Chimera：使用2維狀態空間模型有效地建模多變量時間序列

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

建模多變量時間序列是一個廣泛應用的問題，涵蓋了從醫療保健到金融市場等各種應用。傳統的狀態空間模型（SSMs）是用於單變量時間序列建模的經典方法，因其簡單性和表達能力而聞名，能夠表示線性依賴關係。然而，它們在捕捉非線性依賴關係方面具有根本性的表達能力限制，實際應用中速度較慢，並且無法建模變量間的信息流。儘管最近有嘗試通過使用深度結構SSMs來提高SSMs的表達能力，但現有方法要麼僅限於單變量時間序列，無法建模複雜模式（例如季節性模式），無法動態建模變量和時間維度的依賴關係，或者與輸入無關。我們提出了Chimera，它使用兩個與輸入相關的2-D SSM頭部，具有不同的離散化過程，以學習長期進展和季節性模式。為了提高複雜的2D循環的效率，我們提出了一種新的2維平行選擇掃描，實現快速訓練。我們進一步提出並討論了2維Mamba和Mamba-2作為我們2D SSM的特殊情況。我們的實驗評估顯示Chimera在廣泛和多樣的基準測試中表現優越，包括心電圖和語音時間序列分類、長期和短期時間序列預測，以及時間序列異常檢測。

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.