Kernel

Functions to calculate the kernel matrix - currently support the Radial Basis Function

kernel.rbf(x_train: numpy.ndarray, x_test: numpy.ndarray = None, params: numpy.ndarray = None) → numpy.ndarray

Implementation of the Radial Basis Function

Param

x_train (np.ndarray) : a matrix of size N x d (N > d)

Param

x_test (np.ndarray) : a matrix (or vector)

Param

params (np.ndarray) : kernel hyperparameters (amplitude and lengthscale)

Returns

kernel_matrix (np.ndarray) : the kernel matrix

If the x_test is not part of the training set, following Rasmussen et al. (2006) the following will be returned:

Returns

kernel_s (np.ndarray) : a vector of size N

Returns

kernel_ss (np.ndarray) : a scalar (1 x 1) array

kernel.squared_distance(x1: numpy.ndarray, x2: numpy.ndarray, scale: numpy.ndarray) → numpy.ndarray

Calculate the pairwise Euclidean distance between two input vectors (or matrix)

Param

x1 (np.ndarray) : first vector (or matrix if we have more than 1 training point)

Param

x2 (np.ndarray) : second vector (or matrix if we have more than 1 training point)

Param

scale (np.ndarray) : the characteristic lengthscales for the kernel

Returns

distance (np.ndarray) : pairwise Euclidean distance between the two vectors/matrix