def test_compute_b_matches_sym():
sigma = 1.
X = np.random.randn(10, 2)
R = incomplete_cholesky_gaussian(X, sigma, eta=0.1)["R"]
x = gaussian_low_rank.compute_b(X, X, R.T, R.T, sigma)
y = develop_gaussian_low_rank.compute_b_sym(X, R.T, sigma)
assert_allclose(x, y)
def test_compute_b_matches_sym():
sigma = 1.
X = np.random.randn(10, 2)
R = incomplete_cholesky_gaussian(X, sigma, eta=0.1)["R"]
x = gaussian_low_rank.compute_b(X, X, R.T, R.T, sigma)
y = develop_gaussian_low_rank.compute_b_sym(X, R.T, sigma)
assert_allclose(x, y)
def test_fit_sym_time():
sigma = 1.
lmbda = 1.
N = 20000
Z = np.random.randn(N, 2)
R = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"]
develop_gaussian_low_rank.fit_sym(Z, sigma, lmbda, L=R.T, cg_tol=1e-1)
def test_fit_sym_time():
sigma = 1.
lmbda = 1.
N = 20000
Z = np.random.randn(N, 2)
R = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"]
develop_gaussian_low_rank.fit_sym(Z, sigma, lmbda, L=R.T, cg_tol=1e-1)
def test_compute_b_sym_matches_full():
sigma = 1.
Z = np.random.randn(100, 2)
low_rank_dim = int(len(Z) * .9)
K = gaussian_kernel(Z, sigma=sigma)
R = incomplete_cholesky_gaussian(Z, sigma, eta=low_rank_dim)["R"]
x = develop_gaussian.compute_b_sym(Z, K, sigma)
y = develop_gaussian_low_rank.compute_b_sym(Z, R.T, sigma)
assert_allclose(x, y, atol=5e-1)
def test_fit_sym_matches_full():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
a = develop_gaussian.fit_sym(Z, sigma, lmbda)
R = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"]
a_cholesky_cg = develop_gaussian_low_rank.fit_sym(Z, sigma, lmbda, L=R.T)
assert_allclose(a, a_cholesky_cg, atol=3)
def test_compute_b_sym_matches_full():
sigma = 1.
Z = np.random.randn(100, 2)
low_rank_dim = int(len(Z) * .9)
K = gaussian_kernel(Z, sigma=sigma)
R = incomplete_cholesky_gaussian(Z, sigma, eta=low_rank_dim)["R"]
x = develop_gaussian.compute_b_sym(Z, K, sigma)
y = develop_gaussian_low_rank.compute_b_sym(Z, R.T, sigma)
assert_allclose(x, y, atol=5e-1)
def test_fit_sym_matches_full():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
a = develop_gaussian.fit_sym(Z, sigma, lmbda)
R = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"]
a_cholesky_cg = develop_gaussian_low_rank.fit_sym(Z, sigma, lmbda, L=R.T)
assert_allclose(a, a_cholesky_cg, atol=3)
def fit_wrapper_(self):
self.inc_cholesky = incomplete_cholesky_gaussian(self.X, self.sigma, eta=self.eta)
L_X = self.inc_cholesky["R"].T
logger.debug(
"Incomplete Cholesky using rank %d/%d capturing %.3f/1.0 of the variance "
% (len(self.inc_cholesky["I"]), len(self.X), self.eta)
)
# start optimisation from previous alpha
alpha0 = self.alpha if len(self.alpha) == len(self.X) and len(self.alpha) > 0 else np.zeros(len(self.X))
return fit(self.X, self.X, self.sigma, self.lmbda, L_X, L_X, self.cg_tol, self.cg_maxiter, alpha0)
def test_apply_C_left_sym_matches_full():
sigma = 1.
N = 10
Z = np.random.randn(N, 2)
K = gaussian_kernel(Z, sigma=sigma)
R = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"]
v = np.random.randn(Z.shape[0])
lmbda = 1.
x = (develop_gaussian.compute_C_sym(Z, K, sigma) + lmbda * (K + np.eye(len(K)))).dot(v)
y = develop_gaussian_low_rank.apply_left_C_sym(v, Z, R.T, lmbda)
assert_allclose(x, y, atol=2e-1, rtol=2e-1)
def test_apply_C_left_sym_matches_full():
sigma = 1.
N = 10
Z = np.random.randn(N, 2)
K = gaussian_kernel(Z, sigma=sigma)
R = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"]
v = np.random.randn(Z.shape[0])
lmbda = 1.
x = (develop_gaussian.compute_C_sym(Z, K, sigma) + lmbda *
(K + np.eye(len(K)))).dot(v)
y = develop_gaussian_low_rank.apply_left_C_sym(v, Z, R.T, lmbda)
assert_allclose(x, y, atol=2e-1, rtol=2e-1)
def test_objective_sym_matches_full():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
K = gaussian_kernel(Z, sigma=sigma)
a_opt = develop_gaussian.fit_sym(Z, sigma, lmbda, K)
J_opt = develop_gaussian.objective_sym(Z, sigma, lmbda, a_opt, K)
L = incomplete_cholesky_gaussian(Z, sigma, eta=0.01)["R"].T
a_opt_chol = develop_gaussian_low_rank.fit_sym(Z, sigma, lmbda, L)
J_opt_chol = develop_gaussian_low_rank.objective_sym(Z, sigma, lmbda, a_opt_chol, L)
assert_almost_equal(J_opt, J_opt_chol, delta=2.)
def test_objective_sym_optimum():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
L = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"].T
a = develop_gaussian_low_rank.fit_sym(Z, sigma, lmbda, L)
b = develop_gaussian_low_rank.compute_b_sym(Z, L, sigma)
J_opt = develop_gaussian_low_rank.objective_sym(Z, sigma, lmbda, a, L, b)
for _ in range(10):
a_random = np.random.randn(len(Z))
J = develop_gaussian_low_rank.objective_sym(Z, sigma, lmbda, a_random, L)
assert J >= J_opt
def fit_wrapper_(self):
self.inc_cholesky = incomplete_cholesky_gaussian(self.X,
self.sigma,
eta=self.eta)
L_X = self.inc_cholesky["R"].T
logger.debug("Incomplete Cholesky using rank %d/%d capturing %.3f/1.0 of the variance " % \
(len(self.inc_cholesky['I']), len(self.X), self.eta))
# start optimisation from previous alpha
alpha0 = self.alpha if len(self.alpha) == len(
self.X) and len(self.alpha) > 0 else np.zeros(len(self.X))
return fit(self.X, self.X, self.sigma, self.lmbda, L_X, L_X,
self.cg_tol, self.cg_maxiter, alpha0)
def test_objective_sym_matches_full():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
K = gaussian_kernel(Z, sigma=sigma)
a_opt = develop_gaussian.fit_sym(Z, sigma, lmbda, K)
J_opt = develop_gaussian.objective_sym(Z, sigma, lmbda, a_opt, K)
L = incomplete_cholesky_gaussian(Z, sigma, eta=0.01)["R"].T
a_opt_chol = develop_gaussian_low_rank.fit_sym(Z, sigma, lmbda, L)
J_opt_chol = develop_gaussian_low_rank.objective_sym(
Z, sigma, lmbda, a_opt_chol, L)
assert_almost_equal(J_opt, J_opt_chol, delta=2.)
def test_objective_sym_optimum():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
L = incomplete_cholesky_gaussian(Z, sigma, eta=0.1)["R"].T
a = develop_gaussian_low_rank.fit_sym(Z, sigma, lmbda, L)
b = develop_gaussian_low_rank.compute_b_sym(Z, L, sigma)
J_opt = develop_gaussian_low_rank.objective_sym(Z, sigma, lmbda, a, L, b)
for _ in range(10):
a_random = np.random.randn(len(Z))
J = develop_gaussian_low_rank.objective_sym(Z, sigma, lmbda, a_random,
L)
assert J >= J_opt