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_sample_spike_train(self): inputs = array([ [0, 0, 0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 0, 0, 1, 1], [0, 1, 0, 1, 0, 1, 0, 1]]) outputs = array([[1, 0, 0, 0, 1, 0, 0, 0]]) glm = GLM(3, LogisticFunction, Bernoulli) glm.train(inputs, outputs) # generate a spike train without any stimulus input spike_train = sample_spike_train(empty([0, 100]), glm, 3) # test difference to expected spike train diff = spike_train.ravel()[:10] - [0, 0, 0, 1, 0, 0, 1, 0, 0, 1] self.assertLess(max(abs(diff)), 1e-8) # preconditioner which removes first (uninformative) dimension from input m = zeros([3, 1]) A = array([[0, 1, 0], [0, 0, 1]]) pre = AffineTransform(m, A) glm = GLM(2, LogisticFunction, Bernoulli) glm.train(pre(inputs), outputs) # generate a spike train with preconditioned spike history spike_train = sample_spike_train(empty([0, 100]), glm, 3, pre) # test difference to expected spike train diff = spike_train.ravel()[:10] - [0, 0, 0, 1, 0, 0, 1, 0, 0, 1] self.assertLess(max(abs(diff)), 1e-8)
def test_sample_spike_train(self):
inputs = array([[0, 0, 0, 0, 1, 1, 1, 1], [0, 0, 1, 1, 0, 0, 1, 1],
[0, 1, 0, 1, 0, 1, 0, 1]])
outputs = array([[1, 0, 0, 0, 1, 0, 0, 0]])
glm = GLM(3, LogisticFunction, Bernoulli)
glm.train(inputs, outputs)
# generate a spike train without any stimulus input
spike_train = sample_spike_train(empty([0, 100]), glm, 3)
# test difference to expected spike train
diff = spike_train.ravel()[:10] - [0, 0, 0, 1, 0, 0, 1, 0, 0, 1]
self.assertLess(max(abs(diff)), 1e-8)
# preconditioner which removes first (uninformative) dimension from input
m = zeros([3, 1])
A = array([[0, 1, 0], [0, 0, 1]])
pre = AffineTransform(m, A)
glm = GLM(2, LogisticFunction, Bernoulli)
glm.train(pre(inputs), outputs)
# generate a spike train with preconditioned spike history
spike_train = sample_spike_train(empty([0, 100]), glm, 3, pre)
# test difference to expected spike train
diff = spike_train.ravel()[:10] - [0, 0, 0, 1, 0, 0, 1, 0, 0, 1]
self.assertLess(max(abs(diff)), 1e-8)
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_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)
