def test_sample_posterior(self): isa = ISA(2, 3, num_scales=10) isa.A = asarray([[1., 0., 1.], [0., 1., 1.]]) isa.initialize() params = isa.default_parameters() params['gibbs']['verbosity'] = 0 params['gibbs']['num_iter'] = 100 states_post = isa.sample_posterior(isa.sample(1000), params) states_prio = isa.sample_prior(states_post.shape[1]) states_post = states_post.flatten() states_post = states_post[permutation(states_post.size)] states_prio = states_prio.flatten() states_prio = states_prio[permutation(states_prio.size)] # on average, posterior samples should be distributed like prior samples p = ks_2samp(states_post, states_prio)[1] self.assertGreater(p, 0.0001) samples = isa.sample(100) states = isa.sample_posterior(samples, params) # reconstruction should be perfect self.assertLess(sum(square(dot(isa.A, states) - samples).flatten()), 1e-10)
def test_sample_posterior(self):
isa = ISA(2, 3, num_scales=10)
isa.A = asarray([[1., 0., 1.], [0., 1., 1.]])
isa.initialize()
params = isa.default_parameters()
params['gibbs']['verbosity'] = 0
params['gibbs']['num_iter'] = 100
states_post = isa.sample_posterior(isa.sample(1000), params)
states_prio = isa.sample_prior(states_post.shape[1])
states_post = states_post.flatten()
states_post = states_post[permutation(states_post.size)]
states_prio = states_prio.flatten()
states_prio = states_prio[permutation(states_prio.size)]
# on average, posterior samples should be distributed like prior samples
p = ks_2samp(states_post, states_prio)[1]
self.assertGreater(p, 0.0001)
samples = isa.sample(100)
states = isa.sample_posterior(samples, params)
# reconstruction should be perfect
self.assertLess(sum(square(dot(isa.A, states) - samples).flatten()),
1e-10)
def test_evaluate(self): isa1 = ISA(2) isa1.A = eye(2) subspaces = isa1.subspaces() for gsm in subspaces: gsm.scales = ones(gsm.num_scales) isa1.set_subspaces(subspaces) # equivalent overcomplete model isa2 = ISA(2, 4) A = copy(isa2.A) A[:, :2] = isa1.A / sqrt(2.) A[:, 2:] = isa1.A / sqrt(2.) isa2.A = A subspaces = isa2.subspaces() for gsm in subspaces: gsm.scales = ones(gsm.num_scales) isa2.set_subspaces(subspaces) data = isa1.sample(100) # the results should not depend on the parameters ll1 = isa1.evaluate(data) ll2 = isa2.evaluate(data) self.assertLess(abs(ll1 - ll2), 1e-5) isa1 = ISA(2) isa1.initialize() # equivalent overcomplete model isa2 = ISA(2, 4) isa2.set_subspaces(isa1.subspaces() * 2) A = isa2.basis() A[:, :2] = isa1.basis() A[:, 2:] = 0. isa2.set_basis(A) data = isa1.sample(100) params = isa2.default_parameters() params['ais']['num_iter'] = 100 params['ais']['num_samples'] = 100 ll1 = isa1.evaluate(data) ll2 = isa2.evaluate(data, params) self.assertLess(abs(ll1 - ll2), 0.1)
def test_evaluate(self):
isa1 = ISA(2)
isa1.A = eye(2)
subspaces = isa1.subspaces()
for gsm in subspaces:
gsm.scales = ones(gsm.num_scales)
isa1.set_subspaces(subspaces)
# equivalent overcomplete model
isa2 = ISA(2, 4)
A = copy(isa2.A)
A[:, :2] = isa1.A / sqrt(2.)
A[:, 2:] = isa1.A / sqrt(2.)
isa2.A = A
subspaces = isa2.subspaces()
for gsm in subspaces:
gsm.scales = ones(gsm.num_scales)
isa2.set_subspaces(subspaces)
data = isa1.sample(100)
# the results should not depend on the parameters
ll1 = isa1.evaluate(data)
ll2 = isa2.evaluate(data)
self.assertLess(abs(ll1 - ll2), 1e-5)
isa1 = ISA(2)
isa1.initialize()
# equivalent overcomplete model
isa2 = ISA(2, 4)
isa2.set_subspaces(isa1.subspaces() * 2)
A = isa2.basis()
A[:, :2] = isa1.basis()
A[:, 2:] = 0.
isa2.set_basis(A)
data = isa1.sample(100)
params = isa2.default_parameters()
params['ais']['num_iter'] = 100
params['ais']['num_samples'] = 100
ll1 = isa1.evaluate(data)
ll2 = isa2.evaluate(data, params)
self.assertLess(abs(ll1 - ll2), 0.1)
def test_sample_posterior_ais(self): isa = ISA(2, 3, num_scales=10) isa.A = asarray([[1., 0., 1.], [0., 1., 1.]]) isa.initialize() params = isa.default_parameters() params['ais']['verbosity'] = 0 params['ais']['num_iter'] = 100 samples = isa.sample(100) states, _ = isa.sample_posterior_ais(samples, params) # reconstruction should be perfect self.assertLess(sum(square(dot(isa.A, states) - samples).flatten()), 1e-10)
def test_sample_posterior_ais(self):
isa = ISA(2, 3, num_scales=10)
isa.A = asarray([[1., 0., 1.], [0., 1., 1.]])
isa.initialize()
params = isa.default_parameters()
params['ais']['verbosity'] = 0
params['ais']['num_iter'] = 100
samples = isa.sample(100)
states, _ = isa.sample_posterior_ais(samples, params)
# reconstruction should be perfect
self.assertLess(sum(square(dot(isa.A, states) - samples).flatten()),
1e-10)
def test_train_lbfgs(self): isa = ISA(2) isa.initialize() isa.A = eye(2) samples = isa.sample(10000) # initialize close to original parameters isa.A = asarray([[cos(0.4), sin(0.4)], [-sin(0.4), cos(0.4)]]) params = isa.default_parameters() params['training_method'] = 'LBFGS' params['train_prior'] = False params['max_iter'] = 1 params['lbfgs']['max_iter'] = 50 isa.train(samples, params) # L-BFGS should be able to recover the parameters self.assertLess(sqrt(sum(square(isa.A.flatten() - eye(2).flatten()))), 0.1)
def test_initialize(self):
def sqrtmi(mat):
"""
Compute matrix inverse square root.
@type mat: array_like
@param mat: matrix for which to compute inverse square root
"""
# find eigenvectors
eigvals, eigvecs = eig(mat)
# eliminate eigenvectors whose eigenvalues are zero
eigvecs = eigvecs[:, eigvals > 0.]
eigvals = eigvals[eigvals > 0.]
# inverse square root
return dot(eigvecs, dot(diag(1. / sqrt(eigvals)), eigvecs.T))
# white data
data = randn(5, 1000)
data = dot(sqrtmi(cov(data)), data)
isa = ISA(5, 10)
isa.initialize(data)
# rows of A should be roughly orthogonal
self.assertLess(sum(square(dot(isa.A, isa.A.T) - eye(5)).flatten()),
1e-3)
p = kstest(
isa.sample_prior(100).flatten(),
lambda x: laplace.cdf(x, scale=1. / sqrt(2.)))[1]
# prior marginals should be roughly Laplace
self.assertGreater(p, 0.0001)
# test initialization with larger subspaces
isa = ISA(5, 10, ssize=2)
isa.initialize(data)
def test_initialize(self): def sqrtmi(mat): """ Compute matrix inverse square root. @type mat: array_like @param mat: matrix for which to compute inverse square root """ # find eigenvectors eigvals, eigvecs = eig(mat) # eliminate eigenvectors whose eigenvalues are zero eigvecs = eigvecs[:, eigvals > 0.] eigvals = eigvals[eigvals > 0.] # inverse square root return dot(eigvecs, dot(diag(1. / sqrt(eigvals)), eigvecs.T)) # white data data = randn(5, 1000) data = dot(sqrtmi(cov(data)), data) isa = ISA(5, 10) isa.initialize(data) # rows of A should be roughly orthogonal self.assertLess(sum(square(dot(isa.A, isa.A.T) - eye(5)).flatten()), 1e-3) p = kstest( isa.sample_prior(100).flatten(), lambda x: laplace.cdf(x, scale=1. / sqrt(2.)))[1] # prior marginals should be roughly Laplace self.assertGreater(p, 0.0001) # test initialization with larger subspaces isa = ISA(5, 10, ssize=2) isa.initialize(data)
def test_merge(self): isa1 = ISA(5, ssize=2) isa2 = ISA(5) isa1.initialize() isa1.orthogonalize() isa2.initialize() isa2.A = isa1.A params = isa2.default_parameters() params['train_basis'] = False params['merge_subspaces'] = True params['merge']['verbosity'] = 0 isa2.train(isa1.sample(10000), params) ssizes1 = [gsm.dim for gsm in isa1.subspaces()] ssizes2 = [gsm.dim for gsm in isa2.subspaces()] # algorithm should be able to recover subspace sizes self.assertTrue(all(sort(ssizes1) == sort(ssizes2)))
def test_merge(self):
isa1 = ISA(5, ssize=2)
isa2 = ISA(5)
isa1.initialize()
isa1.orthogonalize()
isa2.initialize()
isa2.A = isa1.A
params = isa2.default_parameters()
params['train_basis'] = False
params['merge_subspaces'] = True
params['merge']['verbosity'] = 0
isa2.train(isa1.sample(10000), params)
ssizes1 = [gsm.dim for gsm in isa1.subspaces()]
ssizes2 = [gsm.dim for gsm in isa2.subspaces()]
# algorithm should be able to recover subspace sizes
self.assertTrue(all(sort(ssizes1) == sort(ssizes2)))
def test_train_lbfgs(self):
isa = ISA(2)
isa.initialize()
isa.A = eye(2)
samples = isa.sample(10000)
# initialize close to original parameters
isa.A = asarray([[cos(0.4), sin(0.4)], [-sin(0.4), cos(0.4)]])
params = isa.default_parameters()
params['training_method'] = 'LBFGS'
params['train_prior'] = False
params['max_iter'] = 1
params['lbfgs']['max_iter'] = 50
isa.train(samples, params)
# L-BFGS should be able to recover the parameters
self.assertLess(sqrt(sum(square(isa.A.flatten() - eye(2).flatten()))),
0.1)
def test_train(self): # make sure train() doesn't throw any errors isa = ISA(2) params = isa.default_parameters() params['verbosity'] = 0 params['max_iter'] = 2 params['training_method'] = 'SGD' params['sgd']['max_iter'] = 1 params['sgd']['batch_size'] = 57 isa.initialize(randn(2, 1000)) isa.train(randn(2, 1000), params) isa = ISA(4, ssize=2) isa.initialize(randn(4, 1000)) isa.train(randn(4, 1000), params) isa = ISA(2, 3) params['gibbs']['ini_iter'] = 2 params['gibbs']['num_iter'] = 2 params['verbosity'] = 0 params['gibbs']['verbosity'] = 0 isa.initialize(randn(2, 1000)) isa.train(randn(2, 1000), params)
def test_train(self):
# make sure train() doesn't throw any errors
isa = ISA(2)
params = isa.default_parameters()
params['verbosity'] = 0
params['max_iter'] = 2
params['training_method'] = 'SGD'
params['sgd']['max_iter'] = 1
params['sgd']['batch_size'] = 57
isa.initialize(randn(2, 1000))
isa.train(randn(2, 1000), params)
isa = ISA(4, ssize=2)
isa.initialize(randn(4, 1000))
isa.train(randn(4, 1000), params)
isa = ISA(2, 3)
params['gibbs']['ini_iter'] = 2
params['gibbs']['num_iter'] = 2
params['verbosity'] = 0
params['gibbs']['verbosity'] = 0
isa.initialize(randn(2, 1000))
isa.train(randn(2, 1000), params)