An important problem in time-series analysis is modeling systems with
time-varying dynamics. Probabilistic models with joint continuous and discrete
latent states offer interpretable, efficient, and experimentally useful
descriptions of such data. Commonly used models include autoregressive hidden
Markov models (ARHMMs) and switching linear dynamical systems (SLDSs), each
with its own advantages and disadvantages. ARHMMs permit exact inference and
easy parameter estimation, but are parameter intensive when modeling long
dependencies, and hence are prone to overfitting. In contrast, SLDSs can
capture long-range dependencies in a parameter efficient way through Markovian
latent dynamics, but present an intractable likelihood and a challenging
parameter estimation task. In this paper, we propose switching autoregressive
low-rank tensor (SALT) models, which retain the advantages of both approaches
while ameliorating the weaknesses. SALT parameterizes the tensor of an ARHMM
with a low-rank factorization to control the number of parameters and allow
longer range dependencies without overfitting. We prove theoretical and discuss
practical connections between SALT, linear dynamical systems, and SLDSs. We
empirically demonstrate quantitative advantages of SALT models on a range of
simulated and real prediction tasks, including behavioral and neural datasets.
Furthermore, the learned low-rank tensor provides novel insights into temporal
dependencies within each discrete state.

本论文提出了一种名为 SALT 模型的概率模型，用于对具有时间变化动态的系统进行的时间序列分析，并在各种模拟和真实预测任务上表现出优越性。

自回归低秩张量模型切换

Switching Autoregressive Low-rank Tensor Models

Many natural systems, such as neurons firing in the brain or basketball teams
traversing a court, give rise to time series data with complex, nonlinear
dynamics. We can gain insight into these systems by decomposing the data into
segments that are each explained by simpler dynamic units. Building on
switching linear dynamical systems (SLDS), we present a new model class that
not only discovers these dynamical units, but also explains how their switching
behavior depends on observations or continuous latent states. These "recurrent"
switching linear dynamical systems provide further insight by discovering the
conditions under which each unit is deployed, something that traditional SLDS
models fail to do. We leverage recent algorithmic advances in approximate
inference to make Bayesian inference in these models easy, fast, and scalable.

通过将数据分解为由简单动态单元解释的片段并研究这些切换的行为，我们展示了一种新的模型类型 —— 递归式切换线性动态系统，以提供更深入的洞察力，并利用近年来的算法进展在这些模型中使用近似推理使贝叶斯推理变得轻松、快速且可扩展。