Training a GP Regressor

A simple regression task involving just two dimensions can be handled by all of heron’s built-in infrastructure at present.

First, import the parts of heron which we’ll need:

from heron import data, regression, priors, training

we’ll also need to import the kernel module from George (but in the near future heron will wrap this up in a sensible way too):

from george import kernels

We now need to load in the training data; we can do that from a text file. A sample training set of waveforms produced by the IMRPhenomPv2 approximant is supplied in the package repository (in the data directory).

training_data = np.loadtxt("IMRPhenomPv2_nonspinning_q1to10.dat")

data = data.Data(training_data[:2,::5].T, training_data[2,::5],
              label_sigma = [0.1],
              target_names = ["t", "q"],
              label_names = ["hx"],)

Heron’s data class handles the preparation of the training data, the selection of a test set, and the normalisation of the training data, so we’re now ready to pass the data to a GPR regression model.

First, however, it’s necessary to define the covariance model.

p0 = data.get_starting()
hyper_priors = [priors.Normal(hyper, 1) for hyper in p0]
kernel = np.std(data.labels) * kernels.Matern52Kernel(sep, ndim=len(sep))

Here we’ve set up a Matern-5/2 covariance function, and we’ve assigned normal distribution priors to the value of each hyperparameter, which are centred at a the value returned by the get_starting() method of the data object.

In order to provide the best possible model, the Gaussian process must now be trained. This can be done with the module.

samples, burn = gp.train("MCMC")

Here we’ve trained the model using an MCMC process, and the samples and the burn-in samples are returned. The training process sets the hyperparameters of the kernel to the point in hyperparameter space which maximises the GP’s evidence. Finally, we can save the Gaussian process, so that it can be called later."")