Python implemenation of iPMCMC: http://proceedings.mlr.press/v48/rainforth16.pdf
To install the package, you must have python 3 installed on your computer. After cloning the repository, go into the root of the repository and type the following command line:
python setup.py install
You can check if the module was correctly installed using pip:
pip show ipmcmc
Then you should be able to use ipmcmc as a package, by simply importing it as follows:
import ipmcmc If the installation did not work or something went wrong, try:
python reset_module.py
We chose to implement the exact same models as in the paper at first where the unobserved states only depend on their previous state, and the observations only depends on the current state. So these are hidden markov models.
The initial state follows a Gaussian distribution centered in mu = (0, 0, 1) with a variance V = 0.1 * Id.
At the time t, the state x_t simply follows a Gaussian distribution, centered on a rotationed version of x_(t-1) (7pi/10, 3pi/10 and pi/20 on the first, second and third dimensions of x_(t-1)), with a variance omega = Id.
The observation model is also a simple Gaussian distribution, so y_t follows this Gaussian centered in Beta * x_t, with Beta an emission matrix with independent columns sampled from a Dirichlet distribution. Its variance Sigma is equal to V.