test_scripts

• cdlgssm_test_filter_TRegular.py checks discrete and continuous-discrete Linear filtering algorithms with regularly sampled observations

  • Note that after SGD learning, comparison between discrete and continuous-discrete models is not easy due to different parameterizations.
    • Although filtered means and covs are not exactly equal, plots showcase they are quite accurate in both models.

• cdlgssm_test_smoother_TRegular.py checks discrete and continuous-discrete Linear smoothing algorithms with regularly sampled observations

  • CD smoother type 1, as in Sarkka's Algorithm 3.17 matches discrete-time solution
  • CD smoother type 2, as in Sarkka's Algorithm 3.18 does not match discrete-time solutions
    • Performance is close though: are these related to differential equation solver differences?

• cdnlgssm_test_filter_linear_TRegular.py checks continuous-discrete Linear and Non-Linear filtering algorithms with regularly sampled observations

  1. A CDNLGSSM model with linearity assumptions is equivalent to a CDLGSSM model

     • Which can be computed based on both first and second order approximations to SDE (equivalent to linear SDEs)

  2. A CDNLGSSM model with EKF filtering provides same results as a KF with a CDLGSSM model

     • Based on first and second order EKF approximations (equivalent for linear SDEs)
     • CD-EKF matches the CD-Kalman filtering performance
     • Both for pre- and post-fit of parameters with SGD, using EKF for logmarginal computations

  3. A CDNLGSSM model with UKF filtering

     • CD-UKF matches the CD-Kalman filtering performance

  4. A CDNLGSSM model with EnKF filtering

     • CD-EnKF provides a close-enough, but not exactly equal performance (even with increased number of particles) to the CD-Kalman filter
       • Pending improvements to EnKF:
         • try to get consistency on Linear Gaussian case.
         • can build jacobian-based observation H within EnKF (instead of particle approximations)

• cdnlgssm_test_smoother_linear_TRegular.py checks continuous-discrete Linear and Non-Linear smoothing algorithms with regularly sampled observations

  1. We compare that a CDNLGSSM model with EKS smoothing (as in Sarkka's Algorithm 3.23) matches CD-linear-KS type 2 (as in Sarkka's Algorithm 3.18)
     • We notice that EKS smoothing (as in Sarkka's Algorithm 3.23) does not match CD-linear-KS type 1 (as in Sarkka's Algorithm 3.17)
       • Performance is close though: are these related to differential equation solver differences?