Dynamical systems with complex behaviours, e.g. immune system cells
interacting with a pathogen, are commonly modelled by splitting the behaviour
into different regimes, or modes, each with simpler dynamics, and then learning
the switching behaviour from one mode to another. Switching Dynamical Systems
(SDS) are a powerful tool that automatically discovers these modes and
mode-switching behaviour from time series data. While effective, these methods
focus on independent objects, where the modes of one object are independent of
the modes of the other objects. In this paper, we focus on the more general
interacting object setting for switching dynamical systems, where the
per-object dynamics also depends on an unknown and dynamically changing subset
of other objects and their modes. To this end, we propose a novel graph-based
approach for switching dynamical systems, GRAph Switching dynamical Systems
(GRASS), in which we use a dynamic graph to characterize interactions between
objects and learn both intra-object and inter-object mode-switching behaviour.
We introduce two new datasets for this setting, a synthesized ODE-driven
particles dataset and a real-world Salsa Couple Dancing dataset. Experiments
show that GRASS can consistently outperforms previous state-of-the-art methods.

本篇论文提出了一种基于动态图表征物体之间的交互，并学习物体之间及物体内模式转换行为的图切换动力系统 (GRASS) 方法，并使用合成的 ODE 驱动的粒子数据集和现实世界的 Salsa 情侣舞蹈数据集为例，证明了该方法的优越性。

图切换动态系统

Graph Switching Dynamical Systems

Switching dynamical systems are an expressive model class for the analysis of
time-series data. As in many fields within the natural and engineering
sciences, the systems under study typically evolve continuously in time, it is
natural to consider continuous-time model formulations consisting of switching
stochastic differential equations governed by an underlying Markov jump
process. Inference in these types of models is however notoriously difficult,
and tractable computational schemes are rare. In this work, we propose a novel
inference algorithm utilizing a Markov Chain Monte Carlo approach. The
presented Gibbs sampler allows to efficiently obtain samples from the exact
continuous-time posterior processes. Our framework naturally enables Bayesian
parameter estimation, and we also include an estimate for the diffusion
covariance, which is oftentimes assumed fixed in stochastic differential
equation models. We evaluate our framework under the modeling assumption and
compare it against an existing variational inference approach.

该文提出了一种基于马尔科夫链蒙特卡罗方法的新型推断算法，用于在连续时间模型中获得精确的后验过程的样本，实现了贝叶斯参数估计，并估计了扩散协方差。

连续时间切换动态系统的马尔可夫链蒙特卡罗方法

Markov Chain Monte Carlo for Continuous-Time Switching Dynamical Systems

Many complex dynamical phenomena can be effectively modeled by a system that
switches among a set of conditionally linear dynamical modes. We consider two
such models: the switching linear dynamical system (SLDS) and the switching
vector autoregressive (VAR) process. Our Bayesian nonparametric approach
utilizes a hierarchical Dirichlet process prior to learn an unknown number of
persistent, smooth dynamical modes. We additionally employ automatic relevance
determination to infer a sparse set of dynamic dependencies allowing us to
learn SLDS with varying state dimension or switching VAR processes with varying
autoregressive order. We develop a sampling algorithm that combines a truncated
approximation to the Dirichlet process with efficient joint sampling of the
mode and state sequences. The utility and flexibility of our model are
demonstrated on synthetic data, sequences of dancing honey bees, the IBOVESPA
stock index, and a maneuvering target tracking application.

使用贝叶斯非参数方法，将层次狄利克雷过程先验应用于两种切换动态模型，学习未知的持续光滑动态模式，同时推断动态依赖性的稀疏集，以学习具有变化状态维数的切换线性动态系统或具有变化自回归顺序的切换 VAR 过程，最终通过舞蹈蜜蜂序列、IBOVESPA 股票指数和机动目标跟踪应用程序展示模型的效用和灵活性