奇美拉：使用二维状态空间模型有效建模多变量时间序列

Chimera: Effectively Modeling Multivariate Time Series with 2-Dimensional State Space Models

June 6, 2024

作者: Ali Behrouz, Michele Santacatterina, Ramin Zabih

cs.AI

摘要

建模多变量时间序列是一个已经被广泛接受的问题，其应用范围涵盖从医疗保健到金融市场等多个领域。传统的状态空间模型（SSMs）是用于建模单变量时间序列的经典方法，因其简单性和表达能力强以表示线性依赖而闻名。然而，它们在捕捉非线性依赖方面的表达能力基本有限，实践中速度较慢，并且无法建模变量间的信息流。尽管最近有尝试通过使用深度结构化SSMs来提升SSMs的表达能力，但现有方法要么局限于单变量时间序列，要么无法建模复杂模式（如季节性模式），要么无法动态建模变量和时间维度的依赖关系，或者是独立于输入的。我们提出了Chimera，它使用两个依赖于输入的2-D SSM头部，采用不同的离散化过程来学习长期进展和季节性模式。为了提高复杂的2D循环的效率，我们提出了一种快速训练方法，使用新的二维并行选择性扫描。我们进一步介绍和讨论了2D SSM的特殊情况，即2D Mamba和Mamba-2。我们的实验评估显示了Chimera在广泛和多样的基准测试中的卓越性能，包括心电图和语音时间序列分类、长期和短期时间序列预测，以及时间序列异常检测。

English

Modeling multivariate time series is a well-established problem with a wide range of applications from healthcare to financial markets. Traditional State Space Models (SSMs) are classical approaches for univariate time series modeling due to their simplicity and expressive power to represent linear dependencies. They, however, have fundamentally limited expressive power to capture non-linear dependencies, are slow in practice, and fail to model the inter-variate information flow. Despite recent attempts to improve the expressive power of SSMs by using deep structured SSMs, the existing methods are either limited to univariate time series, fail to model complex patterns (e.g., seasonal patterns), fail to dynamically model the dependencies of variate and time dimensions, and/or are input-independent. We present Chimera that uses two input-dependent 2-D SSM heads with different discretization processes to learn long-term progression and seasonal patterns. To improve the efficiency of complex 2D recurrence, we present a fast training using a new 2-dimensional parallel selective scan. We further present and discuss 2-dimensional Mamba and Mamba-2 as the spacial cases of our 2D SSM. Our experimental evaluation shows the superior performance of Chimera on extensive and diverse benchmarks, including ECG and speech time series classification, long-term and short-term time series forecasting, and time series anomaly detection.