While time series classification and forecasting problems have been
extensively studied, the cases of noisy time series data with arbitrary time
sequence lengths have remained challenging. Each time series instance can be
thought of as a sample realization of a noisy dynamical model, which is
characterized by a continuous stochastic process. For many applications, the
data are mixed and consist of several types of noisy time series sequences
modeled by multiple stochastic processes, making the forecasting and
classification tasks even more challenging. Instead of regressing data naively
and individually to each time series type, we take a latent variable model
approach using a mixtured Gaussian processes with learned spectral kernels.
More specifically, we auto-assign each type of noisy time series data a
signature vector called its motion code. Then, conditioned on each assigned
motion code, we infer a sparse approximation of the corresponding time series
using the concept of the most informative timestamps. Our unmixing
classification approach involves maximizing the likelihood across all the mixed
noisy time series sequences of varying lengths. This stochastic approach allows
us to learn not only within a single type of noisy time series data but also
across many underlying stochastic processes, giving us a way to learn multiple
dynamical models in an integrated and robust manner. The different learned
latent stochastic models allow us to generate specific sub-type forecasting. We
provide several quantitative comparisons demonstrating the performance of our
approach.

使用混合高斯过程和学习的谱核函数的潜变量模型方法来处理具有任意时间序列长度的噪声时间序列数据，使得在多个潜在随机过程上学习多个动力模型成为可能。