def test_get_gaussian_2d(self): X = asarray([-1, 1]) X = reshape(X, (len(X), 1)) y = asarray([+1 if x >= 0 else -1 for x in X]) covariance = SquaredExponentialCovariance(sigma=1, scale=1) likelihood = LogitLikelihood() gp = GaussianProcess(y, X, covariance, likelihood) laplace = LaplaceApproximation(gp, newton_start=asarray([3, 3])) f_mode, L, steps = laplace.find_mode_newton(return_full=True) gaussian = laplace.get_gaussian(f_mode, L) F = linspace(-10, 10, 20) D = zeros((len(F), len(F))) Q = array(D, copy=True) for i in range(len(F)): for j in range(len(F)): f = asarray([F[i], F[j]]) D[i, j] = gp.log_posterior_unnormalised(f) Q[i, j] = gaussian.log_pdf(f.reshape(1, len(f))) subplot(1, 2, 1) pcolor(F, F, D) hold(True) plot(steps[:, 0], steps[:, 1]) plot(f_mode[1], f_mode[0], 'mo', markersize=10) hold(False) colorbar() subplot(1, 2, 2) pcolor(F, F, Q) hold(True) plot(f_mode[1], f_mode[0], 'mo', markersize=10) hold(False) colorbar() # show() clf()
def test_mode_newton_2d(self): X = asarray([-1, 1]) X = reshape(X, (len(X), 1)) y = asarray([+1 if x >= 0 else -1 for x in X]) covariance = SquaredExponentialCovariance(sigma=1, scale=1) likelihood = LogitLikelihood() gp = GaussianProcess(y, X, covariance, likelihood) laplace = LaplaceApproximation(gp, newton_start=asarray([3, 3])) f_mode, _, steps = laplace.find_mode_newton(return_full=True) F = linspace(-10, 10, 20) D = zeros((len(F), len(F))) for i in range(len(F)): for j in range(len(F)): f = asarray([F[i], F[j]]) D[i, j] = gp.log_posterior_unnormalised(f) idx = unravel_index(D.argmax(), D.shape) empirical_max = asarray([F[idx[0]], F[idx[1]]]) pcolor(F, F, D) hold(True) plot(steps[:, 0], steps[:, 1]) plot(f_mode[1], f_mode[0], 'mo', markersize=10) hold(False) colorbar() clf() # show() self.assertLessEqual(norm(empirical_max - f_mode), 1)