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(self, dtype, low, low_is_samples, high,
high_is_samples, rv_shape, num_samples):
n_dim = 1 + len(rv_shape)
low_np = numpy_array_reshape(low, low_is_samples, n_dim)
high_np = numpy_array_reshape(high, high_is_samples, n_dim)
rv_samples_np = np.random.uniform(low=low_np, high=high_np, size=(num_samples,) + rv_shape)
rand_gen = MockMXNetRandomGenerator(mx.nd.array(rv_samples_np.flatten(), dtype=dtype))
var = Uniform.define_variable(shape=rv_shape, dtype=dtype, rand_gen=rand_gen).factor
low_mx = mx.nd.array(low, dtype=dtype)
if not low_is_samples:
low_mx = add_sample_dimension(mx.nd, low_mx)
high_mx = mx.nd.array(high, dtype=dtype)
if not high_is_samples:
high_mx = add_sample_dimension(mx.nd, high_mx)
variables = {var.low.uuid: low_mx, var.high.uuid: high_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 array_has_samples(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(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})[0]
samples_np = v_np + samples_1_np[:, None] + np.sqrt(0.1)*samples_2_np.reshape(5,10)
assert array_has_samples(mx.nd, samples) and get_num_samples(mx.nd, samples)==5
assert np.allclose(samples.asnumpy(), samples_np)
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 array_has_samples(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_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_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 array_has_samples(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_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_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)
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 array_has_samples(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_draw_samples(self, dtype, mean, mean_is_samples, precision,
precision_is_samples, rv_shape, num_samples):
n_dim = 1 + len(rv_shape)
mean_np = numpy_array_reshape(mean, mean_is_samples, n_dim)
precision_np = numpy_array_reshape(precision, precision_is_samples, n_dim)
rand = np.random.randn(num_samples, *rv_shape)
rv_samples_np = mean_np + rand * np.power(precision_np, -0.5)
rand_gen = MockMXNetRandomGenerator(mx.nd.array(rand.flatten(), dtype=dtype))
var = NormalMeanPrecision.define_variable(shape=rv_shape, dtype=dtype,
rand_gen=rand_gen).factor
mean_mx = mx.nd.array(mean, dtype=dtype)
if not mean_is_samples:
mean_mx = add_sample_dimension(mx.nd, mean_mx)
precision_mx = mx.nd.array(precision, dtype=dtype)
if not precision_is_samples:
precision_mx = add_sample_dimension(mx.nd, precision_mx)
variables = {var.mean.uuid: mean_mx, var.precision.uuid: precision_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 array_has_samples(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_is_samples, precision,
precision_is_samples, rv_shape, num_samples):
mean_mx = mx.nd.array(mean, dtype=dtype)
if not mean_is_samples:
mean_mx = add_sample_dimension(mx.nd, mean_mx)
precision_mx = mx.nd.array(precision, dtype=dtype)
if not precision_is_samples:
precision_mx = add_sample_dimension(mx.nd, precision_mx)
# precision = precision_mx.asnumpy()
# n_dim = 1 + len(rv.shape) if is_samples_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(precision)
# temp1 = np.matmul(lmat, rand_exp).sum(-1)
# rv_samples_np = mean + temp1
normal = MultivariateNormalMeanPrecision.define_variable(shape=rv_shape, dtype=dtype, rand_gen=rand_gen).factor
variables = {normal.mean.uuid: mean_mx, normal.precision.uuid: precision_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 array_has_samples(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_draw_samples_w_mean(self):
D, X, Y, noise_var, lengthscale, variance = self.gen_data()
dtype = 'float64'
rand_gen = MockMXNetRandomGenerator(
mx.nd.array(np.random.rand(20 * D), dtype=dtype))
m, net = self.gen_mxfusion_model_w_mean(dtype, D, noise_var,
lengthscale, variance,
rand_gen)
observed = [m.X]
infr = Inference(ForwardSamplingAlgorithm(m,
observed,
num_samples=2,
target_variables=[m.Y]),
dtype=dtype)
samples = infr.run(X=mx.nd.array(X, dtype=dtype),
Y=mx.nd.array(Y, dtype=dtype))[0].asnumpy()
kern = RBF(3, True, name='rbf', dtype=dtype) + White(3, dtype=dtype)
X_var = Variable(shape=(10, 3))
mean_func = MXFusionGluonFunction(net,
num_outputs=1,
broadcastable=True)
mean_var = mean_func(X_var)
gp = GaussianProcess.define_variable(X=X_var,
kernel=kern,
mean=mean_var,
shape=(10, D),
dtype=dtype,
rand_gen=rand_gen).factor
variables = {
gp.X.uuid:
mx.nd.expand_dims(mx.nd.array(X, dtype=dtype), axis=0),
gp.add_rbf_lengthscale.uuid:
mx.nd.expand_dims(mx.nd.array(lengthscale, dtype=dtype), axis=0),
gp.add_rbf_variance.uuid:
mx.nd.expand_dims(mx.nd.array(variance, dtype=dtype), axis=0),
gp.add_white_variance.uuid:
mx.nd.expand_dims(mx.nd.array(noise_var, dtype=dtype), axis=0),
mean_var.uuid:
mx.nd.expand_dims(net(mx.nd.array(X, dtype=dtype)), axis=0)
}
samples_2 = gp.draw_samples(F=mx.nd,
variables=variables,
num_samples=2).asnumpy()
assert np.allclose(samples, samples_2), (samples, samples_2)
def test_draw_samples(self, dtype, X, X_isSamples, rbf_lengthscale,
rbf_lengthscale_isSamples, rbf_variance,
rbf_variance_isSamples, rv_shape, 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)
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))
gp = GaussianProcess.define_variable(X=X_var,
kernel=rbf,
shape=rv_shape,
dtype=dtype,
rand_gen=rand_gen).factor
variables = {
gp.X.uuid: X_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
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)
L_np = np.linalg.cholesky(K_np)
sample_np = L_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)
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 test_log_pdf_with_broadcast(self, dtype, mean, mean_is_samples, precision, precision_is_samples,
rv, rv_is_samples, num_samples):
mean_mx = mx.nd.array(mean, dtype=dtype)
if not mean_is_samples:
mean_mx = add_sample_dimension(mx.nd, mean_mx)
mean = mean_mx.asnumpy()
precision_mx = mx.nd.array(precision, dtype=dtype)
if not precision_is_samples:
precision_mx = add_sample_dimension(mx.nd, precision_mx)
precision = precision_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 = any([mean_is_samples, precision_is_samples, 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)
mean_np = np.broadcast_to(mean, (5, 3, 2))
precision_np = np.broadcast_to(precision, (5, 3, 2, 2))
rv_np = numpy_array_reshape(rv, is_samples_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], np.linalg.inv(precision_np[s][i])))
r.append(a)
log_pdf_np = np.array(r)
normal = MultivariateNormalMeanPrecision.define_variable(shape=rv_shape, dtype=dtype, rand_gen=rand_gen).factor
variables = {
normal.mean.uuid: mean_mx, normal.precision.uuid: precision_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 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_draw_samples(self, dtype, prob_true, prob_true_is_samples,
rv_shape, num_samples):
rv_full_shape = (num_samples, ) + rv_shape
rand_np = np.random.normal(size=rv_full_shape) > 0
rand_gen = MockMXNetRandomGenerator(
mx.nd.array(rand_np.flatten(), dtype=dtype))
rv_samples_np = rand_np
var = Bernoulli.define_variable(0,
shape=rv_shape,
rand_gen=rand_gen,
dtype=dtype).factor
prob_true_mx = mx.nd.array(prob_true, dtype=dtype)
if not prob_true_is_samples:
prob_true_mx = add_sample_dimension(mx.nd, prob_true_mx)
variables = {var.prob_true.uuid: prob_true_mx}
rv_samples_rt = var.draw_samples(F=mx.nd,
variables=variables,
num_samples=num_samples)
assert array_has_samples(mx.nd, rv_samples_rt)
assert get_num_samples(mx.nd, rv_samples_rt) == num_samples
assert np.array_equal(rv_samples_np,
rv_samples_rt.asnumpy().astype(bool))
# Also make sure the non-mock sampler works
rand_gen = None
var = Bernoulli.define_variable(0,
shape=rv_shape,
rand_gen=rand_gen,
dtype=dtype).factor
prob_true_mx = mx.nd.array(prob_true, dtype=dtype)
if not prob_true_is_samples:
prob_true_mx = add_sample_dimension(mx.nd, prob_true_mx)
variables = {var.prob_true.uuid: prob_true_mx}
rv_samples_rt = var.draw_samples(F=mx.nd,
variables=variables,
num_samples=num_samples)
assert array_has_samples(mx.nd, rv_samples_rt)
assert get_num_samples(mx.nd, rv_samples_rt) == num_samples
assert rv_samples_rt.dtype == dtype
def test_draw_samples_with_broadcast_no_numpy_verification(self, dtype, mean, mean_is_samples, precision,
precision_is_samples, rv_shape, num_samples):
mean_mx = mx.nd.array(mean, dtype=dtype)
if not mean_is_samples:
mean_mx = add_sample_dimension(mx.nd, mean_mx)
precision_mx = mx.nd.array(precision, dtype=dtype)
if not precision_is_samples:
precision_mx = add_sample_dimension(mx.nd, precision_mx)
# precision = precision_mx.asnumpy()
rand = np.random.rand(num_samples, *rv_shape)
rand_gen = MockMXNetRandomGenerator(mx.nd.array(rand.flatten(), dtype=dtype))
normal = MultivariateNormalMeanPrecision.define_variable(shape=rv_shape, dtype=dtype, rand_gen=rand_gen).factor
variables = {normal.mean.uuid: mean_mx, normal.precision.uuid: precision_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 array_has_samples(mx.nd, draw_samples_rt)
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_draw_samples(self, dtype, location, location_is_samples, scale,
scale_is_samples, rv_shape, num_samples):
n_dim = 1 + len(rv_shape)
location_np = numpy_array_reshape(location, location_is_samples, n_dim)
scale_np = numpy_array_reshape(scale, scale_is_samples, n_dim)
rand = np.random.laplace(size=(num_samples, ) + rv_shape)
rv_samples_np = location_np + rand * scale_np
rand_gen = MockMXNetRandomGenerator(
mx.nd.array(rand.flatten(), dtype=dtype))
var = Laplace.define_variable(shape=rv_shape,
dtype=dtype,
rand_gen=rand_gen).factor
location_mx = mx.nd.array(location, dtype=dtype)
if not location_is_samples:
location_mx = add_sample_dimension(mx.nd, location_mx)
scale_mx = mx.nd.array(scale, dtype=dtype)
if not scale_is_samples:
scale_mx = add_sample_dimension(mx.nd, scale_mx)
variables = {var.location.uuid: location_mx, var.scale.uuid: scale_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 array_has_samples(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_draw_samples(self):
np.random.seed(0)
X = np.random.rand(10, 3)
Y = np.random.rand(10, 1)
noise_var = np.random.rand(1)
lengthscale = np.random.rand(3)
variance = np.random.rand(1)
dtype = 'float64'
rand_gen = MockMXNetRandomGenerator(
mx.nd.array(np.random.rand(20), dtype=dtype))
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,
rand_gen=rand_gen)
observed = [m.X]
infr = Inference(ForwardSamplingAlgorithm(m,
observed,
num_samples=2,
target_variables=[m.Y]),
dtype=dtype)
samples = infr.run(X=mx.nd.array(X, dtype=dtype),
Y=mx.nd.array(Y, dtype=dtype))[0].asnumpy()
kern = RBF(3, True, name='rbf', dtype=dtype) + White(3, dtype=dtype)
X_var = Variable(shape=(10, 3))
gp = GaussianProcess.define_variable(X=X_var,
kernel=kern,
shape=(10, 1),
dtype=dtype,
rand_gen=rand_gen).factor
variables = {
gp.X.uuid:
mx.nd.expand_dims(mx.nd.array(X, dtype=dtype), axis=0),
gp.add_rbf_lengthscale.uuid:
mx.nd.expand_dims(mx.nd.array(lengthscale, dtype=dtype), axis=0),
gp.add_rbf_variance.uuid:
mx.nd.expand_dims(mx.nd.array(variance, dtype=dtype), axis=0),
gp.add_white_variance.uuid:
mx.nd.expand_dims(mx.nd.array(noise_var, dtype=dtype), axis=0)
}
samples_2 = gp.draw_samples(F=mx.nd,
variables=variables,
num_samples=2).asnumpy()
assert np.allclose(samples, samples_2), (samples, samples_2)
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)
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_w_mean(self, dtype, X, X_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))
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)
mean_mx = net(X_mx)
mean_np = mean_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))
mean_func = MXFusionGluonFunction(net,
num_outputs=1,
broadcastable=True)
mean_var = mean_func(X_var)
gp = GaussianProcess.define_variable(X=X_var,
kernel=rbf,
shape=rv_shape,
mean=mean_var,
dtype=dtype,
rand_gen=rand_gen).factor
variables = {
gp.X.uuid: X_mx,
gp.rbf_lengthscale.uuid: rbf_lengthscale_mx,
gp.rbf_variance.uuid: rbf_variance_mx,
gp.mean.uuid: mean_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
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)
L_np = np.linalg.cholesky(K_np)
sample_np = L_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)
