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Time-series learning using monotonic logical properties

  • Author(s): Vazquez-Chanlatte, M;
  • Ghosh, S;
  • Deshmukh, JV;
  • Sangiovanni-Vincentelli, A;
  • Seshia, SA
  • et al.

Cyber-physical systems of today are generating large volumes of time-series data. As manual inspection of such data is not tractable, the need for learning methods to help discover logical structure in the data has increased. We propose a logic-based framework that allows domain-specific knowledge to be embedded into formulas in a parametric logical specification over time-series data. The key idea is to then map a time series to a surface in the parameter space of the formula. Given this mapping, we identify the Hausdorff distance between surfaces as a natural distance metric between two time-series data under the lens of the parametric specification. This enables embedding nontrivial domain-specific knowledge into the distance metric and then using off-the-shelf machine learning tools to label the data. After labeling the data, we demonstrate how to extract a logical specification for each label. Finally, we showcase our technique on real world traffic data to learn clas-sifiers/monitors for slow-downs and traffic jams.

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