Multivariate sequential data collected in practice often exhibit temporal
irregularities, including nonuniform time intervals and component misalignment.
However, if uneven spacing and asynchrony are endogenous characteristics of the
data rather than a result of insufficient observation, the information content
of these irregularities plays a defining role in characterizing the
multivariate dependence structure. Existing approaches for probabilistic
forecasting either overlook the resulting statistical heterogeneities, are
susceptible to imputation biases, or impose parametric assumptions on the data
distribution. This paper proposes an end-to-end solution that overcomes these
limitations by allowing the observation arrival times to play the central role
of model construction, which is at the core of temporal irregularities. To
acknowledge temporal irregularities, we first enable unique hidden states for
components so that the arrival times can dictate when, how, and which hidden
states to update. We then develop a conditional flow representation to
non-parametrically represent the data distribution, which is typically
non-Gaussian, and supervise this representation by carefully factorizing the
log-likelihood objective to select conditional information that facilitates
capturing time variation and path dependency. The broad applicability and
superiority of the proposed solution are confirmed by comparing it with
existing approaches through ablation studies and testing on real-world
datasets.

提出了一种解决非均匀时间间隔和时间上的不对齐问题的概率预测模型，该模型通过允许观测时间成为模型构建的核心来克服现有方法的局限性，使用条件流表示来非参数地表示数据分布，并通过精心分解对数似然目标来监督该表示。

具有时序不规则性的多元时间序列的概率学习

Probabilistic Learning of Multivariate Time Series with Temporal  Irregularity

We study how to obtain concise descriptions of discrete multivariate
sequential data. In particular, how to do so in terms of rich multivariate
sequential patterns that can capture potentially highly interesting
(cor)relations between sequences. To this end we allow our pattern language to
span over the domains (alphabets) of all sequences, allow patterns to overlap
temporally, as well as allow for gaps in their occurrences.
We formalise our goal by the Minimum Description Length principle, by which
our objective is to discover the set of patterns that provides the most
succinct description of the data. To discover high-quality pattern sets
directly from data, we introduce DITTO, a highly efficient algorithm that
approximates the ideal result very well.
Experiments show that DITTO correctly discovers the patterns planted in
synthetic data. Moreover, it scales favourably with the length of the data, the
number of attributes, the alphabet sizes. On real data, ranging from sensor
networks to annotated text, DITTO discovers easily interpretable summaries that
provide clear insight in both the univariate and multivariate structure.

本文研究了如何利用富有多变量的序列模式获得离散多元序列数据的简明描述，并通过最小描述长度原则提出了一种高效的算法 DITTO，能够快速而准确地发现数据的高质量模式，从而提供了一个易于理解的数据总结。