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252    CHAPTER 12 Computational Intelligence in the Time




                            Passive solutions do not suffer from false positives and negatives in detecting a
                         change in stationarity/time variance, since the learning-based system/application
                         continuously updates parameters over time by integrating the available novelty
                         content into the model. From this perspective the partial derivative in Eq. (12.2)
                         can be intended as the operator extracting the novelty information content from
                         current data: if there is novelty, the model needs to be updated. As a consequence,
                         passive models are rather sensitive to noise in incoming data: after parameter
                         convergence, the application continues to update the parameters so as to track the
                         particular noise realization. A vast literature on passive approaches exist (also called
                         online learning in the neural networks field) and the interested reader can focus on
                         and implement those results in her/his CPS/IoT application [4,11,14]. However, the
                         computational complexity of a passive approach might be inappropriate for
                         embedded applications given the continuous need to update the model; operations
                         which might end up in a prohibitive energy consumption and processing time
                         whenever the update phase is energy/computation eager. Ensemble solutions and
                         complex neural networks are examples in this direction where the cost we have to
                         pay for high accuracy and flexibility is computational.

                         4.2 ACTIVE ADAPTATION MODALITY
                         In the active adaptation strategy, the presence of a change-detection trigger activates
                         the due application reaction following the detected change in stationarity, for
                         example, by updating the learning-based system. This means that the application
                         running on the embedded device undergoes an update/reconfiguration phase to track
                         the change in stationarity only when triggered by the change detection module. The
                         change detection moduledor Oracledoperates by inspecting features 4 extracted
                         from the input data or preprocessed variables [4,13] to assess the presence of a
                         change. In other terms the Oracle u acts as the indicator function

                                                1; if change in stationarity is detected
                                       uð4Þ¼
                                                          0; otherwise
                         and the update equation becomes

                                                              vLðx; qÞ
                                              q tþ1 ¼ q t   guð4Þ                      (12.3)
                                                                 vq
                                                                     q t
                         In its basic form the Oracle is based on a threshold; in more sophisticated versions,
                         the Oracle also relies on a confidence level, for example, as it happens in statistical
                         testsdor, even, takes control of the occurrence of false positives by setting its
                         expectation to a predefined value.
                            Adaptive strategies at CPSs following the active adaptation modality are known
                         as “detect & react” approaches; such solutions have much focused on classifiers in
                         the related literature, though results are more general [4].
                            It should be commented that if the computational load of passive solutions is
                         negligible they should be preferred than active ones unless the application is
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