import torch


def gaussian_kernel(x, y, alpha):
    """
    compute a Gaussian kernel for vector x and y
    :param x: data list
    :param y: data list
    :param alpha: parameter for the Gaussian kernel
    :return: the Gaussian kernel
    """
    # e^(-a * |x - y|^2)
    return torch.exp(-alpha * (x - y).pow(2))