def test_backward_pass():
npr.seed(1)
eps = 1e-5
N = 10
D = 5
n = Normalization(D)
data = 0.5*npr.rand(N,D)
new_data = n.forward_pass(data)
loss = np.sum(new_data**2)
V = 2*new_data
dloss = n.backward_pass(V)
dloss_est = np.zeros(dloss.shape)
for i in xrange(N):
for j in xrange(D):
data[i,j] += eps
loss_1 = np.sum(n.forward_pass(data)**2)
data[i,j] -= 2*eps
loss_2 = np.sum(n.forward_pass(data)**2)
data[i,j] += eps
dloss_est[i,j] = ((loss_1 - loss_2) / (2*eps))
assert np.linalg.norm(dloss - dloss_est) < 1e-5
def test_backward_pass():
npr.seed(1)
eps = 1e-5
N = 15
D = 10
data = 0.5*npr.rand(N,D)
norm = Normalization(3)
norm_inds = [1,3,5]
bw = BetaWarp(2)
bw_inds = [0,2]
lin = Linear(3)
lin_inds = [6,8,9]
t = Transformer(D)
# Add a layer and test the gradient
t.add_layer((norm, norm_inds), (bw, bw_inds), (lin, lin_inds))
new_data = t.forward_pass(data)
loss = np.sum(new_data**2)
V = 2*new_data
dloss = t.backward_pass(V)
dloss_est = np.zeros(dloss.shape)
for i in xrange(N):
for j in xrange(D):
data[i,j] += eps
loss_1 = np.sum(t.forward_pass(data)**2)
data[i,j] -= 2*eps
loss_2 = np.sum(t.forward_pass(data)**2)
data[i,j] += eps
dloss_est[i,j] = ((loss_1 - loss_2) / (2*eps))
assert np.linalg.norm(dloss - dloss_est) < 1e-6
# Add a second layer and test the gradient
t.add_layer(Linear(9))
new_data = t.forward_pass(data)
loss = np.sum(new_data**2)
V = 2*new_data
dloss = t.backward_pass(V)
dloss_est = np.zeros(dloss.shape)
for i in xrange(N):
for j in xrange(D):
data[i,j] += eps
loss_1 = np.sum(t.forward_pass(data)**2)
data[i,j] -= 2*eps
loss_2 = np.sum(t.forward_pass(data)**2)
data[i,j] += eps
dloss_est[i,j] = ((loss_1 - loss_2) / (2*eps))
assert np.linalg.norm(dloss - dloss_est) < 1e-6
def test_forward_pass():
npr.seed(1)
N = 15
D = 10
data = 0.5*npr.rand(N,D)
norm = Normalization(3)
norm_inds = [1,3,5]
bw = BetaWarp(2)
bw_inds = [0,2]
lin = Linear(3)
lin_inds = [6,8,9]
t = Transformer(D)
t.add_layer((norm, norm_inds), (bw, bw_inds), (lin, lin_inds))
new_data = t.forward_pass(data)
assert new_data.shape[1] == 9
assert np.all(new_data[:,7:] == data[:,[4,7]])
assert np.linalg.norm(new_data[:,0:3].sum(1) - 1) < 1e-10
bw = BetaWarp(9)
t.add_layer(bw)
def test_backward_pass():
npr.seed(1)
eps = 1e-5
N = 10
D = 5
n = Normalization(D)
data = 0.5 * npr.rand(N, D)
new_data = n.forward_pass(data)
loss = np.sum(new_data**2)
V = 2 * new_data
dloss = n.backward_pass(V)
dloss_est = np.zeros(dloss.shape)
for i in xrange(N):
for j in xrange(D):
data[i, j] += eps
loss_1 = np.sum(n.forward_pass(data)**2)
data[i, j] -= 2 * eps
loss_2 = np.sum(n.forward_pass(data)**2)
data[i, j] += eps
dloss_est[i, j] = ((loss_1 - loss_2) / (2 * eps))
assert np.linalg.norm(dloss - dloss_est) < 1e-5
def test_construction():
npr.seed(1)
D = 10
norm = Normalization(3)
norm_inds = [1,3,5]
bw = BetaWarp(2)
bw_inds = [0,2]
lin = Linear(3)
lin_inds = [6,8,9]
t = Transformer(D)
t.add_layer((norm, norm_inds), (bw, bw_inds), (lin, lin_inds))
def test_grad():
npr.seed(1)
eps = 1e-5
N = 10
M = 5
D = 5
beta_warp = BetaWarp(2)
norm = Normalization(2)
lin = Linear(D)
transformer = Transformer(D)
# Each entry is a tuple, (transformation, indices_it_acts_on)
transformer.add_layer(
(beta_warp, [0, 2]),
(norm, [1, 4])) # This is crazy. We would never do this.
# One transformation means apply to all dimensions.
transformer.add_layer(lin)
kernel = TransformKernel(Matern52(lin.num_factors), transformer)
data1 = npr.rand(N, D)
data2 = npr.rand(M, D)
loss = np.sum(kernel.cross_cov(data1, data2))
dloss = kernel.cross_cov_grad_data(data1, data2).sum(0)
dloss_est = np.zeros(dloss.shape)
for i in xrange(M):
for j in xrange(D):
data2[i, j] += eps
loss_1 = np.sum(kernel.cross_cov(data1, data2))
data2[i, j] -= 2 * eps
loss_2 = np.sum(kernel.cross_cov(data1, data2))
data2[i, j] += eps
dloss_est[i, j] = ((loss_1 - loss_2) / (2 * eps))
assert np.linalg.norm(dloss - dloss_est) < 1e-6