  Statistic modeling and data-driven learning are the two vital fields that
attract many attentions. Statistic models intend to capture and interpret the
relationships among variables, while data-based learning attempt to extract
information directly from the data without pre-processing through complex
models. Given the extensive studies in both fields, a subtle issue is how to
properly integrate data based methods with existing knowledge or models. In
this paper, based on the time series data, we propose two different directions
to integrate the two, a decomposition-based method and a method exploiting the
statistic extraction of data features. The first one decomposes the data into
linear stable, nonlinear stable and unstable parts, where suitable statistical
models are used for the linear stable and nonlinear stable parts while the
appropriate machine learning tools are used for the unstable parts. The second
one applies statistic models to extract statistics features of data and feed
them as additional inputs into the machine learning platform for training. The
most critical and challenging thing is how to determine and extract the
valuable information from mathematical or statistical models to boost the
performance of machine learning algorithms. We evaluate the proposal using time
series data with varying degrees of stability. Performance results show that
both methods can outperform existing schemes that use models and learning
separately, and the improvements can be over 60%. Both our proposed methods are
promising in bridging the gap between model-based and data-driven schemes and
integrating the two to provide an overall higher learning performance.
