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VGPA

Variational Gaussian Process Approximation

This project contains a python3 implementation of the original VGPA algorithm for approximate inference in SDEs. It can be directly applied to solve (perform inference) to four (stochastic) dynamical systems, namely:

  1. Double Well
  2. Ornstein-Uhlenbeck
  3. Lorenz63 (3D)
  4. Lorenz96

For any other dynamical system, one has to write the required code (and inherit from the stochastic_process.py) to generate the sample paths and compute the required energy terms.

The forward-backward ODEs can be solved with four different solvers:

  1. Euler's method: 1st order
  2. Heun's method: 1st order (predictor-corrector)
  3. Runge-Kutta 2: 2nd order
  4. Runge-Kutta 4: 4th order

Required packages

The recommended version is Python3.7. The implementation is independent of third-party libraries since all the optimization (SCG) and integration routines (Fwd / Bwd) are custom-made. However, you need to have installed basic packages such as:

numpy, scipy, numba, h5py, json

To simplify the required packages just use:

$ pip install -r requirements.txt

How to run

To execute the program, first navigate to the main directory of the project (i.e. where the vgpa_main.py is located), and then run the following command:

$ python3 vgpa_main.py --params path/to/sim_params.json

The models parameters should be given in the 'sim_params.json' file as follows:

{ ...

  "Time-window": {
    "t0": 0.00,
    "tf": 10.0,
    "dt": 0.01
  },

  "Noise": {
    "sys": 0.80,
    "obs": 0.04
  },

  ...
}

References

The code refers to the initial algorithms as published in:

  1. C. Archambeau, D. Cornford, M. Opper, J. Shawe-Taylor (2007). "Gaussian process approximations of stochastic differential equations", Journal of Machine Learning Research, Workshop and Conference Proceedings. vol. 1, 2007, pp. 1–16.

  2. C. Archambeau, M. Opper, Y. Shen D. Cornford, J. Shawe-Taylor (2007). "Variational Inference for Diffusion Processes", Neural Information Processing Systems (NIPS), vol. 20.

Note

Some of the optimizations are adopted (translated) from NETLAB with the following message:

NOTE: This code is adopted from NETLAB (a free MATLAB library)

Reference Book:
(1) Ian T. Nabney (2001): Netlab: Algorithms for Pattern Recognition.
Advances in Pattern Recognition, Springer.

All the copyrights of this algorithm remain with the original author of the book (Ian T. Nabney).

Contact

For any questions / comments please contact me at: [email protected]