Deep Energy-Based NARX Models

Companion code to the paper:

Deep Energy-Based NARX Models https://arxiv.org/abs/2012.04136

The paper gives four examples of using deep Energy Based Models to predict the conditional distribution of the outputs given that the relationship between the current output and past outputs and inputs is modelled using a nonlinear autoregressive eXogenous (NARX) structure.

• A simulated scalar AR example with four different noise models (section 4.1 of paper)

  • Gausisan noise

    python scalar_example.py -m gaussian  # skip this line to use pregenerated results
    python plot_scalar_example.py -m gaussian

  • Bimodal Gaussian noise

    python scalar_example.py -m bimodal  # skip this line to use pregenerated results
    python plot_scalar_example.py -m bimodal

  • Cauchy noise

    python scalar_example.py -m cauchy  # skip this line to use pregenerated results
    python plot_scalar_example.py -m cauchy

  • Gaussian noise with variance dependent on y_{t-1}

    python scalar_varying.py

• A simulated second order linear ARX model with Gaussian mixture noise (section 4.2 of paper)

  python arx_example.py # skip this line to use pregenerated results
  python plot_arx_example.py

• A simulated nonlinear ARX example (section 4.3 of paper)

  python chen_arx_example.py # skip this line to use pregenerated results
  python plot_chen_example.py

  The comparison of model performance for the hyperparameters described in the appendix can be run using: (warning this will take a long time, as such pregenerated results for the combinations specified in the paper can be used by skipping this step)

  python chen_model_comparison.py -n [N] -s [Sigma]

  where [N] is the number of data points and [Sigma] is the noise level from 0.1 to 1.0 The results can be evaluated by running:

  python load_chen_comparison_results.py -n [N] -s [Sigma]

  Pregenerated results are available for combinations of N={100,250,500} and Sigma = {0.1,0.3,0.5}

• A real data example using the CE8 coupled electric drives benchmark data set (section 4.4 of paper)

  python coupledElectricDrives.py
  python plot_CED_example.py

  The comparison of model performance for the hyperparameters described in the appendix
  

  can be run using: (warning this will take a long time, as such pregenerated results are available)

  python CED_comp.py 

  The results can be evaluated by running:

  python load_CED_comp.py