def test_objective_sym_optimum():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
K = gaussian_kernel(Z, sigma=sigma)
a = develop_gaussian.fit_sym(Z, sigma, lmbda, K)
J_opt = develop_gaussian.objective_sym(Z, sigma, lmbda, a, K)
for _ in range(10):
a_random = np.random.randn(len(Z))
J = develop_gaussian.objective_sym(Z, sigma, lmbda, a_random, K)
assert J >= J_opt
def test_objective_sym_same_as_from_estimation():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
K = gaussian_kernel(Z, sigma=sigma)
a = develop_gaussian.fit_sym(Z, sigma, lmbda, K)
C = develop_gaussian.compute_C_sym(Z, K, sigma)
b = develop_gaussian.compute_b_sym(Z, K, sigma)
J = develop_gaussian.objective_sym(Z, sigma, lmbda, a, K, b, C)
J2 = develop_gaussian.objective_sym(Z, sigma, lmbda, a, K)
assert_almost_equal(J, J2)
def test_objective_sym_same_as_from_estimation():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
K = gaussian_kernel(Z, sigma=sigma)
a = develop_gaussian.fit_sym(Z, sigma, lmbda, K)
C = develop_gaussian.compute_C_sym(Z, K, sigma)
b = develop_gaussian.compute_b_sym(Z, K, sigma)
J = develop_gaussian.objective_sym(Z, sigma, lmbda, a, K, b, C)
J2 = develop_gaussian.objective_sym(Z, sigma, lmbda, a, K)
assert_almost_equal(J, J2)
def test_objective_sym_optimum():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
K = gaussian_kernel(Z, sigma=sigma)
a = develop_gaussian.fit_sym(Z, sigma, lmbda, K)
J_opt = develop_gaussian.objective_sym(Z, sigma, lmbda, a, K)
for _ in range(10):
a_random = np.random.randn(len(Z))
J = develop_gaussian.objective_sym(Z, sigma, lmbda, a_random, K)
assert J >= J_opt
def test_objective_sym_against_naive():
sigma = 1.
D = 2
N = 10
Z = np.random.randn(N, D)
K = gaussian_kernel(Z, sigma=sigma)
num_trials = 10
for _ in range(num_trials):
alpha = np.random.randn(N)
J_naive_a = 0
for d in range(D):
for i in range(N):
for j in range(N):
J_naive_a += alpha[i] * K[i, j] * \
(-1 + 2. / sigma * ((Z[i][d] - Z[j][d]) ** 2))
J_naive_a *= (2. / (N * sigma))
J_naive_b = 0
for d in range(D):
for i in range(N):
temp = 0
for j in range(N):
temp += alpha[j] * (Z[j, d] - Z[i, d]) * K[i, j]
J_naive_b += (temp**2)
J_naive_b *= (2. / (N * (sigma**2)))
J_naive = J_naive_a + J_naive_b
# compare to unregularised objective
lmbda = 0.
J = develop_gaussian.objective_sym(Z, sigma, lmbda, alpha, K)
assert_close(J_naive, J)
def test_objective_sym_against_naive():
sigma = 1.
D = 2
N = 10
Z = np.random.randn(N, D)
K = gaussian_kernel(Z, sigma=sigma)
num_trials = 10
for _ in range(num_trials):
alpha = np.random.randn(N)
J_naive_a = 0
for d in range(D):
for i in range(N):
for j in range(N):
J_naive_a += alpha[i] * K[i, j] * \
(-1 + 2. / sigma * ((Z[i][d] - Z[j][d]) ** 2))
J_naive_a *= (2. / (N * sigma))
J_naive_b = 0
for d in range(D):
for i in range(N):
temp = 0
for j in range(N):
temp += alpha[j] * (Z[j, d] - Z[i, d]) * K[i, j]
J_naive_b += (temp ** 2)
J_naive_b *= (2. / (N * (sigma ** 2)))
J_naive = J_naive_a + J_naive_b
# compare to unregularised objective
lmbda = 0.
J = develop_gaussian.objective_sym(Z, sigma, lmbda, alpha, K)
assert_close(J_naive, J)
def test_objective_matches_sym():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
alpha = np.random.randn(len(Z))
J_sym = develop_gaussian.objective_sym(Z, sigma, lmbda, alpha)
J = gaussian.objective(Z, Z, sigma, lmbda, alpha)
print type(J)
print type(J_sym)
assert_equal(J, J_sym)
def test_objective_matches_sym():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
alpha = np.random.randn(len(Z))
J_sym = develop_gaussian.objective_sym(Z, sigma, lmbda, alpha)
J = gaussian.objective(Z, Z, sigma, lmbda, alpha)
print type(J)
print type(J_sym)
assert_equal(J, J_sym)
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_matches_sym_precomputed_KbC():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
K = gaussian_kernel(Z, sigma=sigma)
alpha = np.random.randn(len(Z))
C = develop_gaussian.compute_C_sym(Z, K, sigma)
b = develop_gaussian.compute_b_sym(Z, K, sigma)
K = gaussian_kernel(Z, sigma=sigma)
J_sym = develop_gaussian.objective_sym(Z, sigma, lmbda, alpha, K, b, C)
J = gaussian.objective(Z, Z, sigma, lmbda, alpha, K_XY=K, b=b, C=C)
assert_equal(J, J_sym)
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_matches_sym_precomputed_KbC():
sigma = 1.
lmbda = 1.
Z = np.random.randn(100, 2)
K = gaussian_kernel(Z, sigma=sigma)
alpha = np.random.randn(len(Z))
C = develop_gaussian.compute_C_sym(Z, K, sigma)
b = develop_gaussian.compute_b_sym(Z, K, sigma)
K = gaussian_kernel(Z, sigma=sigma)
J_sym = develop_gaussian.objective_sym(Z, sigma, lmbda, alpha, K, b, C)
J = gaussian.objective(Z, Z, sigma, lmbda, alpha, K_XY=K, b=b, C=C)
assert_equal(J, J_sym)
