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

Modeling multivariate time series is a well-established problem with a wide range of applications from healthcare to financial markets. It, however, is challenging as it requires methods to (1) have high expressive power of representing complicated dependencies along the time axis to capture both long-term progression and seasonal patterns, (2) capture the inter-variate dependencies when it is informative, (3) dynamically model the dependencies of variate and time dimensions, and (4) have efficient training and inference for very long sequences. 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, an expressive variation of the 2-dimensional SSMs with careful design of parameters to maintain high expressive power while keeping the training complexity linear. Using two SSM heads with different discretization processes and input-dependent parameters, Chimera is provably able to learn long-term progression, seasonal patterns, and desirable dynamic autoregressive processes. To improve the efficiency of complex 2D recurrence, we present a fast training using a new 2-dimensional parallel selective scan. 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.