesaurus tree, thus reducing the generalization
problem to that of estimating the `tree cut models' of the thesaurus. We then
give an efficient algorithm which provably obtains the optimal tree cut model
for the given frequency data, in the sense of MDL. We have used the case-frame
patterns obtained using our method to resolve pp-attachment ambiguity.Our
experimental results indicate that our method improves upon or is at least as
effective as existing methods.

本研究提出了一种新的方法来自动获取文本语料库中的案例框架模式，并使用 MDL 原则来调整模式，以帮助尽可能高效地预测文本中的结构。通过与其他方法进行对比和测试，我们证明了该方法是有效的。