Motion Code: Robust Time series Classification and Forecasting via Sparse Variational Multi-Stochastic Processes Learning

Despite being extensively studied, time series classification and forecasting on noisy data remain highly difficult. The main challenges lie in finding suitable mathematical concepts to describe time series and effectively separating noise from the true signals. Instead of treating time series as a static vector or a data sequence as often seen in previous methods, we introduce a novel framework that considers each time series, not necessarily of fixed length, as a sample realization of a continuous-time stochastic process. Such mathematical model explicitly captures the data dependence across several timestamps and detects the hidden time-dependent signals from noise. However, since the underlying data is often composed of several distinct dynamics, modeling using a single stochastic process is not sufficient. To handle such settings, we first assign each dynamics a signature vector. We then propose the abstract concept of the most informative timestamps to infer a sparse approximation of the individual dynamics based on their assigned vectors. The final model, referred to as Motion Code, contains parameters that can fully capture different underlying dynamics in an integrated manner. This allows unmixing classification and generation of specific sub-type forecasting simultaneously. Extensive experiments on sensors and devices noisy time series data demonstrate Motion Code's competitiveness against time series classification and forecasting benchmarks.