def test_rff_feature_map():
x = 3.
u = 2.
omega = 2.
phi = rff_feature_map_single(x, omega, u)
phi_manual = np.cos(omega * x + u) * np.sqrt(2.)
assert_close(phi, phi_manual)
def test_rff_feature_map():
x = 3.
u = 2.
omega = 2.
phi = rff_feature_map_single(x, omega, u)
phi_manual = np.cos(omega * x + u) * np.sqrt(2.)
assert_close(phi, phi_manual)
def log_pdf(self, x):
if self.theta is None:
raise RuntimeError("Model not fitted yet.")
assert_array_shape(x, ndim=1, dims={0: self.D})
phi = rff_feature_map_single(x, self.omega, self.u)
return np.dot(phi, self.theta)
def log_pdf(self, x):
if self.theta is None:
raise RuntimeError("Model not fitted yet.")
assert_array_shape(x, ndim=1, dims={0: self.D})
phi = rff_feature_map_single(x, self.omega, self.u)
return np.dot(phi, self.theta)
def test_rff_feature_map_single_equals_feature_map():
N = 10
D = 20
m = 3
X = np.random.randn(N, D)
omega = np.random.randn(D, m)
u = np.random.uniform(0, 2 * np.pi, m)
phis = rff_feature_map(X, omega, u)
for i, x in enumerate(X):
phi = rff_feature_map_single(x, omega, u)
assert_allclose(phis[i], phi)
def test_rff_feature_map_single_equals_feature_map():
N = 10
D = 20
m = 3
X = np.random.randn(N, D)
omega = np.random.randn(D, m)
u = np.random.uniform(0, 2 * np.pi, m)
phis = rff_feature_map(X, omega, u)
for i, x in enumerate(X):
phi = rff_feature_map_single(x, omega, u)
assert_allclose(phis[i], phi)
def test_rff_feature_map_comp_theano_result_equals_manual():
if not theano_available:
raise SkipTest("Theano not available.")
D = 2
x = np.random.randn(D)
m = 10
sigma = 1.
omega, u = rff_sample_basis(D, m, sigma)
phi_manual = rff_feature_map_single(x, omega, u)
for i in range(m):
# phi_manual is a monte carlo average, so have to normalise by np.sqrt(m) here
phi = rff_feature_map_comp_theano(x, omega[:, i], u[i]) / np.sqrt(m)
assert_close(phi, phi_manual[i])
def test_rff_feature_map_comp_theano_result_equals_manual():
if not theano_available:
raise SkipTest("Theano not available.")
D = 2
x = np.random.randn(D)
m = 10
sigma = 1.
omega, u = rff_sample_basis(D, m, sigma)
phi_manual = rff_feature_map_single(x, omega, u)
for i in range(m):
# phi_manual is a monte carlo average, so have to normalise by np.sqrt(m) here
phi = rff_feature_map_comp_theano(x, omega[:, i], u[i]) / np.sqrt(m)
assert_close(phi, phi_manual[i])
def update_b_single(x, b, n, omega, u):
D = omega.shape[0]
m = omega.shape[1]
projections_sum = np.zeros(m)
phi = rff_feature_map_single(x, omega, u)
for d in range(D):
# second derivative of feature map
phi2 = -phi * (omega[d, :]**2)
projections_sum -= phi2
# Knuth's running average
n += 1
delta = projections_sum - b
b += delta / n
return b
def update_b_single(x, b, n, omega, u):
D = omega.shape[0]
m = omega.shape[1]
projections_sum = np.zeros(m)
phi = rff_feature_map_single(x, omega, u)
for d in range(D):
# second derivative of feature map
phi2 = -phi * (omega[d, :] ** 2)
projections_sum -= phi2
# Knuth's running average
n += 1
delta = projections_sum - b
b += delta / n
return b
