def test_normal_nonscalar():
s_rng = RandomStreams(234)
n = s_rng.normal()
data = numpy.asarray([1, 2, 3, 4, 5])
p_data = rv.lpdf(n, data)
f = theano.function([], [p_data])
pvals = f()
targets = numpy.log(numpy.exp(-0.5 * (data**2)) / numpy.sqrt(2 * numpy.pi))
assert numpy.allclose(pvals, targets), (pvals, targets)
def test_normal_nonscalar():
s_rng = RandomStreams(234)
n = s_rng.normal()
data = numpy.asarray([1, 2, 3, 4, 5])
p_data = rv.lpdf(n, data)
f = theano.function([], [p_data])
pvals = f()
targets = numpy.log(numpy.exp(-0.5 * (data**2)) / numpy.sqrt(2*numpy.pi))
assert numpy.allclose(pvals,targets), (pvals, targets)
def test_normal_simple():
s_rng = RandomStreams(23)
n = s_rng.normal()
p0 = rv.lpdf(n, 0)
p1 = rv.lpdf(n, 1)
pn1 = rv.lpdf(n, -1)
f = theano.function([], [p0, p1, pn1])
pvals = f()
targets = numpy.asarray([
numpy.log(1.0 / numpy.sqrt(2 * numpy.pi)),
numpy.log(numpy.exp(-0.5) / numpy.sqrt(2 * numpy.pi)),
numpy.log(numpy.exp(-0.5) / numpy.sqrt(2 * numpy.pi)),
])
assert numpy.allclose(pvals, targets), (pvals, targets)
def test_normal_simple():
s_rng = RandomStreams(23)
n = s_rng.normal()
p0 = rv.lpdf(n, 0)
p1 = rv.lpdf(n, 1)
pn1 = rv.lpdf(n, -1)
f = theano.function([], [p0, p1, pn1])
pvals = f()
targets = numpy.asarray([
numpy.log(1.0 / numpy.sqrt(2*numpy.pi)),
numpy.log(numpy.exp(-0.5) / numpy.sqrt(2*numpy.pi)),
numpy.log(numpy.exp(-0.5) / numpy.sqrt(2*numpy.pi)),
])
assert numpy.allclose(pvals,targets), (pvals, targets)
def test_normal_w_params():
s_rng = RandomStreams(23)
n = s_rng.normal(mu=2, sigma=3)
p0 = rv.lpdf(n, 0)
p1 = rv.lpdf(n, 2)
pn1 = rv.lpdf(n, -1)
f = theano.function([], [p0, p1, pn1])
pvals = f()
targets = numpy.asarray([
numpy.log(numpy.exp(-0.5 * ((2.0/3.0)**2)) /
numpy.sqrt(2*numpy.pi*9.0)),
numpy.log(numpy.exp(0) / numpy.sqrt(2*numpy.pi*9)),
numpy.log(numpy.exp(-0.5 * ((3.0/3.0)**2)) /
numpy.sqrt(2*numpy.pi*9.0)),
])
assert numpy.allclose(pvals,targets), (pvals, targets)
class Fitting1D(unittest.TestCase):
def setUp(self):
self.obs = tensor.as_tensor_variable(
numpy.asarray([0.0, 1.01, 0.7, 0.65, 0.3]))
self.rstream = RandomStreams(234)
self.n = self.rstream.normal()
self.u = self.rstream.uniform()
def test_normal_ml(self):
up = self.rstream.ml(self.n, self.obs)
p = self.rstream.params(self.n)
f = theano.function([], [up[p[0]], up[p[1]]])
m,v = f()
assert numpy.allclose([m,v], [.532, 0.34856276335])
def test_uniform_ml(self):
up = self.rstream.ml(self.u, self.obs)
p = self.rstream.params(self.u)
f = theano.function([], [up[p[0]], up[p[1]]])
l,h = f()
assert numpy.allclose([l,h], [0.0, 1.01])
class Fitting1D(unittest.TestCase):
def setUp(self):
self.obs = tensor.as_tensor_variable(
numpy.asarray([0.0, 1.01, 0.7, 0.65, 0.3]))
self.rstream = RandomStreams(234)
self.n = self.rstream.normal()
self.u = self.rstream.uniform()
def test_normal_ml(self):
up = self.rstream.ml(self.n, self.obs)
p = self.rstream.params(self.n)
f = theano.function([], [up[p[0]], up[p[1]]])
m, v = f()
assert numpy.allclose([m, v], [.532, 0.34856276335])
def test_uniform_ml(self):
up = self.rstream.ml(self.u, self.obs)
p = self.rstream.params(self.u)
f = theano.function([], [up[p[0]], up[p[1]]])
l, h = f()
assert numpy.allclose([l, h], [0.0, 1.01])
def test_normal_w_params():
s_rng = RandomStreams(23)
n = s_rng.normal(mu=2, sigma=3)
p0 = rv.lpdf(n, 0)
p1 = rv.lpdf(n, 2)
pn1 = rv.lpdf(n, -1)
f = theano.function([], [p0, p1, pn1])
pvals = f()
targets = numpy.asarray([
numpy.log(
numpy.exp(-0.5 * ((2.0 / 3.0)**2)) /
numpy.sqrt(2 * numpy.pi * 9.0)),
numpy.log(numpy.exp(0) / numpy.sqrt(2 * numpy.pi * 9)),
numpy.log(
numpy.exp(-0.5 * ((3.0 / 3.0)**2)) /
numpy.sqrt(2 * numpy.pi * 9.0)),
])
assert numpy.allclose(pvals, targets), (pvals, targets)
import numpy
import theano
from theano import tensor
from rstreams import RandomStreams
import distributions
from sample import hybridmc_sample
from rv import full_log_likelihood
from max_lik import likelihood_gradient
s_rng = RandomStreams(3424)
# Weight prior:
w = s_rng.normal(0, 2, draw_shape=(3,))
# Linear model:
x = tensor.matrix('x')
y = tensor.nnet.sigmoid(tensor.dot(x, w))
# Bernouilli observation model:
t = s_rng.binomial(p=y, draw_shape=(4,))
# Some data:
X_data = numpy.asarray([[-1.5, -0.4, 1.3, 2.2], [-1.1, -2.2, 1.3, 0], [1., 1., 1., 1.]], dtype=theano.config.floatX).T
Y_data = numpy.asarray([1., 1., 0., 0.], dtype=theano.config.floatX)
# Compute gradient updates:
observations = dict([(t, Y_data)])
params, updates, log_likelihood = likelihood_gradient(observations)
# Compile training function and assign input data as givens:
import numpy, pylab
import theano
from theano import tensor
from rstreams import RandomStreams
import distributions
from sample import hybridmc_sample
from rv import full_log_likelihood
s_rng = RandomStreams(3424)
# Define model
w = s_rng.normal(0, 4, draw_shape=(2, ))
x = tensor.matrix('x')
y = tensor.nnet.sigmoid(tensor.dot(x, w))
t = s_rng.binomial(p=y, draw_shape=(4, ))
# Define data
X_data = numpy.asarray([[-1.5, -0.4, 1.3, 2.2], [-1.1, -2.2, 1.3, 0]],
dtype=theano.config.floatX).T
Y_data = numpy.asarray([1., 1., 0., 0.], dtype=theano.config.floatX)
# Plot full likelihood function
RVs = dict([(t, Y_data)])
lik = full_log_likelihood(RVs)
givens = dict([(x, X_data)])
lik_func = theano.function([w], lik, givens=givens, allow_input_downcast=True)
delta = .1
import numpy, pylab import theano from theano import tensor from rstreams import RandomStreams import distributions from sample import mh2_sample from rv import full_log_likelihood s_rng = RandomStreams(3424) p = s_rng.dirichlet(numpy.asarray([1, 1]))[0] m1 = s_rng.uniform(low=-5, high=5) m2 = s_rng.uniform(low=-5, high=5) v = s_rng.uniform(low=0, high=1) C = s_rng.binomial(1, p, draw_shape=(4,)) m = tensor.switch(C, m1, m2) D = s_rng.normal(m, v, draw_shape=(4,)) D_data = numpy.asarray([1, 1.2, 3, 3.4], dtype=theano.config.floatX) givens = dict([(D, D_data)]) sampler = mh2_sample(s_rng, [p, m1, m2, v], givens) samples = sampler(200, 1000, 100) print samples[0].mean(), samples[1].mean(), samples[2].mean(), samples[3].mean()
import numpy, pylab
import theano
from theano import tensor
from rstreams import RandomStreams
import distributions
from sample import hybridmc_sample
from rv import full_log_likelihood
s_rng = RandomStreams(3424)
# Define model
w = s_rng.normal(0, 4, draw_shape=(2,))
x = tensor.matrix("x")
y = tensor.nnet.sigmoid(tensor.dot(x, w))
t = s_rng.binomial(p=y, draw_shape=(4,))
# Define data
X_data = numpy.asarray([[-1.5, -0.4, 1.3, 2.2], [-1.1, -2.2, 1.3, 0]], dtype=theano.config.floatX).T
Y_data = numpy.asarray([1.0, 1.0, 0.0, 0.0], dtype=theano.config.floatX)
# Plot full likelihood function
RVs = dict([(t, Y_data)])
lik = full_log_likelihood(RVs)
givens = dict([(x, X_data)])
lik_func = theano.function([w], lik, givens=givens, allow_input_downcast=True)
delta = 0.1
x_range = numpy.arange(-10.0, 10.0, delta)
return tensor.concatenate([
tensor.ones([x.shape[1], 1]),
tensor.reshape(result.T, (x.shape[1], x.shape[0] * order))
],
axis=1)
# Define priors to be inverse gamma distributions
alpha = 1 / s_rng.gamma(1., 2.)
beta = 1 / s_rng.gamma(1., .1)
# Order of the model
# TODO: this currently has to be fixed, would be nice if this could also be a RV!
m = 7 #s_rng.random_integers(1, 10)
w = s_rng.normal(0, beta, draw_shape=(m + 1, ))
# Input variable used for training
x = tensor.matrix('x')
# Input variable used for testing
xn = tensor.matrix('xn')
# Actual linear model
y = lambda x_in: tensor.dot(poly_expansion(x_in, m), w)
# Observation model
t = s_rng.normal(y(x), alpha, draw_shape=(10, ))
# Generate some noisy training data (sine + noise)
X_data = numpy.arange(-1, 1, 0.3)
Y_data = numpy.sin(numpy.pi * X_data) + 0.1 * numpy.random.randn(*X_data.shape)
x = x.T
result, updates = theano.scan(fn=lambda prior_result, x: prior_result * x,
outputs_info=tensor.ones_like(x),
non_sequences=x,
n_steps=order)
return tensor.concatenate([tensor.ones([x.shape[1],1]), tensor.reshape(result.T, (x.shape[1], x.shape[0]*order))], axis=1)
# Define priors to be inverse gamma distributions
alpha = 1/s_rng.gamma(1., 2.)
beta = 1/s_rng.gamma(1., .1)
# Order of the model
# TODO: this currently has to be fixed, would be nice if this could also be a RV!
m = 7 #s_rng.random_integers(1, 10)
w = s_rng.normal(0, beta, draw_shape=(m+1,))
# Input variable used for training
x = tensor.matrix('x')
# Input variable used for testing
xn = tensor.matrix('xn')
# Actual linear model
y = lambda x_in: tensor.dot(poly_expansion(x_in, m), w)
# Observation model
t = s_rng.normal(y(x), alpha, draw_shape=(10,))
# Generate some noisy training data (sine + noise)
X_data = numpy.arange(-1,1,0.3)
Y_data = numpy.sin(numpy.pi*X_data) + 0.1*numpy.random.randn(*X_data.shape)
import numpy, pylab import theano from theano import tensor from rstreams import RandomStreams import distributions from sample import mh2_sample from rv import full_log_likelihood s_rng = RandomStreams(3424) p = s_rng.dirichlet(numpy.asarray([1, 1]))[0] m1 = s_rng.uniform(low=-5, high=5) m2 = s_rng.uniform(low=-5, high=5) v = s_rng.uniform(low=0, high=1) C = s_rng.binomial(1, p, draw_shape=(4, )) m = tensor.switch(C, m1, m2) D = s_rng.normal(m, v, draw_shape=(4, )) D_data = numpy.asarray([1, 1.2, 3, 3.4], dtype=theano.config.floatX) givens = dict([(D, D_data)]) sampler = mh2_sample(s_rng, [p, m1, m2, v], givens) samples = sampler(200, 1000, 100) print samples[0].mean(), samples[1].mean(), samples[2].mean(), samples[3].mean( )
