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Chimera: Effectively Modeling Multivariate Time Series with 2-Dimensional State Space Models (2406.04320v1)

Published 6 Jun 2024 in cs.LG and cs.AI

Abstract: 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.

Citations (1)

Summary

  • The paper introduces Chimera, a novel 2D state space model that extends traditional SSMs to capture dependencies along both time and variate dimensions.
  • It employs companion and diagonal matrices with a bi-directional recurrent structure and data-dependent parameters to achieve high expressive power and computational efficiency.
  • Experimental results show Chimera delivers state-of-the-art performance in long-term forecasting, classification, and anomaly detection across diverse benchmarks.

An Overview of "Chimera: Effectively Modeling Multivariate Time Series with 2-Dimensional State Space Models"

This paper introduces Chimera, a novel and expressive variation of 2-dimensional State Space Models (SSMs) aimed at effectively modeling multivariate time series data. The approach integrates deep learning with traditional SSMs to address the limitations of previous univariate and multivariate time series modeling techniques. Chimera’s architecture leverages two SSM heads, each with different discretization processes along time and variate axes to dynamically capture complex dependencies and patterns.

Key Contributions

  1. Two-Dimensional Discretization: The paper extends the classical SSM framework to two dimensions, where each state is a function of both time and variate axes. This enables the modeling of intricate dependencies that are characteristic of multivariate time series data.
  2. Companion and Diagonal Matrices: Chimera uses companion matrices for transition along the time axis and diagonal matrices for the variate axis to ensure the model retains high expressive power while maintaining computational efficiency.
  3. Bi-Directional Modeling: To enhance the information flow along the non-causal variate dimension, the model employs a bi-directional recurrent structure, allowing it to capture dependencies from both forward and backward passes along the variate dimension.
  4. Data-Dependent Parameters: Recognizing the need for dynamic adaptation, Chimera utilizes data-dependent parameters, including input-dependent transformation matrices and discretization parameters, ensuring the model can dynamically filter irrelevant variates and capture essential cross-variate dependencies.
  5. Efficient Training via 2D Scan: The authors present a novel training algorithm using 2D parallel selective scan, significantly improving the efficiency of the 2D SSM recurrence, enabling faster convergence without compromising on the model's complexity.

Experimental Evaluation

Chimera’s performance was rigorously evaluated across a diverse set of benchmarks encompassing ECG classification, speech time series classification, both long-term and short-term time series forecasting, and anomaly detection tasks. Key findings include:

  • Long-Term Forecasting: Chimera outperformed state-of-the-art models on several datasets, achieving the best results in 5 out of 8 benchmarks (see Table 1). The model demonstrated superior accuracy and efficiency, thereby addressing the limitations of both classical and recent deep learning methodologies.
  • Short-Term Forecasting: On the M4 benchmark datasets, Chimera consistently excelled, further demonstrating its robustness in capturing shorter temporal dependencies (see Table 2).
  • Classification and Anomaly Detection: In classification tasks, including multivariate datasets from the UEA Time Series Classification Archive, Chimera achieved the highest average accuracy. For anomaly detection, the model showed high precision and recall scores, underscoring its ability to identify abnormal patterns effectively (see Figure 1 and Table 3).

Theoretical and Practical Implications

Theoretically, Chimera bridges the gap between traditional SSMs and advanced deep learning models by leveraging both structured parameterization and adaptable discretization. This allows the model to inherently understand and capture the long-term and seasonal patterns in multivariate time series, making it highly versatile across different domains.

Practically, the implications are significant:

  • Healthcare: Improved ECG classification can lead to better diagnosis and patient outcomes.
  • Finance and Energy Management: Accurate long-term and short-term forecasting translates to better resource allocation and financial planning.
  • Speech and Audio Processing: Enhanced modeling of speech time series contributes to advancements in automatic speech recognition and real-time audio processing.

Future Directions

The paper hints at several promising future avenues:

  • Applications Beyond Time Series: Leveraging the 2D inductive biases, Chimera could be adapted for other high-dimensional data such as images and videos, potentially alleviating the shortcomings of existing vision models with 1D selective mechanisms.
  • Hardware-Aware Implementations: Enhancing the efficiency of the 2D parallel scan through more hardware-friendly implementations could further reduce computational overheads.
  • Variants Exploration: Examining constrained versions of Chimera (e.g., 2D Mamba) could reveal insights into optimal model configurations for specific tasks or datasets.

Conclusion

Chimera stands out as an innovative and effective model for multivariate time series data, blending the strengths of classical techniques and modern deep learning paradigms. Its robust architecture and efficient training processes make it a compelling tool for a wide range of applications in various domains. The paper brilliantly showcases how careful design and parameterization within the SSM framework can lead to tangible improvements in both performance and computational efficiency.

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