def test_glm_fisher_information(self):
N = 2000
T = 1000
glm = GLM(4)
glm.weights = randn(glm.dim_in, 1)
glm.bias = -2.
inputs = randn(glm.dim_in, N)
outputs = glm.sample(inputs)
x = glm._parameters()
I = glm._fisher_information(inputs, outputs)
x_mle = []
# repeated maximum likelihood estimation
for t in range(T):
inputs = randn(glm.dim_in, N)
outputs = glm.sample(inputs)
# initialize at true parameters for fast convergence
glm_ = GLM(glm.dim_in)
glm_.weights = glm.weights
glm_.bias = glm.bias
glm_.train(inputs, outputs)
x_mle.append(glm_._parameters())
C = cov(hstack(x_mle), ddof=1)
# inv(I) should be sufficiently close to C
self.assertLess(max(abs(inv(I) - C) / (abs(C) + .1)),
max(abs(C) / (abs(C) + .1)) / 2.)
def test_glm_fisher_information(self): N = 1000 T = 100 glm = GLM(3) glm.weights = randn(glm.dim_in, 1) glm.bias = -2. inputs = randn(glm.dim_in, N) outputs = glm.sample(inputs) x = glm._parameters() I = glm._fisher_information(inputs, outputs) x_mle = [] # repeated maximum likelihood estimation for t in range(T): inputs = randn(glm.dim_in, N) outputs = glm.sample(inputs) # initialize at true parameters for fast convergence glm_ = GLM(glm.dim_in) glm_.weights = glm.weights glm_.bias = glm.bias glm_.train(inputs, outputs) x_mle.append(glm_._parameters()) C = cov(hstack(x_mle), ddof=1) # inv(I) should be sufficiently close to C self.assertLess(max(abs(inv(I) - C) / (abs(C) + .1)), max(abs(C) / (abs(C) + .1)) / 2.)
def test_glm_train(self):
w = asarray([[-1., 0., 1., 2.]]).T
b = 1.
x = randn(4, 100000)
p = 1. / (1. + exp(-dot(w.T, x) - b))
y = rand(*p.shape) < p
glm = GLM(4, LogisticFunction, Bernoulli)
# test gradient
err = glm._check_gradient(x, y, 1e-5, parameters={
'train_weights': False,
'train_bias': True})
self.assertLess(err, 1e-8)
err = glm._check_gradient(x, y, 1e-5, parameters={
'train_weights': True,
'train_bias': False})
self.assertLess(err, 1e-8)
err = glm._check_gradient(x, y, 1e-5)
self.assertLess(err, 1e-8)
err = glm._check_gradient(x, y, 1e-5, parameters={
'regularize_weights': 10.,
'regularize_bias': 10.})
self.assertLess(err, 1e-8)
# test training
glm.train(x, y, parameters={'verbosity': 0})
self.assertLess(max(abs(glm.weights - w)), 0.1)
self.assertLess(max(abs(glm.bias - b)), 0.1)
glm.weights = w
glm.bias = -1.
glm.train(x, y, parameters={'verbosity': 0, 'train_weights': False})
self.assertLess(max(abs(glm.weights - w)), 1e-12)
self.assertLess(max(abs(glm.bias - b)), 0.1)
glm.weights = randn(*glm.weights.shape)
glm.bias = b
glm.train(x, y, parameters={'verbosity': 0, 'train_bias': False})
self.assertLess(max(abs(glm.weights - w)), 0.1)
self.assertLess(max(abs(glm.bias - b)), 1e-12)
def test_train(self):
stm = STM(8, 4, 4, 10)
parameters = stm._parameters()
stm.train(
randint(2, size=[stm.dim_in, 2000]),
randint(2, size=[stm.dim_out, 2000]),
parameters={
'verbosity': 0,
'max_iter': 0,
})
# parameters should not have changed
self.assertLess(max(abs(stm._parameters() - parameters)), 1e-20)
def callback(i, stm):
callback.counter += 1
return
callback.counter = 0
max_iter = 10
stm.train(
randint(2, size=[stm.dim_in, 10000]),
randint(2, size=[stm.dim_out, 10000]),
parameters={
'verbosity': 0,
'max_iter': max_iter,
'threshold': 0.,
'batch_size': 1999,
'callback': callback,
'cb_iter': 2,
})
self.assertEqual(callback.counter, max_iter / 2)
# test zero-dimensional nonlinear inputs
stm = STM(0, 5, 5)
glm = GLM(stm.dim_in_linear, LogisticFunction, Bernoulli)
glm.weights = randn(*glm.weights.shape)
input = randn(stm.dim_in_linear, 10000)
output = glm.sample(input)
stm.train(input, output, parameters={'max_iter': 20})
# STM should be able to learn GLM behavior
self.assertAlmostEqual(glm.evaluate(input, output), stm.evaluate(input, output), 1)
# test zero-dimensional inputs
stm = STM(0, 0, 10)
input = empty([0, 10000])
output = rand(1, 10000) < 0.35
stm.train(input, output)
self.assertLess(abs(mean(stm.sample(input)) - mean(output)), 0.1)
def test_blob_nonlinearity(self):
# generate test data
x = randn(1, 10000) * 4.
y = exp(-(x - 2.)**2) / 2. + exp(-(x + 5.)**2 / 4.) / 4.
z = (rand(*y.shape) < y) * 1.
glm = GLM(1, BlobNonlinearity(3))
glm.weights = [[.5 + rand()]]
err = glm._check_gradient(x,
z,
parameters={
'train_weights': False,
'train_bias': False,
'train_nonlinearity': True
})
self.assertLess(err, 1e-6)
err = glm._check_gradient(x,
z,
parameters={
'train_weights': True,
'train_bias': False,
'train_nonlinearity': False
})
self.assertLess(err, 1e-6)
def test_blob_nonlinearity(self):
# generate test data
x = randn(1, 10000) * 4.
y = exp(-(x - 2.)**2) / 2. + exp(-(x + 5.)**2 / 4.) / 4.
z = (rand(*y.shape) < y) * 1.
glm = GLM(1, BlobNonlinearity(3))
glm.weights = [[.5 + rand()]]
err = glm._check_gradient(x, z,
parameters={'train_weights': False, 'train_bias': False, 'train_nonlinearity': True})
self.assertLess(err, 1e-6)
err = glm._check_gradient(x, z,
parameters={'train_weights': True, 'train_bias': False, 'train_nonlinearity': False})
self.assertLess(err, 1e-6)
def test_glm_pickle(self):
tmp_file = mkstemp()[1]
model0 = GLM(5, BlobNonlinearity, Bernoulli)
model0.weights = randn(*model0.weights.shape)
model0.bias = randn()
# store model
with open(tmp_file, 'w') as handle:
dump({'model': model0}, handle)
# load model
with open(tmp_file) as handle:
model1 = load(handle)['model']
# make sure parameters haven't changed
self.assertLess(max(abs(model0.bias - model1.bias)), 1e-20)
self.assertLess(max(abs(model0.weights - model1.weights)), 1e-20)
x = randn(model0.dim_in, 100)
y = model0.sample(x)
self.assertEqual(model0.evaluate(x, y), model1.evaluate(x, y))
def test_glm_pickle(self):
tmp_file = mkstemp()[1]
model0 = GLM(5, BlobNonlinearity, Bernoulli)
model0.weights = randn(*model0.weights.shape)
model0.bias = randn()
# store model
with open(tmp_file, 'w') as handle:
dump({'model': model0}, handle)
# load model
with open(tmp_file) as handle:
model1 = load(handle)['model']
# make sure parameters haven't changed
self.assertLess(max(abs(model0.bias - model1.bias)), 1e-20)
self.assertLess(max(abs(model0.weights - model1.weights)), 1e-20)
x = randn(model0.dim_in, 100)
y = model0.sample(x)
self.assertEqual(
model0.evaluate(x, y),
model1.evaluate(x, y))
def test_glm_train(self):
w = asarray([[-1., 0., 1., 2.]]).T
b = 1.
x = randn(4, 100000)
p = 1. / (1. + exp(-dot(w.T, x) - b))
y = rand(*p.shape) < p
glm = GLM(4, LogisticFunction, Bernoulli)
# test gradient
err = glm._check_gradient(x,
y,
1e-5,
parameters={
'train_weights': False,
'train_bias': True
})
self.assertLess(err, 1e-8)
err = glm._check_gradient(x,
y,
1e-5,
parameters={
'train_weights': True,
'train_bias': False
})
self.assertLess(err, 1e-8)
err = glm._check_gradient(x, y, 1e-5)
self.assertLess(err, 1e-8)
err = glm._check_gradient(x,
y,
1e-5,
parameters={
'regularize_weights': 10.,
'regularize_bias': 10.
})
self.assertLess(err, 1e-8)
# test training
glm.train(x, y, parameters={'verbosity': 0})
self.assertLess(max(abs(glm.weights - w)), 0.1)
self.assertLess(max(abs(glm.bias - b)), 0.1)
glm.weights = w
glm.bias = -1.
glm.train(x, y, parameters={'verbosity': 0, 'train_weights': False})
self.assertLess(max(abs(glm.weights - w)), 1e-12)
self.assertLess(max(abs(glm.bias - b)), 0.1)
glm.weights = randn(*glm.weights.shape)
glm.bias = b
glm.train(x, y, parameters={'verbosity': 0, 'train_bias': False})
self.assertLess(max(abs(glm.weights - w)), 0.1)
self.assertLess(max(abs(glm.bias - b)), 1e-12)
