def test_draw_samples_with_broadcast_no_numpy_verification(
self, dtype, mean, mean_isSamples, var, var_isSamples, rv_shape,
num_samples):
mean_mx = mx.nd.array(mean, dtype=dtype)
if not mean_isSamples:
mean_mx = add_sample_dimension(mx.nd, mean_mx)
var_mx = mx.nd.array(var, dtype=dtype)
if not var_isSamples:
var_mx = add_sample_dimension(mx.nd, var_mx)
var = var_mx.asnumpy()
rand = np.random.rand(num_samples, *rv_shape)
rand_gen = MockMXNetRandomGenerator(
mx.nd.array(rand.flatten(), dtype=dtype))
normal = MultivariateNormal.define_variable(shape=rv_shape,
dtype=dtype,
rand_gen=rand_gen).factor
variables = {normal.mean.uuid: mean_mx, normal.covariance.uuid: var_mx}
draw_samples_rt = normal.draw_samples(F=mx.nd,
variables=variables,
num_samples=num_samples)
assert np.issubdtype(draw_samples_rt.dtype, dtype)
assert is_sampled_array(mx.nd, draw_samples_rt) == True
def test_log_pdf_no_broadcast(self, dtype, mean, mean_isSamples, var,
var_isSamples, rv, rv_isSamples,
num_samples):
mean_mx = mx.nd.array(mean, dtype=dtype)
if not mean_isSamples:
mean_mx = add_sample_dimension(mx.nd, mean_mx)
mean = mean_mx.asnumpy()
var_mx = mx.nd.array(var, dtype=dtype)
if not var_isSamples:
var_mx = add_sample_dimension(mx.nd, var_mx)
var = var_mx.asnumpy()
rv_mx = mx.nd.array(rv, dtype=dtype)
if not rv_isSamples:
rv_mx = add_sample_dimension(mx.nd, rv_mx)
rv = rv_mx.asnumpy()
from scipy.stats import multivariate_normal
isSamples_any = any([mean_isSamples, var_isSamples, rv_isSamples])
rv_shape = rv.shape[1:]
n_dim = 1 + len(
rv.shape) if isSamples_any and not rv_isSamples else len(rv.shape)
mean_np = numpy_array_reshape(mean, isSamples_any, n_dim)
var_np = numpy_array_reshape(var, isSamples_any, n_dim)
rv_np = numpy_array_reshape(rv, isSamples_any, n_dim)
rand = np.random.rand(num_samples, *rv_shape)
rand_gen = MockMXNetRandomGenerator(
mx.nd.array(rand.flatten(), dtype=dtype))
r = []
for s in range(len(rv_np)):
a = []
for i in range(len(rv_np[s])):
a.append(
multivariate_normal.logpdf(rv_np[s][i], mean_np[s][i],
var_np[s][i]))
r.append(a)
log_pdf_np = np.array(r)
normal = MultivariateNormal.define_variable(shape=rv_shape,
dtype=dtype,
rand_gen=rand_gen).factor
variables = {
normal.mean.uuid: mean_mx,
normal.covariance.uuid: var_mx,
normal.random_variable.uuid: rv_mx
}
log_pdf_rt = normal.log_pdf(F=mx.nd, variables=variables)
assert np.issubdtype(log_pdf_rt.dtype, dtype)
assert is_sampled_array(mx.nd, log_pdf_rt) == isSamples_any
if isSamples_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_eval(self, dtype, A, A_isSamples, B, B_isSamples, num_samples,
broadcastable):
np_isSamples = A_isSamples or B_isSamples
if np_isSamples:
if not A_isSamples:
A_np = np.expand_dims(A, axis=0)
else:
A_np = A
if not B_isSamples:
B_np = np.expand_dims(B, axis=0)
else:
B_np = B
res_np = np.einsum('ijk, ikh -> ijh', A_np, B_np)
else:
res_np = A.dot(B)
eval = self._make_gluon_function_evaluation(dtype, broadcastable)
A_mx = mx.nd.array(A, dtype=dtype)
if not A_isSamples:
A_mx = add_sample_dimension(mx.nd, A_mx)
B_mx = mx.nd.array(B, dtype=dtype)
if not B_isSamples:
B_mx = add_sample_dimension(mx.nd, B_mx)
variables = {eval.dot_input_0.uuid: A_mx, eval.dot_input_1.uuid: B_mx}
res_rt = eval.eval(F=mx.nd, variables=variables)
assert np_isSamples == is_sampled_array(mx.nd, res_rt)
assert np.allclose(res_np, res_rt.asnumpy())
def test_draw_samples(self, dtype, log_prob, log_prob_isSamples, rv_shape,
num_samples, one_hot_encoding, normalization):
n_dim = 1 + len(rv_shape)
log_prob_np = numpy_array_reshape(log_prob, log_prob_isSamples, n_dim)
rv_full_shape = (num_samples, ) + rv_shape
log_prob_np = np.broadcast_to(log_prob_np, rv_full_shape[:-1] + (3, ))
rand_np = np.random.randint(0, 3, size=rv_full_shape[:-1])
rand_gen = MockMXNetRandomGenerator(
mx.nd.array(rand_np.flatten(), dtype=dtype))
if one_hot_encoding:
rand_np = np.identity(3)[rand_np].reshape(*rv_full_shape)
else:
rand_np = np.expand_dims(rand_np, axis=-1)
rv_samples_np = rand_np
cat = Categorical.define_variable(0,
num_classes=3,
one_hot_encoding=one_hot_encoding,
normalization=normalization,
shape=rv_shape,
rand_gen=rand_gen,
dtype=dtype).factor
log_prob_mx = mx.nd.array(log_prob, dtype=dtype)
if not log_prob_isSamples:
log_prob_mx = add_sample_dimension(mx.nd, log_prob_mx)
variables = {cat.log_prob.uuid: log_prob_mx}
rv_samples_rt = cat.draw_samples(F=mx.nd,
variables=variables,
num_samples=num_samples)
assert is_sampled_array(mx.nd, rv_samples_rt)
assert get_num_samples(mx.nd, rv_samples_rt) == num_samples
assert np.allclose(rv_samples_np, rv_samples_rt.asnumpy())
def test_draw_samples_with_broadcast(self, dtype, mean, mean_isSamples,
var, var_isSamples, rv_shape,
num_samples):
mean_mx = mx.nd.array(mean, dtype=dtype)
if not mean_isSamples:
mean_mx = add_sample_dimension(mx.nd, mean_mx)
var_mx = mx.nd.array(var, dtype=dtype)
if not var_isSamples:
var_mx = add_sample_dimension(mx.nd, var_mx)
var = var_mx.asnumpy()
isSamples_any = any([mean_isSamples, var_isSamples])
rand = np.random.rand(num_samples, *rv_shape)
rand_gen = MockMXNetRandomGenerator(
mx.nd.array(rand.flatten(), dtype=dtype))
rv_samples_np = mean + np.matmul(np.linalg.cholesky(var),
np.expand_dims(rand, axis=-1)).sum(-1)
normal = MultivariateNormal.define_variable(shape=rv_shape,
dtype=dtype,
rand_gen=rand_gen).factor
variables = {normal.mean.uuid: mean_mx, normal.covariance.uuid: var_mx}
draw_samples_rt = normal.draw_samples(F=mx.nd, variables=variables)
assert np.issubdtype(draw_samples_rt.dtype, dtype)
assert is_sampled_array(mx.nd, draw_samples_rt) == isSamples_any
if isSamples_any:
assert get_num_samples(
mx.nd, draw_samples_rt) == num_samples, (get_num_samples(
mx.nd, draw_samples_rt), num_samples)
def test_draw_samples_with_broadcast(self, dtype_dof, dtype, degrees_of_freedom, scale, scale_is_samples, rv_shape,
num_samples):
degrees_of_freedom_mx = mx.nd.array([degrees_of_freedom], dtype=dtype_dof)
scale_mx = mx.nd.array(scale, dtype=dtype)
if not scale_is_samples:
scale_mx = add_sample_dimension(mx.nd, scale_mx)
rand = np.random.rand(num_samples, *rv_shape)
rand_gen = MockMXNetRandomGenerator(mx.nd.array(rand.flatten(), dtype=dtype))
reps = 1000
mins = np.zeros(reps)
maxs = np.zeros(reps)
for i in range(reps):
rvs = wishart.rvs(df=degrees_of_freedom, scale=scale, size=num_samples)
mins[i] = rvs.min()
maxs[i] = rvs.max()
# rv_samples_np = wishart.rvs(df=degrees_of_freedom, scale=scale, size=num_samples)
var = Wishart.define_variable(shape=rv_shape, dtype=dtype, rand_gen=rand_gen).factor
variables = {var.degrees_of_freedom.uuid: degrees_of_freedom_mx, var.scale.uuid: scale_mx}
draw_samples_rt = var.draw_samples(F=mx.nd, variables=variables)
assert np.issubdtype(draw_samples_rt.dtype, dtype)
assert is_sampled_array(mx.nd, draw_samples_rt) == scale_is_samples
if scale_is_samples:
assert get_num_samples(mx.nd, draw_samples_rt) == num_samples, (get_num_samples(mx.nd, draw_samples_rt),
num_samples)
assert mins.min() < draw_samples_rt.asnumpy().min()
assert maxs.max() > draw_samples_rt.asnumpy().max()
def test_clone_gp(self, dtype, X, X_isSamples, rbf_lengthscale,
rbf_lengthscale_isSamples, rbf_variance,
rbf_variance_isSamples, rv, rv_isSamples, num_samples):
X_mx = prepare_mxnet_array(X, X_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)
m = Model()
m.X_var = Variable(shape=(5, 2))
m.Y = GaussianProcess.define_variable(X=m.X_var,
kernel=rbf,
shape=rv_shape,
dtype=dtype)
gp = m.clone()[0].Y.factor
variables = {
gp.X.uuid: X_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
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)
log_pdf_np.append(
multivariate_normal.logpdf(rv_i[:, 0], mean=None, cov=K_np))
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 is_sampled_array(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_mean_variance(self, dtype, mean, mean_isSamples,
variance, variance_isSamples, rv_shape,
num_samples):
n_dim = 1 + len(rv_shape)
out_shape = (num_samples, ) + rv_shape
mean_np = mx.nd.array(np.broadcast_to(numpy_array_reshape(
mean, mean_isSamples, n_dim),
shape=out_shape),
dtype=dtype)
variance_np = mx.nd.array(np.broadcast_to(numpy_array_reshape(
variance, variance_isSamples, n_dim),
shape=out_shape),
dtype=dtype)
gamma = GammaMeanVariance.define_variable(shape=rv_shape,
dtype=dtype).factor
mean_mx = mx.nd.array(mean, dtype=dtype)
if not mean_isSamples:
mean_mx = add_sample_dimension(mx.nd, mean_mx)
variance_mx = mx.nd.array(variance, dtype=dtype)
if not variance_isSamples:
variance_mx = add_sample_dimension(mx.nd, variance_mx)
variables = {
gamma.mean.uuid: mean_mx,
gamma.variance.uuid: variance_mx
}
mx.random.seed(0)
rv_samples_rt = gamma.draw_samples(F=mx.nd,
variables=variables,
num_samples=num_samples)
mx.random.seed(0)
beta_np = mean_np / variance_np
alpha_np = mean_np * beta_np
rv_samples_mx = mx.nd.random.gamma(alpha=alpha_np,
beta=beta_np,
dtype=dtype)
assert np.issubdtype(rv_samples_rt.dtype, dtype)
assert is_sampled_array(mx.nd, rv_samples_rt)
assert get_num_samples(mx.nd, rv_samples_rt) == num_samples
if np.issubdtype(dtype, np.float64):
rtol, atol = 1e-7, 1e-10
else:
rtol, atol = 1e-4, 1e-5
assert np.allclose(rv_samples_mx.asnumpy(),
rv_samples_rt.asnumpy(),
rtol=rtol,
atol=atol)
def test_log_pdf_mean_variance(self, dtype, mean, mean_isSamples, variance,
variance_isSamples, rv, rv_isSamples,
num_samples):
import scipy as sp
isSamples_any = any([mean_isSamples, variance_isSamples, rv_isSamples])
rv_shape = rv.shape[1:] if rv_isSamples else rv.shape
n_dim = 1 + len(
rv.shape) if isSamples_any and not rv_isSamples else len(rv.shape)
mean_np = numpy_array_reshape(mean, mean_isSamples, n_dim)
variance_np = numpy_array_reshape(variance, variance_isSamples, n_dim)
rv_np = numpy_array_reshape(rv, rv_isSamples, n_dim)
beta_np = mean_np / variance_np
alpha_np = mean_np * beta_np
log_pdf_np = sp.stats.gamma.logpdf(rv_np,
a=alpha_np,
loc=0,
scale=1. / beta_np)
mean_mx = mx.nd.array(mean, dtype=dtype)
if not mean_isSamples:
mean_mx = add_sample_dimension(mx.nd, mean_mx)
variance_mx = mx.nd.array(variance, dtype=dtype)
if not variance_isSamples:
variance_mx = add_sample_dimension(mx.nd, variance_mx)
rv_mx = mx.nd.array(rv, dtype=dtype)
if not rv_isSamples:
rv_mx = add_sample_dimension(mx.nd, rv_mx)
gamma = GammaMeanVariance.define_variable(mean=mean_mx,
variance=variance_mx,
shape=rv_shape,
dtype=dtype).factor
variables = {
gamma.mean.uuid: mean_mx,
gamma.variance.uuid: variance_mx,
gamma.random_variable.uuid: rv_mx
}
log_pdf_rt = gamma.log_pdf(F=mx.nd, variables=variables)
assert np.issubdtype(log_pdf_rt.dtype, dtype)
assert is_sampled_array(mx.nd, log_pdf_rt) == isSamples_any
if isSamples_any:
assert get_num_samples(mx.nd, log_pdf_rt) == num_samples
if np.issubdtype(dtype, np.float64):
rtol, atol = 1e-7, 1e-10
else:
rtol, atol = 1e-4, 1e-5
assert np.allclose(log_pdf_np,
log_pdf_rt.asnumpy(),
rtol=rtol,
atol=atol)
def test_log_pdf(self, dtype_dof, dtype, degrees_of_freedom, random_state,
scale_is_samples, rv_is_samples, num_data_points, num_samples, broadcast):
# Create positive semi-definite matrices
rv = make_spd_matrices_4d(num_samples, num_data_points, degrees_of_freedom, random_state=random_state)
if broadcast:
scale = make_spd_matrix(n_dim=degrees_of_freedom, random_state=random_state)
else:
scale = make_spd_matrices_4d(num_samples, num_data_points, degrees_of_freedom, random_state=random_state)
degrees_of_freedom_mx = mx.nd.array([degrees_of_freedom], dtype=dtype_dof)
degrees_of_freedom = degrees_of_freedom_mx.asnumpy()[0] # ensures the correct dtype
scale_mx = mx.nd.array(scale, dtype=dtype)
if not scale_is_samples:
scale_mx = add_sample_dimension(mx.nd, scale_mx)
scale = scale_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 = scale_is_samples or rv_is_samples
if broadcast:
scale_np = np.broadcast_to(scale, rv.shape)
else:
n_dim = 1 + len(rv.shape) if is_samples_any and not rv_is_samples else len(rv.shape)
scale_np = numpy_array_reshape(scale, is_samples_any, n_dim)
rv_np = numpy_array_reshape(rv, is_samples_any, degrees_of_freedom)
r = []
for s in range(num_samples):
a = []
for i in range(num_data_points):
a.append(wishart.logpdf(rv_np[s][i], df=degrees_of_freedom, scale=scale_np[s][i]))
r.append(a)
log_pdf_np = np.array(r)
var = Wishart.define_variable(shape=rv.shape[1:], dtype=dtype, rand_gen=None).factor
variables = {var.degrees_of_freedom.uuid: degrees_of_freedom_mx, var.scale.uuid: scale_mx,
var.random_variable.uuid: rv_mx}
log_pdf_rt = var.log_pdf(F=mx.nd, variables=variables)
assert np.issubdtype(log_pdf_rt.dtype, dtype)
assert is_sampled_array(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_draw_samples(self, dtype, a_shape, a_is_samples, b_shape,
b_is_samples, rv_shape, num_samples):
# Note: Tests above have been commented as they are very slow to run.
# Note: Moved random number generation to here as the seed wasn't set if used above
a = np.random.uniform(0.5, 2, size=a_shape)
b = np.random.uniform(0.5, 2, size=b_shape)
n_dim = 1 + len(rv_shape)
a_np = numpy_array_reshape(a, a_is_samples, n_dim)
b_np = numpy_array_reshape(b, b_is_samples, n_dim)
rv_samples_np = np.random.beta(a_np,
b_np,
size=(num_samples, ) + rv_shape)
var = Beta.define_variable(shape=rv_shape, dtype=dtype,
rand_gen=None).factor
a_mx = mx.nd.array(a, dtype=dtype)
if not a_is_samples:
a_mx = add_sample_dimension(mx.nd, a_mx)
b_mx = mx.nd.array(b, dtype=dtype)
if not b_is_samples:
b_mx = add_sample_dimension(mx.nd, b_mx)
variables = {var.a.uuid: a_mx, var.b.uuid: b_mx}
rv_samples_rt = var.draw_samples(F=mx.nd,
variables=variables,
num_samples=num_samples)
assert np.issubdtype(rv_samples_rt.dtype, dtype)
assert is_sampled_array(mx.nd, rv_samples_rt)
assert get_num_samples(mx.nd, rv_samples_rt) == num_samples
rtol, atol = 1e-1, 1e-1
from itertools import product
fits_np = [
beta.fit(rv_samples_np[:, i, j])[0:2]
for i, j in (product(*map(range, rv_shape)))
]
fits_rt = [
beta.fit(rv_samples_rt.asnumpy()[:, i, j])[0:2]
for i, j in (product(*map(range, rv_shape)))
]
assert np.allclose(fits_np, fits_rt, rtol=rtol, atol=atol)
def test_draw_samples_with_broadcast_no_numpy_verification(self, dtype_dof, dtype, degrees_of_freedom, scale,
scale_is_samples, rv_shape, num_samples):
degrees_of_freedom_mx = mx.nd.array([degrees_of_freedom], dtype=dtype_dof)
scale_mx = mx.nd.array(scale, dtype=dtype)
if not scale_is_samples:
scale_mx = add_sample_dimension(mx.nd, scale_mx)
rand = np.random.rand(num_samples, *rv_shape)
rand_gen = MockMXNetRandomGenerator(mx.nd.array(rand.flatten(), dtype=dtype))
var = Wishart.define_variable(shape=rv_shape, dtype=dtype, rand_gen=rand_gen).factor
variables = {var.degrees_of_freedom.uuid: degrees_of_freedom_mx, var.scale.uuid: scale_mx}
draw_samples_rt = var.draw_samples(F=mx.nd, variables=variables, num_samples=num_samples)
assert np.issubdtype(draw_samples_rt.dtype, dtype)
assert is_sampled_array(mx.nd, draw_samples_rt)
def test_eval_gluon_parameters(self, dtype, A, A_isSamples, B, B_isSamples,
C, C_isSamples, num_samples, broadcastable):
np_isSamples = A_isSamples or B_isSamples
if np_isSamples:
if not A_isSamples:
A_np = np.expand_dims(A, axis=0)
else:
A_np = A
if not B_isSamples:
B_np = np.expand_dims(B, axis=0)
else:
B_np = B
res_np = np.einsum('ijk, ikh -> ijh', A_np, B_np)
if C_isSamples:
res_np += C[:, :, None]
else:
res_np += C
else:
res_np = A.dot(B)
if C_isSamples:
res_np = res_np[None, :, :] + C[:, :, None]
else:
res_np += C
np_isSamples = np_isSamples or C_isSamples
eval = self._make_gluon_function_evaluation_rand_param(
dtype, broadcastable)
A_mx = mx.nd.array(A, dtype=dtype)
if not A_isSamples:
A_mx = add_sample_dimension(mx.nd, A_mx)
B_mx = mx.nd.array(B, dtype=dtype)
if not B_isSamples:
B_mx = add_sample_dimension(mx.nd, B_mx)
C_mx = mx.nd.array(C, dtype=dtype)
if not C_isSamples:
C_mx = add_sample_dimension(mx.nd, C_mx)
variables = {
eval.dot_input_0.uuid: A_mx,
eval.dot_input_1.uuid: B_mx,
eval.dot_const.uuid: C_mx
}
res_rt = eval.eval(F=mx.nd, variables=variables)
assert np_isSamples == is_sampled_array(mx.nd, res_rt)
assert np.allclose(res_np, res_rt.asnumpy())
def test_log_pdf(self, dtype, alpha, alpha_isSamples, beta, beta_isSamples,
rv, rv_isSamples, num_samples):
import scipy as sp
isSamples_any = any([alpha_isSamples, beta_isSamples, rv_isSamples])
rv_shape = rv.shape[1:] if rv_isSamples else rv.shape
n_dim = 1 + len(
rv.shape) if isSamples_any and not rv_isSamples else len(rv.shape)
alpha_np = numpy_array_reshape(alpha, alpha_isSamples, n_dim)
beta_np = numpy_array_reshape(beta, beta_isSamples, n_dim)
rv_np = numpy_array_reshape(rv, rv_isSamples, n_dim)
log_pdf_np = sp.stats.gamma.logpdf(rv_np,
a=alpha_np,
loc=0,
scale=1. / beta_np)
gamma = Gamma.define_variable(shape=rv_shape, dtype=dtype).factor
alpha_mx = mx.nd.array(alpha, dtype=dtype)
if not alpha_isSamples:
alpha_mx = add_sample_dimension(mx.nd, alpha_mx)
beta_mx = mx.nd.array(beta, dtype=dtype)
if not beta_isSamples:
beta_mx = add_sample_dimension(mx.nd, beta_mx)
rv_mx = mx.nd.array(rv, dtype=dtype)
if not rv_isSamples:
rv_mx = add_sample_dimension(mx.nd, rv_mx)
variables = {
gamma.alpha.uuid: alpha_mx,
gamma.beta.uuid: beta_mx,
gamma.random_variable.uuid: rv_mx
}
log_pdf_rt = gamma.log_pdf(F=mx.nd, variables=variables)
assert np.issubdtype(log_pdf_rt.dtype, dtype)
assert is_sampled_array(mx.nd, log_pdf_rt) == isSamples_any
if isSamples_any:
assert get_num_samples(mx.nd, log_pdf_rt) == num_samples
if np.issubdtype(dtype, np.float64):
rtol, atol = 1e-7, 1e-10
else:
rtol, atol = 1e-4, 1e-5
assert np.allclose(log_pdf_np,
log_pdf_rt.asnumpy(),
rtol=rtol,
atol=atol)
def test_draw_samples(self, dtype, alpha, alpha_isSamples, beta,
beta_isSamples, rv_shape, num_samples):
n_dim = 1 + len(rv_shape)
out_shape = (num_samples, ) + rv_shape
alpha_np = mx.nd.array(np.broadcast_to(numpy_array_reshape(
alpha, alpha_isSamples, n_dim),
shape=out_shape),
dtype=dtype)
beta_np = mx.nd.array(np.broadcast_to(numpy_array_reshape(
beta, beta_isSamples, n_dim),
shape=out_shape),
dtype=dtype)
gamma = Gamma.define_variable(shape=rv_shape, dtype=dtype).factor
alpha_mx = mx.nd.array(alpha, dtype=dtype)
if not alpha_isSamples:
alpha_mx = add_sample_dimension(mx.nd, alpha_mx)
beta_mx = mx.nd.array(beta, dtype=dtype)
if not beta_isSamples:
beta_mx = add_sample_dimension(mx.nd, beta_mx)
variables = {gamma.alpha.uuid: alpha_mx, gamma.beta.uuid: beta_mx}
mx.random.seed(0)
rv_samples_rt = gamma.draw_samples(F=mx.nd,
variables=variables,
num_samples=num_samples)
mx.random.seed(0)
rv_samples_mx = mx.nd.random.gamma(alpha=alpha_np,
beta=beta_np,
dtype=dtype)
assert np.issubdtype(rv_samples_rt.dtype, dtype)
assert is_sampled_array(mx.nd, rv_samples_rt)
assert get_num_samples(mx.nd, rv_samples_rt) == num_samples
if np.issubdtype(dtype, np.float64):
rtol, atol = 1e-7, 1e-10
else:
rtol, atol = 1e-4, 1e-5
assert np.allclose(rv_samples_mx.asnumpy(),
rv_samples_rt.asnumpy(),
rtol=rtol,
atol=atol)
def test_log_pdf(self, dtype, a, a_is_samples, b, b_is_samples, rv,
rv_is_samples, num_samples):
is_samples_any = any([a_is_samples, b_is_samples, rv_is_samples])
rv_shape = rv.shape[1:] if rv_is_samples else rv.shape
n_dim = 1 + len(
rv.shape) if is_samples_any and not rv_is_samples else len(
rv.shape)
a_np = numpy_array_reshape(a, a_is_samples, n_dim)
b_np = numpy_array_reshape(b, b_is_samples, n_dim)
rv_np = numpy_array_reshape(rv, rv_is_samples, n_dim)
log_pdf_np = beta.logpdf(rv_np, a_np, b_np)
var = Beta.define_variable(shape=rv_shape, dtype=dtype).factor
a_mx = mx.nd.array(a, dtype=dtype)
if not a_is_samples:
a_mx = add_sample_dimension(mx.nd, a_mx)
b_mx = mx.nd.array(b, dtype=dtype)
if not b_is_samples:
b_mx = add_sample_dimension(mx.nd, b_mx)
rv_mx = mx.nd.array(rv, dtype=dtype)
if not rv_is_samples:
rv_mx = add_sample_dimension(mx.nd, rv_mx)
variables = {
var.a.uuid: a_mx,
var.b.uuid: b_mx,
var.random_variable.uuid: rv_mx
}
log_pdf_rt = var.log_pdf(F=mx.nd, variables=variables)
assert np.issubdtype(log_pdf_rt.dtype, dtype)
assert is_sampled_array(mx.nd, log_pdf_rt) == is_samples_any
if is_samples_any:
assert get_num_samples(mx.nd, log_pdf_rt) == num_samples
if np.issubdtype(dtype, np.float64):
rtol, atol = 1e-7, 1e-10
else:
rtol, atol = 1e-4, 1e-5
assert np.allclose(log_pdf_np,
log_pdf_rt.asnumpy(),
rtol=rtol,
atol=atol)
def test_draw_samples(self):
np.random.seed(0)
samples_1_np = np.random.randn(5)
samples_1 = mx.nd.array(samples_1_np)
samples_2_np = np.random.randn(50)
samples_2 = mx.nd.array(samples_2_np)
m = Model()
v = Variable(shape=(1, ))
m.v2 = Normal.define_variable(
mean=v,
variance=mx.nd.array([1]),
rand_gen=MockMXNetRandomGenerator(samples_1))
m.v3 = Normal.define_variable(
mean=m.v2,
variance=mx.nd.array([0.1]),
shape=(10, ),
rand_gen=MockMXNetRandomGenerator(samples_2))
np.random.seed(0)
v_np = np.random.rand(1)
v_mx = mx.nd.array(v_np)
v_rt = add_sample_dimension(mx.nd, v_mx)
variance = m.v2.factor.variance
variance2 = m.v3.factor.variance
variance_rt = add_sample_dimension(mx.nd, variance.constant)
variance2_rt = add_sample_dimension(mx.nd, variance2.constant)
samples = m.draw_samples(F=mx.nd,
num_samples=5,
targets=[m.v3.uuid],
variables={
v.uuid: v_rt,
variance.uuid: variance_rt,
variance2.uuid: variance2_rt
})[m.v3.uuid]
samples_np = v_np + samples_1_np[:, None] + np.sqrt(
0.1) * samples_2_np.reshape(5, 10)
assert is_sampled_array(mx.nd, samples) and get_num_samples(
mx.nd, samples) == 5
assert np.allclose(samples.asnumpy(), samples_np)
def test_log_pdf(self, dtype, mean, mean_isSamples, var, var_isSamples, rv,
rv_isSamples, num_samples):
from scipy.stats import norm
isSamples_any = any([mean_isSamples, var_isSamples, rv_isSamples])
rv_shape = rv.shape[1:] if rv_isSamples else rv.shape
n_dim = 1 + len(
rv.shape) if isSamples_any and not rv_isSamples else len(rv.shape)
mean_np = numpy_array_reshape(mean, mean_isSamples, n_dim)
var_np = numpy_array_reshape(var, var_isSamples, n_dim)
rv_np = numpy_array_reshape(rv, rv_isSamples, n_dim)
log_pdf_np = norm.logpdf(rv_np, mean_np, np.sqrt(var_np))
normal = Normal.define_variable(shape=rv_shape, dtype=dtype).factor
mean_mx = mx.nd.array(mean, dtype=dtype)
if not mean_isSamples:
mean_mx = add_sample_dimension(mx.nd, mean_mx)
var_mx = mx.nd.array(var, dtype=dtype)
if not var_isSamples:
var_mx = add_sample_dimension(mx.nd, var_mx)
rv_mx = mx.nd.array(rv, dtype=dtype)
if not rv_isSamples:
rv_mx = add_sample_dimension(mx.nd, rv_mx)
variables = {
normal.mean.uuid: mean_mx,
normal.variance.uuid: var_mx,
normal.random_variable.uuid: rv_mx
}
log_pdf_rt = normal.log_pdf(F=mx.nd, variables=variables)
assert np.issubdtype(log_pdf_rt.dtype, dtype)
assert is_sampled_array(mx.nd, log_pdf_rt) == isSamples_any
if isSamples_any:
assert get_num_samples(mx.nd, log_pdf_rt) == num_samples
if np.issubdtype(dtype, np.float64):
rtol, atol = 1e-7, 1e-10
else:
rtol, atol = 1e-4, 1e-5
assert np.allclose(log_pdf_np,
log_pdf_rt.asnumpy(),
rtol=rtol,
atol=atol)
def test_draw_samples(self, dtype, mean, mean_isSamples, var,
var_isSamples, rv_shape, num_samples):
n_dim = 1 + len(rv_shape)
mean_np = numpy_array_reshape(mean, mean_isSamples, n_dim)
var_np = numpy_array_reshape(var, var_isSamples, n_dim)
rand = np.random.randn(num_samples, *rv_shape)
rv_samples_np = mean_np + rand * np.sqrt(var_np)
rand_gen = MockMXNetRandomGenerator(
mx.nd.array(rand.flatten(), dtype=dtype))
normal = Normal.define_variable(shape=rv_shape,
dtype=dtype,
rand_gen=rand_gen).factor
mean_mx = mx.nd.array(mean, dtype=dtype)
if not mean_isSamples:
mean_mx = add_sample_dimension(mx.nd, mean_mx)
var_mx = mx.nd.array(var, dtype=dtype)
if not var_isSamples:
var_mx = add_sample_dimension(mx.nd, var_mx)
variables = {normal.mean.uuid: mean_mx, normal.variance.uuid: var_mx}
rv_samples_rt = normal.draw_samples(F=mx.nd,
variables=variables,
num_samples=num_samples)
assert np.issubdtype(rv_samples_rt.dtype, dtype)
assert is_sampled_array(mx.nd, rv_samples_rt)
assert get_num_samples(mx.nd, rv_samples_rt) == num_samples
if np.issubdtype(dtype, np.float64):
rtol, atol = 1e-7, 1e-10
else:
rtol, atol = 1e-4, 1e-5
assert np.allclose(rv_samples_np,
rv_samples_rt.asnumpy(),
rtol=rtol,
atol=atol)
def test_draw_samples_no_broadcast(self, dtype, mean, mean_isSamples, var,
var_isSamples, rv_shape, num_samples):
mean_mx = mx.nd.array(mean, dtype=dtype)
if not mean_isSamples:
mean_mx = add_sample_dimension(mx.nd, mean_mx)
var_mx = mx.nd.array(var, dtype=dtype)
if not var_isSamples:
var_mx = add_sample_dimension(mx.nd, var_mx)
var = var_mx.asnumpy()
# var = (var[:,:,:,None]*var[:,None,:,:]).sum(-2)+np.eye(2)
# var_mx = mx.nd.array(var, dtype=dtype)
isSamples_any = any([mean_isSamples, var_isSamples])
# n_dim = 1 + len(rv.shape) if isSamples_any else len(rv.shape)
# mean_np = numpy_array_reshape(mean, mean_isSamples, n_dim)
# var_np = numpy_array_reshape(var, var_isSamples, n_dim)
rand = np.random.rand(num_samples, *rv_shape)
rand_gen = MockMXNetRandomGenerator(
mx.nd.array(rand.flatten(), dtype=dtype))
rand_exp = np.expand_dims(rand, axis=-1)
lmat = np.linalg.cholesky(var)
temp1 = np.matmul(lmat, rand_exp).sum(-1)
rv_samples_np = mean + temp1
normal = MultivariateNormal.define_variable(shape=rv_shape,
dtype=dtype,
rand_gen=rand_gen).factor
variables = {normal.mean.uuid: mean_mx, normal.covariance.uuid: var_mx}
draw_samples_rt = normal.draw_samples(F=mx.nd, variables=variables)
assert np.issubdtype(draw_samples_rt.dtype, dtype)
assert is_sampled_array(mx.nd, draw_samples_rt) == isSamples_any
if isSamples_any:
assert get_num_samples(
mx.nd, draw_samples_rt) == num_samples, (get_num_samples(
mx.nd, draw_samples_rt), num_samples)
def test_draw_samples_no_broadcast(self, dtype_dof, dtype, degrees_of_freedom, scale,
scale_is_samples, rv_shape, num_samples):
degrees_of_freedom_mx = mx.nd.array([degrees_of_freedom], dtype=dtype_dof)
scale_mx = mx.nd.array(scale, dtype=dtype)
if not scale_is_samples:
scale_mx = add_sample_dimension(mx.nd, scale_mx)
# n_dim = 1 + len(rv.shape) if isSamples_any else len(rv.shape)
rand = np.random.rand(num_samples, *rv_shape)
rand_gen = MockMXNetRandomGenerator(mx.nd.array(rand.flatten(), dtype=dtype))
# rand_exp = np.expand_dims(rand, axis=-1)
# lmat = np.linalg.cholesky(var)
# temp1 = np.matmul(lmat, rand_exp).sum(-1)
# rv_samples_np = mean + temp1
var = Wishart.define_variable(shape=rv_shape, dtype=dtype, rand_gen=rand_gen).factor
variables = {var.degrees_of_freedom.uuid: degrees_of_freedom_mx, var.scale.uuid: scale_mx}
draw_samples_rt = var.draw_samples(F=mx.nd, variables=variables, num_samples=num_samples)
assert np.issubdtype(draw_samples_rt.dtype, dtype)
assert is_sampled_array(mx.nd, draw_samples_rt)
assert get_num_samples(mx.nd, draw_samples_rt) == num_samples, (get_num_samples(mx.nd, draw_samples_rt),
num_samples)
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 is_sampled_array(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)
