tune_hyperparms_regression.py 文件源码

def gradient_ascent(a, b, sigma, l, alpha, K_y):
    """
    tune hyperparameters sigma and l for RBF kernel
    :param a: input vector a
    :param b: input vector b
    :param sigma: output variance determines the average distance of your function away from its mean
    :param l: lengthscale determines the length of the 'wiggles' in your function.
    :param alpha: equals to K_inv * y
    :param K_y: K_inv
    :return: current sigmal and l
    """
    step_size = 0.01
    sqdist = ((a[:, :, None] - b[:, :, None].T) ** 2).sum(1)

    # fix the output variance of RBF kernel in order to visualize it in one dimension
    '''
    # tune hyperparameter sigma
    sigma_grad = 2 * sigma * np.exp(-.5*sqdist/(l**2))
    sigma_matrix = np.dot(np.dot(alpha, alpha.T) - K_y, sigma_grad)
    tr_sigma = np.diagonal(sigma_matrix).sum()
    sigma_var = .5 * tr_sigma
    '''
    # tune hyperparameter l
    l_grad = sigma**2 * np.exp(-.5*sqdist/(l**2)) * (sqdist/l**3)
    l_matrix = np.dot(np.dot(alpha, alpha.T) - K_y, l_grad)
    tr_l = np.diagonal(l_matrix).sum()
    l_var = .5 * tr_l

    # gradient ascent to maximum log marginal likelihood simultaneously
    '''
    sigma = sigma + step_size * sigma_var
    '''
    l = l + step_size * l_var
    return sigma, l