PyGaussian

PyGaussian is a simple Python Framework for using Gaussian Processes (GPs). You can find more information about GPs here.

Using GP with PyGaussian

For the following we want to train a GP to approximate the following function:

def function_1D(X):
    """1D Test Function"""
    y = (X * 6 - 2) ** 2 * np.cos(X * 12 - 4)
    return y


def function_1D_noisy(X):
    """1D Test Function with noise"""
    y = function_1D(X) + np.random.normal(0.1, 0.3, size=X.shape)
    return y

First we have to create our train and test data:

# True data (in reality not available to us)
x = np.linspace(0.0, 1, 100)
y = function_1D(x)

# Training data (observed with noise)
x_train = np.array([0, 0.1, 0.15, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8])
y_train = function_1D_noisy(x_train)

# Testing data
x_test = np.linspace(0.0, 1, 100)

Then we initialize our GP:

from PyGaussian.model import GaussianProcess

model = GaussianProcess(kernel_method="periodic", n_restarts=20)

Now we have to use the .fit() to initialize the hyperparameters of our kernel method. As default GaussianProcess() uses the squared exponential kernel.

model.fit(x_train, y_train)

After fitting the model we can now use the GP to make inferences on new unseen data points. Notice that GPs are stochastic models, so they give us their prediction as well as how uncertainty the prediction is.

y_test, cov = model.predict(x_test, return_cov=True)

To summarize all up, the following plots shows how well the GP approximate the true function, given the few data points we have. It shows how sample efficient and highly interpreatable GPs are.

Future Features

The following list defines features, that are currently on work:

• Add more kernel functions (Matérn, Sum, ...) to PyGaussian