def compare_against_mmd_test():
    data = loadmat("../data/02-solar.mat")
    X = data["X"]
    y = data["y"]

    X_train, y_train, X_test, y_test, N, N_test = prepare_dataset(X, y)

    kernel = RBF(input_dim=1, variance=0.608, lengthscale=0.207)
    m = GPRegression(X_train, y_train, kernel, noise_var=0.283)
    m.optimize()
    pred_mean, pred_std = m.predict(X_test)

    s = GaussianQuadraticTest(None)
    gradients = compute_gp_regression_gradients(y_test, pred_mean, pred_std)
    U_matrix, stat = s.get_statistic_multiple_custom_gradient(y_test[:, 0], gradients[:, 0])
    num_test_samples = 10000
    null_samples = bootstrap_null(U_matrix, num_bootstrap=num_test_samples)
    #     null_samples = sample_null_simulated_gp(s, pred_mean, pred_std, num_test_samples)
    p_value_ours = 1.0 - np.mean(null_samples <= stat)

    y_rep = np.random.randn(len(X_test)) * pred_std.flatten() + pred_mean.flatten()
    y_rep = np.atleast_2d(y_rep).T
    A = np.hstack((X_test, y_test))
    B = np.hstack((X_test, y_rep))
    feats_p = RealFeatures(A.T)
    feats_q = RealFeatures(B.T)
    width = 1
    kernel = GaussianKernel(10, width)
    mmd = QuadraticTimeMMD()
    mmd.set_kernel(kernel)
    mmd.set_p(feats_p)
    mmd.set_q(feats_q)
    mmd_stat = mmd.compute_statistic()

    # sample from null
    num_null_samples = 10000
    mmd_null_samples = np.zeros(num_null_samples)
    for i in range(num_null_samples):
        # fix y_rep from above, and change the other one (that would replace y_test)
        y_rep2 = np.random.randn(len(X_test)) * pred_std.flatten() + pred_mean.flatten()
        y_rep2 = np.atleast_2d(y_rep2).T
        A = np.hstack((X_test, y_rep2))
        feats_p = RealFeatures(A.T)
        width = 1
        kernel = GaussianKernel(10, width)
        mmd = QuadraticTimeMMD()
        mmd.set_kernel(kernel)
        mmd.set_p(feats_p)
        mmd.set_q(feats_q)
        mmd_null_samples[i] = mmd.compute_statistic()

    p_value_mmd = 1.0 - np.mean(mmd_null_samples <= mmd_stat)

    return p_value_ours, p_value_mmd
    # sample from GP, and perform MMD two sample test between test data and sampled data
    y_rep = np.random.randn(len(X_test)) * pred_std.flatten() + pred_mean.flatten()
    y_rep = np.atleast_2d(y_rep).T

    # stack together (X_test,y_test) and (X_test, y_pred)
    A = np.hstack((X_test, y_test))
    B = np.hstack((X_test, y_rep))

    # compute MMD between (X_test,y_test) and (X_test, y_pred)
    feats_p = RealFeatures(A.T)
    feats_q = RealFeatures(B.T)
    width = 1
    kernel = GaussianKernel(10, width)
    mmd = QuadraticTimeMMD()
    mmd.set_kernel(kernel)
    mmd.set_p(feats_p)
    mmd.set_q(feats_q)
    mmd_stat = mmd.compute_statistic()

    # sample from null
    num_null_samples = 10000
    mmd_null_samples = np.zeros(num_null_samples)
    for i in range(num_null_samples):
        # fix y_rep from above, and change the other one (that would replace y_test)
        y_rep2 = np.random.randn(len(X_test)) * pred_std.flatten() + pred_mean.flatten()
        y_rep2 = np.atleast_2d(y_rep2).T

        A = np.hstack((X_test, y_rep2))

        feats_p = RealFeatures(A.T)
        width = 1