def test_mean_argument(self):
with pytest.raises(ModelSpecificationError):
dtype = 'float64'
net = nn.HybridSequential(prefix='nn_')
with net.name_scope():
net.add(
nn.Dense(1,
flatten=False,
activation="tanh",
in_units=2,
dtype=dtype))
net.initialize(mx.init.Xavier(magnitude=3))
rbf = RBF(2, True, 1., 1., 'rbf', None, dtype)
X_var = Variable(shape=(5, 2))
X_cond_var = Variable(shape=(8, 2))
Y_cond_var = Variable(shape=(8, 1))
mean_func = MXFusionGluonFunction(net,
num_outputs=1,
broadcastable=True)
mean_var = mean_func(X_var)
mean_cond_var = mean_func(X_cond_var)
gp = ConditionalGaussianProcess.define_variable(
X=X_var,
X_cond=X_cond_var,
Y_cond=Y_cond_var,
mean_cond=mean_cond_var,
kernel=rbf,
shape=(5, 1),
dtype=dtype)
def test_kernel_as_MXFusionFunction(self, dtype, X, X_isSamples, X2,
X2_isSamples, lengthscale, lengthscale_isSamples, variance,
variance_isSamples, num_samples, input_dim, ARD):
X_mx = prepare_mxnet_array(X, X_isSamples, dtype)
X2_mx = prepare_mxnet_array(X2, X2_isSamples, dtype)
var_mx = prepare_mxnet_array(variance, variance_isSamples, dtype)
l_mx = prepare_mxnet_array(lengthscale, lengthscale_isSamples,
dtype)
X_mf = Variable(shape=X.shape)
l_mf = Variable(shape=lengthscale.shape)
var_mf = Variable(shape=variance.shape)
rbf = RBF(input_dim, ARD, 1., 1., 'rbf', None, dtype)
eval = rbf(X_mf, rbf_lengthscale=l_mf, rbf_variance=var_mf).factor
variables = {eval.X.uuid: X_mx, eval.rbf_lengthscale.uuid: l_mx, eval.rbf_variance.uuid: var_mx}
res_eval = eval.eval(F=mx.nd, variables=variables)
kernel_params = rbf.fetch_parameters(variables)
res_direct = rbf.K(F=mx.nd, X=X_mx, **kernel_params)
assert np.allclose(res_eval.asnumpy(), res_direct.asnumpy())
X_mf = Variable(shape=X.shape)
X2_mf = Variable(shape=X2.shape)
l_mf = Variable(shape=lengthscale.shape)
var_mf = Variable(shape=variance.shape)
rbf = RBF(input_dim, ARD, 1., 1., 'rbf', None, dtype)
eval = rbf(X_mf, X2_mf, rbf_lengthscale=l_mf, rbf_variance=var_mf).factor
variables = {eval.X.uuid: X_mx, eval.X2.uuid: X2_mx, eval.rbf_lengthscale.uuid: l_mx, eval.rbf_variance.uuid: var_mx}
res_eval = eval.eval(F=mx.nd, variables=variables)
kernel_params = rbf.fetch_parameters(variables)
res_direct = rbf.K(F=mx.nd, X=X_mx, X2=X2_mx, **kernel_params)
assert np.allclose(res_eval.asnumpy(), res_direct.asnumpy())
def test_draw_samples_with_broadcast_no_numpy_verification(self, dtype, a, a_is_samples, rv_shape, num_samples):
a_mx = mx.nd.array(a, dtype=dtype)
if not a_is_samples:
a_mx = add_sample_dimension(mx.nd, a_mx)
dirichlet = Dirichlet.define_variable(alpha=Variable(), shape=rv_shape, dtype=dtype).factor
variables = {dirichlet.alpha.uuid: a_mx}
draw_samples_rt = dirichlet.draw_samples(F=mx.nd, variables=variables, num_samples=num_samples)
assert np.issubdtype(draw_samples_rt.dtype, dtype)
assert draw_samples_rt.shape == (5,) + rv_shape
def test_draw_samples_no_broadcast(self, dtype, a, a_is_samples, rv_shape, num_samples):
a_mx = mx.nd.array(a, dtype=dtype)
if not a_is_samples:
a_mx = add_sample_dimension(mx.nd, a_mx)
rand = np.random.gamma(shape=a, scale=np.ones(a.shape), size=(num_samples,)+rv_shape)
draw_samples_np = rand / np.sum(rand)
rand_gen = MockMXNetRandomGenerator(mx.nd.array(rand.flatten(), dtype=dtype))
dirichlet = Dirichlet.define_variable(alpha=Variable(), shape=rv_shape, dtype=dtype, rand_gen=rand_gen).factor
variables = {dirichlet.alpha.uuid: a_mx}
draw_samples_rt = dirichlet.draw_samples(F=mx.nd, variables=variables, num_samples=num_samples)
assert np.issubdtype(draw_samples_rt.dtype, dtype)
assert np.allclose(draw_samples_np, draw_samples_rt.asnumpy())
def make_gpregr_model(self, lengthscale, variance, noise_var):
from mxfusion.models import Model
from mxfusion.components.variables import Variable, PositiveTransformation
from mxfusion.modules.gp_modules import GPRegression
from mxfusion.components.distributions.gp.kernels import RBF
dtype = 'float64'
m = Model()
m.N = Variable()
m.X = Variable(shape=(m.N, 3))
m.noise_var = Variable(transformation=PositiveTransformation(),
initial_value=mx.nd.array(noise_var,
dtype=dtype))
kernel = RBF(input_dim=3,
ARD=True,
variance=mx.nd.array(variance, dtype=dtype),
lengthscale=mx.nd.array(lengthscale, dtype=dtype),
dtype=dtype)
m.Y = GPRegression.define_variable(X=m.X,
kernel=kernel,
noise_var=m.noise_var,
shape=(m.N, 1),
dtype=dtype)
return m
def test_log_pdf_with_broadcast(self, dtype, a, a_is_samples, rv, rv_is_samples, num_samples):
# Add sample dimension if varaible is not samples
a_mx = mx.nd.array(a, dtype=dtype)
if not a_is_samples:
a_mx = add_sample_dimension(mx.nd, a_mx)
a = a_mx.asnumpy()
rv_mx = mx.nd.array(rv, dtype=dtype)
if not rv_is_samples:
rv_mx = add_sample_dimension(mx.nd, rv_mx)
rv = rv_mx.asnumpy()
is_samples_any = a_is_samples or rv_is_samples
rv_shape = rv.shape[1:]
n_dim = 1 + len(rv.shape) if is_samples_any and not rv_is_samples else len(rv.shape)
a_np = np.broadcast_to(a, (num_samples, 3, 2))
rv_np = numpy_array_reshape(rv, is_samples_any, n_dim)
# Initialize rand_gen
rand = np.random.rand(num_samples, *rv_shape)
rand_gen = MockMXNetRandomGenerator(mx.nd.array(rand.flatten(), dtype=dtype))
# Calculate correct Dirichlet logpdf
r = []
for s in range(len(rv_np)):
a = []
for i in range(len(rv_np[s])):
a.append(scipy_dirichlet.logpdf(rv_np[s][i]/sum(rv_np[s][i]), a_np[s][i]))
r.append(a)
log_pdf_np = np.array(r)
dirichlet = Dirichlet.define_variable(alpha=Variable(), shape=rv_shape, dtype=dtype, rand_gen=rand_gen).factor
variables = {dirichlet.alpha.uuid: a_mx, dirichlet.random_variable.uuid: rv_mx}
log_pdf_rt = dirichlet.log_pdf(F=mx.nd, variables=variables)
assert np.issubdtype(log_pdf_rt.dtype, dtype)
assert array_has_samples(mx.nd, log_pdf_rt) == is_samples_any
if is_samples_any:
assert get_num_samples(mx.nd, log_pdf_rt) == num_samples, (get_num_samples(mx.nd, log_pdf_rt), num_samples)
assert np.allclose(log_pdf_np, log_pdf_rt.asnumpy())
def test_log_pdf(self, dtype, X, X_isSamples, X_cond, X_cond_isSamples,
Y_cond, Y_cond_isSamples, rbf_lengthscale,
rbf_lengthscale_isSamples, rbf_variance,
rbf_variance_isSamples, rv, rv_isSamples, num_samples):
from scipy.linalg.lapack import dtrtrs
X_mx = prepare_mxnet_array(X, X_isSamples, dtype)
X_cond_mx = prepare_mxnet_array(X_cond, X_cond_isSamples, dtype)
Y_cond_mx = prepare_mxnet_array(Y_cond, Y_cond_isSamples, dtype)
rbf_lengthscale_mx = prepare_mxnet_array(rbf_lengthscale,
rbf_lengthscale_isSamples,
dtype)
rbf_variance_mx = prepare_mxnet_array(rbf_variance,
rbf_variance_isSamples, dtype)
rv_mx = prepare_mxnet_array(rv, rv_isSamples, dtype)
rv_shape = rv.shape[1:] if rv_isSamples else rv.shape
rbf = RBF(2, True, 1., 1., 'rbf', None, dtype)
X_var = Variable(shape=(5, 2))
X_cond_var = Variable(shape=(8, 2))
Y_cond_var = Variable(shape=(8, 1))
gp = ConditionalGaussianProcess.define_variable(X=X_var,
X_cond=X_cond_var,
Y_cond=Y_cond_var,
kernel=rbf,
shape=rv_shape,
dtype=dtype).factor
variables = {
gp.X.uuid: X_mx,
gp.X_cond.uuid: X_cond_mx,
gp.Y_cond.uuid: Y_cond_mx,
gp.rbf_lengthscale.uuid: rbf_lengthscale_mx,
gp.rbf_variance.uuid: rbf_variance_mx,
gp.random_variable.uuid: rv_mx
}
log_pdf_rt = gp.log_pdf(F=mx.nd, variables=variables).asnumpy()
log_pdf_np = []
for i in range(num_samples):
X_i = X[i] if X_isSamples else X
X_cond_i = X_cond[i] if X_cond_isSamples else X_cond
Y_cond_i = Y_cond[i] if Y_cond_isSamples else Y_cond
lengthscale_i = rbf_lengthscale[
i] if rbf_lengthscale_isSamples else rbf_lengthscale
variance_i = rbf_variance[
i] if rbf_variance_isSamples else rbf_variance
rv_i = rv[i] if rv_isSamples else rv
rbf_np = GPy.kern.RBF(input_dim=2, ARD=True)
rbf_np.lengthscale = lengthscale_i
rbf_np.variance = variance_i
K_np = rbf_np.K(X_i)
Kc_np = rbf_np.K(X_cond_i, X_i)
Kcc_np = rbf_np.K(X_cond_i)
L = np.linalg.cholesky(Kcc_np)
LInvY = dtrtrs(L, Y_cond_i, lower=1, trans=0)[0]
LinvKxt = dtrtrs(L, Kc_np, lower=1, trans=0)[0]
mu = LinvKxt.T.dot(LInvY)
cov = K_np - LinvKxt.T.dot(LinvKxt)
log_pdf_np.append(
multivariate_normal.logpdf(rv_i[:, 0], mean=mu[:, 0], cov=cov))
log_pdf_np = np.array(log_pdf_np)
isSamples_any = any([
X_isSamples, rbf_lengthscale_isSamples, rbf_variance_isSamples,
rv_isSamples
])
assert np.issubdtype(log_pdf_rt.dtype, dtype)
assert array_has_samples(mx.nd, log_pdf_rt) == isSamples_any
if isSamples_any:
assert get_num_samples(mx.nd, log_pdf_rt) == num_samples
assert np.allclose(log_pdf_np, log_pdf_rt)
def test_draw_samples_w_mean(self, dtype, X, X_isSamples, X_cond,
X_cond_isSamples, Y_cond, Y_cond_isSamples,
rbf_lengthscale, rbf_lengthscale_isSamples,
rbf_variance, rbf_variance_isSamples,
rv_shape, num_samples):
net = nn.HybridSequential(prefix='nn_')
with net.name_scope():
net.add(
nn.Dense(rv_shape[-1],
flatten=False,
activation="tanh",
in_units=X.shape[-1],
dtype=dtype))
net.initialize(mx.init.Xavier(magnitude=3))
from scipy.linalg.lapack import dtrtrs
X_mx = prepare_mxnet_array(X, X_isSamples, dtype)
X_cond_mx = prepare_mxnet_array(X_cond, X_cond_isSamples, dtype)
Y_cond_mx = prepare_mxnet_array(Y_cond, Y_cond_isSamples, dtype)
rbf_lengthscale_mx = prepare_mxnet_array(rbf_lengthscale,
rbf_lengthscale_isSamples,
dtype)
rbf_variance_mx = prepare_mxnet_array(rbf_variance,
rbf_variance_isSamples, dtype)
mean_mx = net(X_mx)
mean_np = mean_mx.asnumpy()
mean_cond_mx = net(X_cond_mx)
mean_cond_np = mean_cond_mx.asnumpy()
rand = np.random.randn(num_samples, *rv_shape)
rand_gen = MockMXNetRandomGenerator(
mx.nd.array(rand.flatten(), dtype=dtype))
rbf = RBF(2, True, 1., 1., 'rbf', None, dtype)
X_var = Variable(shape=(5, 2))
X_cond_var = Variable(shape=(8, 2))
Y_cond_var = Variable(shape=(8, 1))
mean_func = MXFusionGluonFunction(net,
num_outputs=1,
broadcastable=True)
mean_var = mean_func(X_var)
mean_cond_var = mean_func(X_cond_var)
gp = ConditionalGaussianProcess.define_variable(
X=X_var,
X_cond=X_cond_var,
Y_cond=Y_cond_var,
mean=mean_var,
mean_cond=mean_cond_var,
kernel=rbf,
shape=rv_shape,
dtype=dtype,
rand_gen=rand_gen).factor
variables = {
gp.X.uuid: X_mx,
gp.X_cond.uuid: X_cond_mx,
gp.Y_cond.uuid: Y_cond_mx,
gp.rbf_lengthscale.uuid: rbf_lengthscale_mx,
gp.rbf_variance.uuid: rbf_variance_mx,
gp.mean.uuid: mean_mx,
gp.mean_cond.uuid: mean_cond_mx
}
samples_rt = gp.draw_samples(F=mx.nd,
variables=variables,
num_samples=num_samples).asnumpy()
samples_np = []
for i in range(num_samples):
X_i = X[i] if X_isSamples else X
X_cond_i = X_cond[i] if X_cond_isSamples else X_cond
Y_cond_i = Y_cond[i] if Y_cond_isSamples else Y_cond
Y_cond_i = Y_cond_i - mean_cond_np[
i] if X_cond_isSamples else Y_cond_i - mean_cond_np[0]
lengthscale_i = rbf_lengthscale[
i] if rbf_lengthscale_isSamples else rbf_lengthscale
variance_i = rbf_variance[
i] if rbf_variance_isSamples else rbf_variance
rand_i = rand[i]
rbf_np = GPy.kern.RBF(input_dim=2, ARD=True)
rbf_np.lengthscale = lengthscale_i
rbf_np.variance = variance_i
K_np = rbf_np.K(X_i)
Kc_np = rbf_np.K(X_cond_i, X_i)
Kcc_np = rbf_np.K(X_cond_i)
L = np.linalg.cholesky(Kcc_np)
LInvY = dtrtrs(L, Y_cond_i, lower=1, trans=0)[0]
LinvKxt = dtrtrs(L, Kc_np, lower=1, trans=0)[0]
mu = LinvKxt.T.dot(LInvY)
cov = K_np - LinvKxt.T.dot(LinvKxt)
L_cov_np = np.linalg.cholesky(cov)
sample_np = mu + L_cov_np.dot(rand_i)
samples_np.append(sample_np)
samples_np = np.array(samples_np) + mean_np
assert np.issubdtype(samples_rt.dtype, dtype)
assert get_num_samples(mx.nd, samples_rt) == num_samples
assert np.allclose(samples_np, samples_rt)
def test_draw_samples(self, dtype, X, X_isSamples, X_cond,
X_cond_isSamples, Y_cond, Y_cond_isSamples,
rbf_lengthscale, rbf_lengthscale_isSamples,
rbf_variance, rbf_variance_isSamples, rv_shape,
num_samples):
from scipy.linalg.lapack import dtrtrs
X_mx = prepare_mxnet_array(X, X_isSamples, dtype)
X_cond_mx = prepare_mxnet_array(X_cond, X_cond_isSamples, dtype)
Y_cond_mx = prepare_mxnet_array(Y_cond, Y_cond_isSamples, dtype)
rbf_lengthscale_mx = prepare_mxnet_array(rbf_lengthscale,
rbf_lengthscale_isSamples,
dtype)
rbf_variance_mx = prepare_mxnet_array(rbf_variance,
rbf_variance_isSamples, dtype)
rand = np.random.randn(num_samples, *rv_shape)
rand_gen = MockMXNetRandomGenerator(
mx.nd.array(rand.flatten(), dtype=dtype))
rbf = RBF(2, True, 1., 1., 'rbf', None, dtype)
X_var = Variable(shape=(5, 2))
X_cond_var = Variable(shape=(8, 2))
Y_cond_var = Variable(shape=(8, 1))
gp = ConditionalGaussianProcess.define_variable(
X=X_var,
X_cond=X_cond_var,
Y_cond=Y_cond_var,
kernel=rbf,
shape=rv_shape,
dtype=dtype,
rand_gen=rand_gen).factor
variables = {
gp.X.uuid: X_mx,
gp.X_cond.uuid: X_cond_mx,
gp.Y_cond.uuid: Y_cond_mx,
gp.rbf_lengthscale.uuid: rbf_lengthscale_mx,
gp.rbf_variance.uuid: rbf_variance_mx
}
samples_rt = gp.draw_samples(F=mx.nd,
variables=variables,
num_samples=num_samples).asnumpy()
samples_np = []
for i in range(num_samples):
X_i = X[i] if X_isSamples else X
X_cond_i = X_cond[i] if X_cond_isSamples else X_cond
Y_cond_i = Y_cond[i] if Y_cond_isSamples else Y_cond
lengthscale_i = rbf_lengthscale[
i] if rbf_lengthscale_isSamples else rbf_lengthscale
variance_i = rbf_variance[
i] if rbf_variance_isSamples else rbf_variance
rand_i = rand[i]
rbf_np = GPy.kern.RBF(input_dim=2, ARD=True)
rbf_np.lengthscale = lengthscale_i
rbf_np.variance = variance_i
K_np = rbf_np.K(X_i)
Kc_np = rbf_np.K(X_cond_i, X_i)
Kcc_np = rbf_np.K(X_cond_i)
L = np.linalg.cholesky(Kcc_np)
LInvY = dtrtrs(L, Y_cond_i, lower=1, trans=0)[0]
LinvKxt = dtrtrs(L, Kc_np, lower=1, trans=0)[0]
mu = LinvKxt.T.dot(LInvY)
cov = K_np - LinvKxt.T.dot(LinvKxt)
L_cov_np = np.linalg.cholesky(cov)
sample_np = mu + L_cov_np.dot(rand_i)
samples_np.append(sample_np)
samples_np = np.array(samples_np)
assert np.issubdtype(samples_rt.dtype, dtype)
assert get_num_samples(mx.nd, samples_rt) == num_samples
assert np.allclose(samples_np, samples_rt)