def _make_gluon_function_evaluation_rand_param(self, dtype, broadcastable):
class Dot(HybridBlock):
def __init__(self, params=None, prefix=None):
super(Dot, self).__init__(params=params, prefix=prefix)
with self.name_scope():
self.const = self.params.get('const',
shape=(1, ),
dtype=dtype,
init=Zero())
def hybrid_forward(self, F, a, b, const):
return F.broadcast_add(F.linalg.gemm2(a, b), const)
dot = Dot(prefix='dot_')
dot.initialize()
dot.hybridize()
print(dot.collect_params())
func_wrapper = MXFusionGluonFunction(dot,
1,
dtype=dtype,
broadcastable=broadcastable)
from mxfusion.components.distributions.normal import Normal
rand_var = Normal.define_variable(shape=(1, ))
out = func_wrapper(Variable(shape=(3, 4)),
Variable(shape=(4, 5)),
dot_const=rand_var)
return out.factor
def gen_mxfusion_model(self,
dtype,
D,
Z,
noise_var,
lengthscale,
variance,
rand_gen=None):
m = Model()
m.N = Variable()
m.X = Variable(shape=(m.N, 3))
m.Z = Variable(shape=(3, 3), initial_value=mx.nd.array(Z, dtype=dtype))
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 = SVGPRegression.define_variable(X=m.X,
kernel=kernel,
noise_var=m.noise_var,
inducing_inputs=m.Z,
shape=(m.N, D),
dtype=dtype)
gp = m.Y.factor
m.Y.factor.svgp_log_pdf.jitter = 1e-8
return m, gp
def gen_mxfusion_model(self,
dtype,
D,
noise_var,
lengthscale,
variance,
rand_gen=None):
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, D),
dtype=dtype,
rand_gen=rand_gen)
return m
def test_with_samples(self):
from mxfusion.common import config
config.DEFAULT_DTYPE = 'float64'
dtype = 'float64'
D, X, Y, noise_var, lengthscale, variance = self.gen_data()
m = Model()
m.N = Variable()
m.X = Normal.define_variable(mean=0, variance=1, 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, D))
q = create_Gaussian_meanfield(model=m, observed=[m.Y])
infr = GradBasedInference(
inference_algorithm=StochasticVariationalInference(
model=m, posterior=q, num_samples=10, observed=[m.Y]))
infr.run(Y=mx.nd.array(Y, dtype='float64'),
max_iter=2,
learning_rate=0.1,
verbose=True)
infr2 = Inference(
ForwardSamplingAlgorithm(model=m, observed=[m.X], num_samples=5))
infr2.run(X=mx.nd.array(X, dtype='float64'))
infr_pred = TransferInference(ModulePredictionAlgorithm(
model=m, observed=[m.X], target_variables=[m.Y]),
infr_params=infr.params)
xt = np.random.rand(13, 3)
res = infr_pred.run(X=mx.nd.array(xt, dtype=dtype))[0]
gp = m.Y.factor
gp.attach_prediction_algorithms(
targets=gp.output_names,
conditionals=gp.input_names,
algorithm=GPRegressionSamplingPrediction(gp._module_graph,
gp._extra_graphs[0],
[gp._module_graph.X]),
alg_name='gp_predict')
gp.gp_predict.diagonal_variance = False
gp.gp_predict.jitter = 1e-6
infr_pred2 = TransferInference(ModulePredictionAlgorithm(
model=m, observed=[m.X], target_variables=[m.Y]),
infr_params=infr.params)
xt = np.random.rand(13, 3)
res = infr_pred2.run(X=mx.nd.array(xt, dtype=dtype))[0]
def make_gpregr_model(self):
m = Model()
m.N = Variable()
m.X = Variable(shape=(m.N, 3))
m.noise_var = Variable(transformation=PositiveTransformation(), initial_value=mx.nd.array([1.]))
kernel = RBF(input_dim=3, variance=mx.nd.array([1.]), lengthscale=mx.nd.array([1.]))
m.Y = GPRegression.define_variable(X=m.X, kernel=kernel, noise_var=m.noise_var, shape=(m.N, 2))
return m
def test_prediction(self):
np.random.seed(0)
np.random.seed(0)
X = np.random.rand(10, 3)
Y = np.random.rand(10, 1)
Z = np.random.rand(3, 3)
qU_mean = np.random.rand(3, 1)
qU_cov_W = np.random.rand(3, 3)
qU_cov_diag = np.random.rand(3,)
noise_var = np.random.rand(1)
lengthscale = np.random.rand(3)
variance = np.random.rand(1)
qU_chol = np.linalg.cholesky(qU_cov_W.dot(qU_cov_W.T)+np.diag(qU_cov_diag))[None,:,:]
Xt = np.random.rand(5, 3)
m_gpy = GPy.core.SVGP(X=X, Y=Y, Z=Z, kernel=GPy.kern.RBF(3, ARD=True, lengthscale=lengthscale, variance=variance), likelihood=GPy.likelihoods.Gaussian(variance=noise_var))
m_gpy.q_u_mean = qU_mean
m_gpy.q_u_chol = GPy.util.choleskies.triang_to_flat(qU_chol)
dtype = 'float64'
m = Model()
m.N = Variable()
m.X = Variable(shape=(m.N, 3))
m.Z = Variable(shape=(3, 3), initial_value=mx.nd.array(Z, dtype=dtype))
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 = SVGPRegression.define_variable(X=m.X, kernel=kernel, noise_var=m.noise_var, inducing_inputs=m.Z, shape=(m.N, 1), dtype=dtype)
gp = m.Y.factor
observed = [m.X, m.Y]
infr = Inference(MAP(model=m, observed=observed), dtype=dtype)
infr.initialize(X=X.shape, Y=Y.shape)
infr.params[gp._extra_graphs[0].qU_mean] = mx.nd.array(qU_mean, dtype=dtype)
infr.params[gp._extra_graphs[0].qU_cov_W] = mx.nd.array(qU_cov_W, dtype=dtype)
infr.params[gp._extra_graphs[0].qU_cov_diag] = mx.nd.array(qU_cov_diag, dtype=dtype)
loss, _ = infr.run(X=mx.nd.array(X, dtype=dtype), Y=mx.nd.array(Y, dtype=dtype))
# noise_free, diagonal
mu_gpy, var_gpy = m_gpy.predict_noiseless(Xt)
infr2 = TransferInference(ModulePredictionAlgorithm(m, observed=[m.X], target_variables=[m.Y]), infr_params=infr.params, dtype=np.float64)
res = infr2.run(X=mx.nd.array(Xt, dtype=dtype))[0]
mu_mf, var_mf = res[0].asnumpy()[0], res[1].asnumpy()[0]
assert np.allclose(mu_gpy, mu_mf), (mu_gpy, mu_mf)
assert np.allclose(var_gpy[:,0], var_mf), (var_gpy[:,0], var_mf)
# noisy, diagonal
mu_gpy, var_gpy = m_gpy.predict(Xt)
infr2 = TransferInference(ModulePredictionAlgorithm(m, observed=[m.X], target_variables=[m.Y]), infr_params=infr.params, dtype=np.float64)
infr2.inference_algorithm.model.Y.factor.svgp_predict.noise_free = False
res = infr2.run(X=mx.nd.array(Xt, dtype=dtype))[0]
mu_mf, var_mf = res[0].asnumpy()[0], res[1].asnumpy()[0]
assert np.allclose(mu_gpy, mu_mf), (mu_gpy, mu_mf)
assert np.allclose(var_gpy[:,0], var_mf), (var_gpy[:,0], var_mf)
def __init__(self):
inputs = [('A', Variable(shape=(3, 4))), ('B', Variable(shape=(4, 5)))]
outputs = [('output', Variable(shape=(3, 5)))]
input_names = ['A', 'B']
output_names = ['output']
super(DotFuncEval, self).__init__(inputs=inputs, outputs=outputs,
input_names=input_names,
output_names=output_names,
broadcastable=broadcastable)
def test_sampling_prediction(self):
np.random.seed(0)
X = np.random.rand(10, 3)
Xt = np.random.rand(20, 3)
Y = np.random.rand(10, 1)
noise_var = np.random.rand(1)
lengthscale = np.random.rand(3)
variance = np.random.rand(1)
m_gpy = GPy.models.GPRegression(X=X,
Y=Y,
kernel=GPy.kern.RBF(
3,
ARD=True,
lengthscale=lengthscale,
variance=variance),
noise_var=noise_var)
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)
observed = [m.X, m.Y]
infr = Inference(MAP(model=m, observed=observed), dtype=dtype)
loss, _ = infr.run(X=mx.nd.array(X, dtype=dtype),
Y=mx.nd.array(Y, dtype=dtype))
infr_pred = TransferInference(ModulePredictionAlgorithm(
model=m, observed=[m.X], target_variables=[m.Y], num_samples=5),
infr_params=infr.params)
gp = m.Y.factor
gp.attach_prediction_algorithms(
targets=gp.output_names,
conditionals=gp.input_names,
algorithm=GPRegressionSamplingPrediction(gp._module_graph,
gp._extra_graphs[0],
[gp._module_graph.X]),
alg_name='gp_predict')
gp.gp_predict.diagonal_variance = False
gp.gp_predict.jitter = 1e-6
y_samples = infr_pred.run(X=mx.nd.array(Xt, dtype=dtype))[0].asnumpy()
def _make_gluon_function_evaluation(self, dtype, broadcastable):
class Dot(HybridBlock):
def hybrid_forward(self, F, a, b):
return F.linalg.gemm2(a, b)
dot = Dot(prefix='dot')
dot.initialize()
dot.hybridize()
func_wrapper = MXFusionGluonFunction(dot, 1, dtype=dtype,
broadcastable=broadcastable)
out = func_wrapper(Variable(shape=(3, 4)), Variable(shape=(4, 5)))
return out.factor
def test_sampling_prediction(self):
np.random.seed(0)
np.random.seed(0)
X = np.random.rand(10, 3)
Y = np.random.rand(10, 1)
Z = np.random.rand(3, 3)
qU_mean = np.random.rand(3, 1)
qU_cov_W = np.random.rand(3, 3)
qU_cov_diag = np.random.rand(3,)
noise_var = np.random.rand(1)
lengthscale = np.random.rand(3)
variance = np.random.rand(1)
qU_chol = np.linalg.cholesky(qU_cov_W.dot(qU_cov_W.T)+np.diag(qU_cov_diag))[None,:,:]
Xt = np.random.rand(5, 3)
m_gpy = GPy.core.SVGP(X=X, Y=Y, Z=Z, kernel=GPy.kern.RBF(3, ARD=True, lengthscale=lengthscale, variance=variance), likelihood=GPy.likelihoods.Gaussian(variance=noise_var))
m_gpy.q_u_mean = qU_mean
m_gpy.q_u_chol = GPy.util.choleskies.triang_to_flat(qU_chol)
dtype = 'float64'
m = Model()
m.N = Variable()
m.X = Variable(shape=(m.N, 3))
m.Z = Variable(shape=(3, 3), initial_value=mx.nd.array(Z, dtype=dtype))
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 = SVGPRegression.define_variable(X=m.X, kernel=kernel, noise_var=m.noise_var, inducing_inputs=m.Z, shape=(m.N, 1), dtype=dtype)
gp = m.Y.factor
observed = [m.X, m.Y]
infr = Inference(MAP(model=m, observed=observed), dtype=dtype)
infr.initialize(X=X.shape, Y=Y.shape)
infr.params[gp._extra_graphs[0].qU_mean] = mx.nd.array(qU_mean, dtype=dtype)
infr.params[gp._extra_graphs[0].qU_cov_W] = mx.nd.array(qU_cov_W, dtype=dtype)
infr.params[gp._extra_graphs[0].qU_cov_diag] = mx.nd.array(qU_cov_diag, dtype=dtype)
loss, _ = infr.run(X=mx.nd.array(X, dtype=dtype), Y=mx.nd.array(Y, dtype=dtype))
# noise_free, diagonal
infr_pred = TransferInference(ModulePredictionAlgorithm(model=m, observed=[m.X], target_variables=[m.Y], num_samples=5),
infr_params=infr.params)
gp = m.Y.factor
gp.attach_prediction_algorithms(
targets=gp.output_names, conditionals=gp.input_names,
algorithm=SVGPRegressionSamplingPrediction(
gp._module_graph, gp._extra_graphs[0], [gp._module_graph.X]),
alg_name='svgp_predict')
gp.svgp_predict.diagonal_variance = False
gp.svgp_predict.jitter = 1e-6
y_samples = infr_pred.run(X=mx.nd.array(Xt, dtype=dtype))[0].asnumpy()
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_compute_log_prob(self):
m = Model()
v = Variable(shape=(1,))
m.v2 = Normal.define_variable(mean=v, variance=mx.nd.array([1]))
m.v3 = Normal.define_variable(mean=m.v2, variance=mx.nd.array([1]), shape=(10,))
np.random.seed(0)
v_mx = mx.nd.array(np.random.randn(1))
v2_mx = mx.nd.array(np.random.randn(1))
v3_mx = mx.nd.array(np.random.randn(10))
v_rt = add_sample_dimension(mx.nd, v_mx)
v2_rt = add_sample_dimension(mx.nd, v2_mx)
v3_rt = add_sample_dimension(mx.nd, v3_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)
log_pdf = m.log_pdf(F=mx.nd, variables={m.v2.uuid: v2_rt, m.v3.uuid:v3_rt, variance.uuid: variance_rt, variance2.uuid: variance2_rt, v.uuid: v_rt}).asscalar()
variables = {m.v2.factor.mean.uuid: v_rt, m.v2.factor.variance.uuid: variance_rt, m.v2.factor.random_variable.uuid: v2_rt}
log_pdf_1 = mx.nd.sum(m.v2.factor.log_pdf(F=mx.nd, variables=variables))
variables = {m.v3.factor.mean.uuid: v2_rt, m.v3.factor.variance.uuid: variance2_rt, m.v3.factor.random_variable.uuid: v3_rt}
log_pdf_2 = mx.nd.sum(m.v3.factor.log_pdf(F=mx.nd, variables=variables))
assert log_pdf == (log_pdf_1 + log_pdf_2).asscalar()
def test_log_pdf(self):
np.random.seed(0)
D = 2
X = np.random.rand(10, 3)
Y = np.random.rand(10, D)
noise_var = np.random.rand(1)
lengthscale = np.random.rand(3)
variance = np.random.rand(1)
m_gpy = GPy.models.GPRegression(X=X,
Y=Y,
kernel=GPy.kern.RBF(
3,
ARD=True,
lengthscale=lengthscale,
variance=variance),
noise_var=noise_var)
l_gpy = m_gpy.log_likelihood()
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, D),
dtype=dtype)
observed = [m.X, m.Y]
infr = Inference(MAP(model=m, observed=observed), dtype=dtype)
loss, _ = infr.run(X=mx.nd.array(X, dtype=dtype),
Y=mx.nd.array(Y, dtype=dtype))
l_mf = -loss
assert np.allclose(l_mf.asnumpy(), l_gpy)
def test_function_execution(self):
f, f_mx = self.instantialize_customize_function()
np.random.seed(0)
A = mx.nd.array(np.random.rand(1, 3, 2))
B = mx.nd.array(np.random.rand(1, 3, 2))
C = mx.nd.array(np.random.rand(1))
A_mf = Variable(shape=A.shape)
B_mf = Variable(shape=B.shape)
outs = f(A_mf, B_mf)
assert len(outs) == 2
eval = f(A_mf, B_mf)[0].factor
variables = {A_mf.uuid: A, B_mf.uuid: B, eval.C.uuid: C}
res_eval = eval.eval(F=mx.nd, variables=variables)
res_mx = f_mx(A, B, C)
assert np.allclose(res_eval[0].asnumpy(), res_mx[0].asnumpy())
assert np.allclose(res_eval[1].asnumpy(), res_mx[1].asnumpy())
def test_module_clone(self):
D, X, Y, Z, noise_var, lengthscale, variance, qU_mean, \
qU_cov_W, qU_cov_diag, qU_chol = self.gen_data()
dtype = 'float64'
m = Model()
m.N = Variable()
m.X = Variable(shape=(m.N, 3))
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 = SVGPRegression.define_variable(X=mx.nd.zeros((2, 3)),
kernel=kernel,
noise_var=mx.nd.ones((1, )),
dtype=dtype)
m.clone()
def gen_mxfusion_model_w_mean(self, dtype, D, Z, noise_var, lengthscale,
variance, rand_gen=None):
net = nn.HybridSequential(prefix='nn_')
with net.name_scope():
net.add(nn.Dense(D, flatten=False, activation="tanh",
in_units=3, dtype=dtype))
net.initialize(mx.init.Xavier(magnitude=3))
m = Model()
m.N = Variable()
m.X = Variable(shape=(m.N, 3))
m.Z = Variable(shape=(3, 3), initial_value=mx.nd.array(Z, dtype=dtype))
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.mean_func = MXFusionGluonFunction(net, num_outputs=1,
broadcastable=True)
m.Y = SparseGPRegression.define_variable(X=m.X, kernel=kernel, noise_var=m.noise_var, mean=m.mean_func(m.X), inducing_inputs=m.Z, shape=(m.N, D), dtype=dtype)
m.Y.factor.sgp_log_pdf.jitter = 1e-8
return m, net
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().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 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_log_pdf(self):
np.random.seed(0)
D = 2
X = np.random.rand(10, 3)
Y = np.random.rand(10, D)
Z = np.random.rand(3, 3)
qU_mean = np.random.rand(3, D)
qU_cov_W = np.random.rand(3, 3)
qU_cov_diag = np.random.rand(3,)
noise_var = np.random.rand(1)
lengthscale = np.random.rand(3)
variance = np.random.rand(1)
qU_chol = np.linalg.cholesky(qU_cov_W.dot(qU_cov_W.T)+np.diag(qU_cov_diag))[None,:,:]
m_gpy = GPy.core.SVGP(X=X, Y=Y, Z=Z, kernel=GPy.kern.RBF(3, ARD=True, lengthscale=lengthscale, variance=variance), likelihood=GPy.likelihoods.Gaussian(variance=noise_var))
m_gpy.q_u_mean = qU_mean
m_gpy.q_u_chol = GPy.util.choleskies.triang_to_flat(qU_chol)
l_gpy = m_gpy.log_likelihood()
dtype = 'float64'
m = Model()
m.N = Variable()
m.X = Variable(shape=(m.N, 3))
m.Z = Variable(shape=(3, 3), initial_value=mx.nd.array(Z, dtype=dtype))
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 = SVGPRegression.define_variable(X=m.X, kernel=kernel, noise_var=m.noise_var, inducing_inputs=m.Z, shape=(m.N, D), dtype=dtype)
gp = m.Y.factor
observed = [m.X, m.Y]
infr = Inference(MAP(model=m, observed=observed), dtype=dtype)
infr.initialize(X=X.shape, Y=Y.shape)
infr.params[gp._extra_graphs[0].qU_mean] = mx.nd.array(qU_mean, dtype=dtype)
infr.params[gp._extra_graphs[0].qU_cov_W] = mx.nd.array(qU_cov_W, dtype=dtype)
infr.params[gp._extra_graphs[0].qU_cov_diag] = mx.nd.array(qU_cov_diag, dtype=dtype)
loss, _ = infr.run(X=mx.nd.array(X, dtype=dtype), Y=mx.nd.array(Y, dtype=dtype))
l_mf = -loss
assert np.allclose(l_mf.asnumpy(), l_gpy)
def test_log_pdf_w_samples_of_noise_var(self):
D, X, Y, Z, noise_var, lengthscale, variance, qU_mean, \
qU_cov_W, qU_cov_diag, qU_chol = self.gen_data()
dtype = 'float64'
D = 2
Y = np.random.rand(10, D)
qU_mean = np.random.rand(3, D)
m = Model()
m.N = Variable()
m.X = Variable(shape=(m.N, 3))
m.Z = Variable(shape=(3, 3), initial_value=mx.nd.array(Z, dtype=dtype))
m.noise_var = Variable(transformation=PositiveTransformation(),
shape=(m.N, D))
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 = SVGPRegression.define_variable(X=m.X,
kernel=kernel,
noise_var=m.noise_var,
inducing_inputs=m.Z,
shape=(m.N, D),
dtype=dtype)
gp = m.Y.factor
m.Y.factor.svgp_log_pdf.jitter = 1e-8
observed = [m.X, m.Y]
infr = Inference(MAP(model=m, observed=observed), dtype=dtype)
infr.initialize(X=X.shape, Y=Y.shape)
infr.params[gp._extra_graphs[0].qU_mean] = mx.nd.array(qU_mean,
dtype=dtype)
infr.params[gp._extra_graphs[0].qU_cov_W] = mx.nd.array(qU_cov_W,
dtype=dtype)
infr.params[gp._extra_graphs[0].qU_cov_diag] = mx.nd.array(qU_cov_diag,
dtype=dtype)
loss, _ = infr.run(X=mx.nd.array(X, dtype=dtype),
Y=mx.nd.array(Y, dtype=dtype),
max_iter=1)
def test_gluon_parameters(self):
self.setUp()
m = Model()
m.x = Variable(shape=(1, 1))
m.f = MXFusionGluonFunction(self.net, num_outputs=1)
m.y = m.f(m.x)
infr = Inference(ForwardSamplingAlgorithm(m, observed=[m.x]))
infr.run(x=mx.nd.ones((1, 1)))
assert all([
v.uuid in infr.params.param_dict for v in m.f.parameters.values()
])
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_save_reload_constants(self):
constants = {Variable(): 5, 'uuid': mx.nd.array([1])}
ip = InferenceParameters(constants=constants)
ip.save(prefix="constants_test")
# assert the file is there
ip2 = InferenceParameters.load_parameters(
mxnet_constants_file='constants_test_mxnet_constants.json',
variable_constants_file='constants_test_variable_constants.json')
print(ip.constants)
print(ip2.constants)
assert ip.constants == ip2.constants
self.remove_saved_files("constants_test")
def test_decode_component(self):
v = Variable()
v2 = Variable()
v.predecessors = [('first', v2)]
v.attributes = [Variable()] #[('shape', (Variable(), 1))]
data = {
"var": v
}
a = json.dumps(data, cls=ModelComponentEncoder, indent=2)
b = json.loads(a, cls=ModelComponentDecoder)
assert b == data
def test_encode_component(self):
v = Variable()
v2 = Variable()
v.predecessors = [('first', v2)]
# TODO: extend attributes to support generic representation
v.attributes = [Variable()]#[('shape', (Variable(), 1))]
data = {
"var": v
}
a = json.dumps(data, cls=ModelComponentEncoder, indent=2)
print(a)
def make_simple_model(self):
m = Model()
mean = Variable()
variance = Variable()
m.r = Normal.define_variable(mean=mean, variance=variance)
return m
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_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)
def test_log_pdf_w_mean(self, dtype, X, X_isSamples, rbf_lengthscale,
rbf_lengthscale_isSamples, rbf_variance,
rbf_variance_isSamples, rv, rv_isSamples,
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)
rv_mx = prepare_mxnet_array(rv, rv_isSamples, dtype)
rv_shape = rv.shape[1:] if rv_isSamples else rv.shape
mean_mx = net(X_mx)
mean_np = mean_mx.asnumpy()
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).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,
gp.mean.uuid: mean_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
rv_i = rv_i - mean_np[i] if X_isSamples else rv_i - mean_np[0]
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 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_success(self):
self.setUp()
f = MXFusionGluonFunction(self.net, num_outputs=1)
x = Variable()
y = f(x)
