sisl/ceem

Certainty-Equivalent Expectation Maximization: a scalable algorithm for system identification of partially observed systems

CE-EM

Official implementation of the the algorithm CE-EM and baseline Particle EM from "Scalable Identification of Partially Observed Systems with Certainty-Equivalent EM".

Website

Usage

Ensure you are using at least Python 3.6

pip install CEEM

Run python -m pytest to ensure everything works.

A Jupyter notebook demonstrating usage can be found in the examples subfolder.

Code overview

• ceem/dynamics.py defines the system API used by the CEEM algorithm.
• ceem/systems/*.py define various systems used in the experiments
• ceem/ceem.py contains the CEEM algorithm.
• ceem/smoother.py defines different smoothing routines used by the CEEM algorithm in the smoothing step.
• ceem/learner.py defines different learning routines used by the CEEM algorithm in the learning step.
• ceem/opt_criteria.py defines different optimization criteria used by the CEEM algorithm.
• ceem/particleem.py implements Particle EM

Experiments

Lorenz

Unbiased Estimation in Deterministic Settings

To regenerate the data in data/lorenz/bias_experiment run:

python experiments/lorenz/bias_experiment.py

To generate Table 1 run:

python experiments/lorenz/plotting/process_bias.py

Comparison to Particle Based Methods

To regenerate the data in data/lorenz/comp run:

python experiments/lorenz/comp_pem.py
python experiments/lorenz/comp_ceem.py

To generate Figure 2 run:

python experiments/lorenz/plotting/process_comp.py

Convergence of CE-EM on High Dimensional Problems

To regenerate data in data/lorenz/convergence_experiment run:

python experiments/lorenz/convergence_experiment_pem.py
python experiments/lorenz/convergence_experiment_ceem.py

To generate Figure 3 run:

python experiments/lorenz/plotting/process_convergence.py

Helicopter

The following are scripts for training models in Section 4.2. Pretrained models are provided in the pretrained_models folder.

Data download

The dataset used in our experiments can be downloaded by running:

wget 'https://zenodo.org/record/3662987/files/datasets.zip?download=1' -O datasets.zip
unzip datasets.zip

Baselines

Naive

Run the experiment with default parameters:

python experiments/heli/baselines.py --model naive

H25

Run the experiment with default parameters:

python experiments/heli/baselines.py --model H25
cp data/h25/best_net.th trained_models/h25.th

SID

Prepare the data first for residual training:

cp data/naive/best_net.th trained_models/naive_baseline.th
python experiments/heli/prepare_residual_dataset.py

Ensure you have MATLAB with the System Identification Toolbox installed then run from within MATLAB:

run_n4sid.m

LSTM

python experiments/heli/train_lstm.py
cp data/heli_lstm/ckpts/best_model.th trained_models/lstm.th

NL (Ours)

Prepare the data first for residual training:

cp data/naive/best_net.th trained_models/naive_baseline.th
python experiments/heli/prepare_residual_dataset.py

Run the experiment with default parameters:

python experiments/heli/ceemnl.py 

Move the best model to trained_models

cp data/NLobsLdyn/ckpts/best_model.th trained_models/NL_model.th

Evaluating and plotting test trajectories

First evaluate the models (uses pretrained by default) by running:

python experiments/heli/evaluate_models.py

python experiments/heli/plotting/plotbar.py

Then plot the n th trajectory in the test set by running:

python experiments/heli/plotting/plot_trajectories.py --trajectory 9

To plot the circular acceleration prediction (instead of horizontal) on the n th trajectory in the test set:

python experiments/heli/plotting/plot_trajectories.py --trajectory 9 --moments