def test_feature_map_derivative2_d():
X = np.array([[1.]])
u = np.array([2.])
omega = np.array([[2.]])
d = 0
phi_derivative2 = feature_map_derivative2_d(X, omega, u, d)
phi_derivative2_manual = -feature_map(X, omega, u) * (omega[:, d]**2)
assert_close(phi_derivative2, phi_derivative2_manual)
def predict(x, alphas):
D = len(x)
f = 0.
for i in range(len(alphas)):
np.random.seed(seed_offset + i)
omega, u = sample_basis(D=D, m=1, gamma=gamma)
phi_x = feature_map(x, omega, u)
f += alphas[i] * phi_x
return f
def test_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 = feature_map(X, omega, u)
for i, x in enumerate(X):
phi = feature_map_single(x, omega, u)
assert_allclose(phis[i], phi)
def test_feature_map_equals_scikit_learn():
sigma = 2.
gamma = sigma**2
N = 10
D = 20
m = 3
X = np.random.randn(N, D)
np.random.seed(1)
omega = sigma * np.random.randn(D, m)
u = np.random.uniform(0, 2 * np.pi, m)
# make sure basis is the same
np.random.seed(1)
rbf_sampler = RBFSampler(gamma, m, random_state=1)
rbf_sampler.fit(X)
assert_allclose(rbf_sampler.random_weights_, omega)
assert_allclose(rbf_sampler.random_offset_, u)
phi_scikit = rbf_sampler.transform(X)
phi_mine = feature_map(X, omega, u)
assert_allclose(phi_scikit, phi_mine)
# estimate density in rkhs
N = 800
mu = np.zeros(D)
Z = np.random.standard_t(df=nu, size=(N, D))
lmbda = 0.0001
sigma = 0.5
gamma = 0.5 * (sigma**2)
m = N
omega = gamma * np.random.randn(D, m)
u = np.random.uniform(0, 2 * np.pi, m)
logger.info("Estimating density")
theta = score_matching_sym(Z, lmbda, omega, u)
logq_est = lambda x: log_pdf_estimate(feature_map(x, omega, u), theta)
dlogq_est = lambda x: log_pdf_estimate_grad(
feature_map_grad_single(x, omega, u), theta)
# momentum
Sigma_p = np.eye(D)
L_p = np.linalg.cholesky(Sigma_p)
logp = lambda x: log_gaussian_pdf(
x, Sigma=L_p, compute_grad=False, is_cholesky=True)
dlogp = lambda x: log_gaussian_pdf(
x, Sigma=L_p, compute_grad=True, is_cholesky=True)
p_sample = lambda: sample_gaussian(
N=1, mu=np.zeros(D), Sigma=L_p, is_cholesky=True)[0]
# starting state
p0 = p_sample()
omega, u = sample_basis(D=D, m=1, gamma=gamma)
phi_x = feature_map(x, omega, u)
f += alphas[i] * phi_x
return f
alphas = np.zeros(num_iterations)
for i in range(num_iterations):
logger.info("Iteration %d" % i)
x = X[i]
# sample random feature
np.random.seed(seed_offset + i)
omega, u = sample_basis(D=D, m=1, gamma=gamma)
phi_x = feature_map(x, omega, u)
# sample data point and predict
f = predict(x, alphas[:i]) * phi_x
# gradient of f at x
f_grad = feature_map_grad_single(x, omega, u) * f
# gradient
grad = 0
for d in range(D):
phi_derivative_d = feature_map_derivative_d(x, omega, u, d)
phi_derivative2_d = feature_map_derivative2_d(x, omega, u, d)
grad += phi_derivative_d * f_grad[d] + phi_derivative2_d