Gaussian ProcessΒΆ

A Gaussian process is a stochastic process whose realizations consist of random values associated with every point in a range of times (or of space) such that each such random variable has a normal distribution. Moreover, every finite collection of those random variables has a multivariate normal distribution.

A Gaussian process can be used as a prior probability distribution over functions in Bayesian inference. Given any set of N points in the desired domain of your functions, take a multivariate Gaussian whose covariance matrix parameter is the Gram matrix of N points with some desired kernel, and sample from that Gaussian. Inference of continuous values with a Gaussian process prior is known as Gaussian process regression.

from miml import datasets
from miml.regression import GaussianProcessRegression

fn = os.path.join(datasets.get_data_home(), 'regression',
df = DataFrame.read_table(fn, delimiter=',',
    format='%64f', index_col=0)

x = df.values
y = array(

model = GaussianProcessRegression(sigma=0.06, L=0.01), y)

>>> run script...
array([149.63350796115427, 74.28911292438774, 139.68088364423298, 203.983666653454, 134.05095165718586, 96.03965267973412, 136.64741122676267, 62.37623771726341, 108.97096286320787, 306.95039738967637])