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 test_gp_module_save_and_load(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)
dtype = 'float64'
m = self.make_gpregr_model(lengthscale, variance, noise_var)
observed = [m.X, m.Y]
from mxfusion.inference import MAP, Inference
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.save(prefix=self.PREFIX)
m2 = self.make_gpregr_model(lengthscale, variance, noise_var)
observed2 = [m2.X, m2.Y]
infr2 = Inference(MAP(model=m2, observed=observed2), dtype=dtype)
infr2.initialize(X=mx.nd.array(X, dtype=dtype),
Y=mx.nd.array(Y, dtype=dtype))
# Load previous parameters
infr2.load(
graphs_file=self.PREFIX + '_graphs.json',
parameters_file=self.PREFIX + '_params.json',
inference_configuration_file=self.PREFIX + '_configuration.json',
mxnet_constants_file=self.PREFIX + '_mxnet_constants.json',
variable_constants_file=self.PREFIX + '_variable_constants.json')
for original_uuid, original_param in infr.params.param_dict.items():
original_data = original_param.data().asnumpy()
reloaded_data = infr2.params.param_dict[
infr2._uuid_map[original_uuid]].data().asnumpy()
assert np.all(np.isclose(original_data, reloaded_data))
for original_uuid, original_param in infr.params.constants.items():
if isinstance(original_param, mx.ndarray.ndarray.NDArray):
original_data = original_param.asnumpy()
reloaded_data = infr2.params.constants[
infr2._uuid_map[original_uuid]].asnumpy()
else:
original_data = original_param
reloaded_data = infr2.params.constants[
infr2._uuid_map[original_uuid]]
assert np.all(np.isclose(original_data, reloaded_data))
loss2, _ = infr2.run(X=mx.nd.array(X, dtype=dtype),
Y=mx.nd.array(Y, dtype=dtype))
self.remove_saved_files(self.PREFIX)
def test_sampling_prediction(self):
D, X, Y, Z, noise_var, lengthscale, variance, qU_mean, \
qU_cov_W, qU_cov_diag, qU_chol = self.gen_data()
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, gp = self.gen_mxfusion_model(dtype, D, Z, noise_var, lengthscale,
variance)
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.noise_free = False
gp.svgp_predict.jitter = 1e-6
y_samples = infr_pred.run(X=mx.nd.array(Xt, dtype=dtype))[0].asnumpy()
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_prediction_w_mean(self):
D, X, Y, Z, noise_var, lengthscale, variance, qU_mean, \
qU_cov_W, qU_cov_diag, qU_chol = self.gen_data()
Xt = np.random.rand(5, 3)
dtype = 'float64'
m, gp, net = self.gen_mxfusion_model_w_mean(dtype, D, Z, noise_var,
lengthscale, variance)
mean = net(mx.nd.array(X, dtype=dtype)).asnumpy()
mean_t = net(mx.nd.array(Xt, dtype=dtype)).asnumpy()
m_gpy = GPy.core.SVGP(
X=X,
Y=Y - mean,
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)
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)
mu_gpy += mean_t
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, rtol=1e-04,
atol=1e-05), (mu_gpy, mu_mf)
assert np.allclose(var_gpy, var_mf, rtol=1e-04,
atol=1e-05), (var_gpy, var_mf)
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_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_mean(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, gp, net = self.gen_mxfusion_model_w_mean(dtype, D, Z, noise_var,
lengthscale, variance)
mean = net(mx.nd.array(X, dtype=dtype)).asnumpy()
m_gpy = GPy.core.SVGP(
X=X,
Y=Y - mean,
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()
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_prediction(self):
D, X, Y, Z, noise_var, lengthscale, variance, qU_mean, \
qU_cov_W, qU_cov_diag, qU_chol = self.gen_data()
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, gp = self.gen_mxfusion_model(dtype, D, Z, noise_var, lengthscale,
variance)
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)
# TODO: The full covariance matrix prediction with SVGP in GPy may not be correct. Need further investigation.
# noise_free, full_cov
mu_gpy, var_gpy = m_gpy.predict_noiseless(Xt, full_cov=True)
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.diagonal_variance = False
infr2.inference_algorithm.model.Y.factor.svgp_predict.noise_free = True
res = infr2.run(X=mx.nd.array(Xt, dtype=dtype))[0]
mu_mf, var_mf = res[0].asnumpy()[0], res[1].asnumpy()[0]
print(var_gpy.shape, var_mf.shape)
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, full_cov
mu_gpy, var_gpy = m_gpy.predict(Xt, full_cov=True)
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.diagonal_variance = False
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)