Given taxi-ride counts information between departure and destination locations, how can we forecast their future demands?

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.

Time series forecasting typically needs to address non-stationary data with evolving trend and seasonal patterns. To address the non-stationarity, reversible instance normalization has been recently proposed to alleviate impacts from the trend with certain statistical measures, e.g., mean and variance. Although they demonstrate improved predictive accuracy, they are limited to expressing basic trends and are incapable of handling seasonal patterns. To address this limitation, this paper proposes a new instance normalization solution, called frequency adaptive normalization (FAN), which extends instance normalization in handling both dynamic trend and seasonal patterns. Specifically, we employ the Fourier transform to identify instance-wise predominant frequent components that cover most non-stationary factors. Furthermore, the discrepancy of those frequency components between inputs and outputs is explicitly modeled as a prediction task with a simple MLP model. FAN is a model-agnostic method that can be applied to arbitrary predictive backbones. We instantiate FAN on four widely used forecasting models as the backbone and evaluate their prediction performance improvements on eight benchmark datasets.

Given taxi-ride counts information between departure and destination locations, how can we forecast their future demands? In general, given a data stream of events with seasonal patterns that innovate over time, how can we effectively and efficiently forecast future events? In this paper, we propose Shifting Seasonal Matrix Factorization approach, namely SSMF, that can adaptively learn multiple seasonal patterns (called regimes), as well as switching between them. Our proposed method has the following properties: (a) it accurately forecasts future events by detecting regime shifts in seasonal patterns as the data stream evolves; (b) it works in an online setting, i.e., processes each observation in constant time and memory; (c) it effectively realizes regime shifts without human intervention by using a lossless data compression scheme. We demonstrate that our algorithm outperforms state-of-the-art baseline methods by accurately forecasting upcoming events on three real-world data streams.

In this paper we mainly focus on classification and forecasting tasks.

These dynamics pose significant challenges in forecasting.

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.