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_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_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_matches_full():
sigma = 1.
lmbda = 1.
X = np.random.randn(100, 2)
Y = np.random.randn(10, 2)
low_rank_dim = int(len(X) * 0.9)
kernel = lambda X, Y: gaussian_kernel(X, Y, sigma=sigma)
alpha = np.random.randn(len(X))
K_XY = kernel(X, Y)
C = gaussian.compute_C(X, Y, K_XY, sigma)
b = gaussian.compute_b(X, Y, K_XY, sigma)
J_full = gaussian.objective(X, Y, sigma, lmbda, alpha, K_XY=K_XY, b=b, C=C)
temp = incomplete_cholesky(X, kernel, eta=low_rank_dim)
I, R, nu = (temp["I"], temp["R"], temp["nu"])
R_test = incomplete_cholesky_new_points(X, Y, kernel, I, R, nu)
b = gaussian_low_rank.compute_b(X, Y, R.T, R_test.T, sigma)
J = gaussian_low_rank.objective(X, Y, sigma, lmbda, alpha, R.T, R_test.T, b)
assert_close(J, J_full, decimal=1)
def test_objective_matches_full():
sigma = 1.
lmbda = 1.
X = np.random.randn(100, 2)
Y = np.random.randn(10, 2)
low_rank_dim = int(len(X) * 0.9)
kernel = lambda X, Y: gaussian_kernel(X, Y, sigma=sigma)
alpha = np.random.randn(len(X))
K_XY = kernel(X, Y)
C = gaussian.compute_C(X, Y, K_XY, sigma)
b = gaussian.compute_b(X, Y, K_XY, sigma)
J_full = gaussian.objective(X, Y, sigma, lmbda, alpha, K_XY=K_XY, b=b, C=C)
temp = incomplete_cholesky(X, kernel, eta=low_rank_dim)
I, R, nu = (temp["I"], temp["R"], temp["nu"])
R_test = incomplete_cholesky_new_points(X, Y, kernel, I, R, nu)
b = gaussian_low_rank.compute_b(X, Y, R.T, R_test.T, sigma)
J = gaussian_low_rank.objective(X, Y, sigma, lmbda, alpha, R.T, R_test.T,
b)
assert_close(J, J_full, decimal=1)
def test_objective_against_naive():
sigma = 1.
D = 2
NX = 10
NY = 20
X = np.random.randn(NX, D)
Y = np.random.randn(NY, D)
K_XY = gaussian_kernel(X, Y, sigma=sigma)
num_trials = 10
for _ in range(num_trials):
alpha = np.random.randn(NX)
J_naive_a = 0
for d in range(D):
for i in range(NX):
for j in range(NY):
J_naive_a += alpha[i] * K_XY[i, j] * \
(-1 + 2. / sigma * ((X[i][d] - Y[j][d]) ** 2))
J_naive_a *= (2. / (NX * sigma))
J_naive_b = 0
for d in range(D):
for i in range(NY):
temp = 0
for j in range(NX):
temp += alpha[j] * (X[j, d] - Y[i, d]) * K_XY[j, i]
J_naive_b += (temp**2)
J_naive_b *= (2. / (NX * (sigma**2)))
J_naive = J_naive_a + J_naive_b
# compare to unregularised objective
lmbda = 0.
J = gaussian.objective(X, Y, sigma, lmbda, alpha, K_XY=K_XY)
assert_close(J_naive, J)
def test_objective_against_naive():
sigma = 1.
D = 2
NX = 10
NY = 20
X = np.random.randn(NX, D)
Y = np.random.randn(NY, D)
K_XY = gaussian_kernel(X, Y, sigma=sigma)
num_trials = 10
for _ in range(num_trials):
alpha = np.random.randn(NX)
J_naive_a = 0
for d in range(D):
for i in range(NX):
for j in range(NY):
J_naive_a += alpha[i] * K_XY[i, j] * \
(-1 + 2. / sigma * ((X[i][d] - Y[j][d]) ** 2))
J_naive_a *= (2. / (NX * sigma))
J_naive_b = 0
for d in range(D):
for i in range(NY):
temp = 0
for j in range(NX):
temp += alpha[j] * (X[j, d] - Y[i, d]) * K_XY[j, i]
J_naive_b += (temp ** 2)
J_naive_b *= (2. / (NX * (sigma ** 2)))
J_naive = J_naive_a + J_naive_b
# compare to unregularised objective
lmbda = 0.
J = gaussian.objective(X, Y, sigma, lmbda, alpha, K_XY=K_XY)
assert_close(J_naive, J)
