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)
def test_predict(self):
# define some easy training data and predict predictive distribution
circle1 = Ring(variance=1, radius=3)
circle2 = Ring(variance=1, radius=10)
n = 100
X = circle1.sample(n / 2).samples
X = vstack((X, circle2.sample(n / 2).samples))
y = ones(n)
y[:n / 2] = -1.0
# plot(X[:n/2,0], X[:n/2,1], 'ro')
# hold(True)
# plot(X[n/2:,0], X[n/2:,1], 'bo')
# hold(False)
# show()
covariance = SquaredExponentialCovariance(1, 1)
likelihood = LogitLikelihood()
gp = GaussianProcess(y, X, covariance, likelihood)
# predict on mesh
n_test = 20
P = linspace(X[:, 0].min() - 1, X[:, 1].max() + 1, n_test)
Q = linspace(X[:, 1].min() - 1, X[:, 1].max() + 1, n_test)
X_test = asarray(list(itertools.product(P, Q)))
# Y_test = exp(LaplaceApproximation(gp).predict(X_test).reshape(n_test, n_test))
Y_train = exp(LaplaceApproximation(gp).predict(X))
print Y_train
print Y_train>0.5
print y