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MLHGP_variational.py
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MLHGP_variational.py
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'''
Author: Edoardo Caldarelli
Affiliation: Institut de Robòtica i Informàtica Industrial, CSIC-UPC
email: ecaldarelli@iri.upc.edu
October 2023
'''
import numpy as np
import numpy.linalg
from scipy.linalg import cholesky, cho_solve
import gpflow
from gp_utilities import *
import matplotlib.pyplot as plt
import time
import tensorflow_probability as tfp
def mlhgp_svgp(Xs, X, Y, niter=20, train=True, params_mean=None, params_variance=None, num_feat=50, lth=.1, bounds=False, R=None, Rs=None):
"""
This function trains a heteroscedastic GP with expectation-maximization.
:param niter: number of iterations to be used in the training.
:param bounds: whether to set bounds of the hyperparameters of the GPs.
:param lth: initial value of the lengthscale.
:param params_variance: hyperparameters for the GP on the noise variance.
:param params_mean: hyperparameters for the GP on the mean function.
:param train: whether the GP should be trained (True) or used for testing only (False).
:param Xs: prediction inputs.
:param X: training inputs.
:param Y: training outputs.
:return: Posterior mean, covariance and GP hyperparameters.
"""
# Normalization of the observations.
Ymean = np.mean(Y, axis=0)
Ystd = np.std(Y, axis=0)
Y = (Y - Ymean) / Ystd
init_ind_points = np.random.uniform(np.amin(X), np.amax(X), num_feat).reshape([-1, 1]) #np.random.choice(X.squeeze(), (num_feat, 1))## np.arange(0, num_feat) / num_feat).reshape([-1, 1])
prediction_times = []
optimization_times = []
# Step 1
kernel = gpflow.kernels.RBF(variance=1.0, lengthscales=lth)
model_gpflow = gpflow.models.SVGP(
kernel=kernel,
inducing_variable=init_ind_points,
likelihood=gpflow.likelihoods.Gaussian()
)
# gpflow.utilities.set_trainable(model_gpflow.inducing_variable, False)
if train:
old_parameter = model_gpflow.kernel.variance
new_parameter = gpflow.Parameter(
1e0,
trainable=old_parameter.trainable,
prior=old_parameter.prior,
name=old_parameter.name.split(":")[0], # tensorflow is weird and adds ':0' to the name
transform=tfp.bijectors.Sigmoid(np.float64(1e-2), np.float64(2)),
)
model_gpflow.kernel.variance = new_parameter
old_parameter = model_gpflow.kernel.lengthscales
new_parameter = gpflow.Parameter(
1e-1,
trainable=old_parameter.trainable,
prior=old_parameter.prior,
name=old_parameter.name.split(":")[0], # tensorflow is weird and adds ':0' to the name
transform=tfp.bijectors.Sigmoid(np.float64(1e-2), np.float64(1e0)),
)
model_gpflow.kernel.lengthscales = new_parameter
old_parameter = model_gpflow.likelihood.variance
new_parameter = gpflow.Parameter(
1e0,
trainable=old_parameter.trainable,
prior=old_parameter.prior,
name=old_parameter.name.split(":")[0], # tensorflow is weird and adds ':0' to the name
transform=tfp.bijectors.Sigmoid(np.float64(1e-2), np.float64(2)),
)
model_gpflow.likelihood.variance = new_parameter
opt = gpflow.optimizers.Scipy()
print('starting opt...')
start_opti_time = time.time()
opt.minimize(model_gpflow.training_loss_closure((X, Y)), model_gpflow.trainable_variables, options={'maxiter':100})
# run_adam(model_gpflow, 1000, (X, Y))
optimization_times.append(time.time() - start_opti_time)
else:
param = params_mean
kernel.lengthscales = param[0]
kernel.variance = param[1]
model_gpflow.likelihood.variance = param[2]
g1m, g1cov = model_gpflow.predict_f(X)
g1m = g1m.numpy()
g1cov = np.diag(g1cov.numpy().ravel())
# EM
for i in range(0, niter):
print("Iteration ", i)
# Step 2
r1 = 0.5 * ((Y.ravel() - g1m.ravel()) ** 2 + np.diag(g1cov).ravel())
Z = np.log(r1).reshape(-1, 1)
# Step 3
kernel2 = gpflow.kernels.RBF(variance=1.0, lengthscales=lth)
init_ind_points = np.random.uniform(np.amin(X), np.amax(X), num_feat).reshape([-1,
1]) # np.random.choice(X.squeeze(), (num_feat, 1))## np.arange(0, num_feat) / num_feat).reshape([-1, 1])
model_gpflow2 = gpflow.models.SVGP(
kernel=kernel2,
inducing_variable=init_ind_points,
likelihood=gpflow.likelihoods.Gaussian()
)
# gpflow.utilities.set_trainable(model_gpflow2.inducing_variable, False)
if train:
old_parameter = model_gpflow2.kernel.variance
new_parameter = gpflow.Parameter(
1e0,
trainable=old_parameter.trainable,
prior=old_parameter.prior,
name=old_parameter.name.split(":")[0], # tensorflow is weird and adds ':0' to the name
transform=tfp.bijectors.Sigmoid(np.float64(1e-2), np.float64(2)),
)
model_gpflow2.kernel.variance = new_parameter
old_parameter = model_gpflow2.kernel.lengthscales
new_parameter = gpflow.Parameter(
1e-1,
trainable=old_parameter.trainable,
prior=old_parameter.prior,
name=old_parameter.name.split(":")[0], # tensorflow is weird and adds ':0' to the name
transform=tfp.bijectors.Sigmoid(np.float64(1e-2), np.float64(1e0)),
)
model_gpflow2.kernel.lengthscales = new_parameter
old_parameter = model_gpflow2.likelihood.variance
new_parameter = gpflow.Parameter(
1e0,
trainable=old_parameter.trainable,
prior=old_parameter.prior,
name=old_parameter.name.split(":")[0], # tensorflow is weird and adds ':0' to the name
transform=tfp.bijectors.Sigmoid(np.float64(1e-2), np.float64(2)),
)
model_gpflow2.likelihood.variance = new_parameter
opt2 = gpflow.optimizers.Scipy()
start_opti_time = time.time()
opt2.minimize(model_gpflow2.training_loss_closure((X,Z)), model_gpflow2.trainable_variables, options={'maxiter': 100})
# run_adam(model_gpflow2, 1000, (X, Z))
optimization_times.append(time.time() - start_opti_time)
g2m, g2cov = model_gpflow2.predict_f(X)
g2ms, g2covs = model_gpflow2.predict_f(Xs)
g2m = g2m.numpy()
g2cov = g2cov.numpy()
g2ms = g2ms.numpy()
g2covs = g2covs.numpy()
# Step 4
R = np.exp(g2m + g2cov / 2.0)
Rs = np.exp(g2ms + g2covs / 2.0)
else:
model_gpflow2.kernel.lengthscales = params_variance[0]
model_gpflow2.kernel.variance = params_variance[1]
model_gpflow2.likelihood.variance = params_variance[2]
R = R
Rs = Rs
# K = kernel.K(X, X).numpy() + np.diag(R.ravel()) + 1e-8 * np.eye(len(X))
# Ks = kernel.K(X, X).numpy()
# Kss = kernel.K(X, X).numpy() + np.diag(R.ravel())
#
# L = cholesky(K, lower=True)
# alpha = cho_solve((L, True), Y)
# v = cho_solve((L, True), Ks.T)
#
# g1m = Ks.dot(alpha)
# g1cov = Kss - Ks.dot(v)
model_gpflow.likelihood.variance = R.ravel().reshape([-1, 1])
g1m, g1cov = model_gpflow.predict_f(Xnew=X)
g1m = g1m.numpy()
g1cov = g1cov.numpy()
g1cov = np.diag((g1cov + R).ravel())
# Final GP
start_pred_time = time.time()
model_gpflow.likelihood.variance = R.ravel().reshape([-1, 1])
mu, cov = model_gpflow.predict_f(Xs)
mu = mu.numpy()
cov = cov.numpy()
cov = cov + Rs
# K = kernel.K(X, X).numpy() + np.diag(R.ravel()) + 1e-8 * np.eye(len(X))
# Ks = kernel.K(Xs, X).numpy()
# Kss = kernel.K(Xs, Xs).numpy() + np.diag(Rs.ravel())
#
# L = cholesky(K, lower=True)
# alpha = cho_solve((L, True), Y)
# v = cho_solve((L, True), Ks.T)
#
# mu = Ks.dot(alpha)
# cov = Kss - Ks.dot(v)
#
mu = Ystd * mu + Ymean
cov = cov * Ystd ** 2
prediction_times.append(time.time() - start_pred_time)
gp_var_params = [model_gpflow2.kernel.lengthscales, model_gpflow2.kernel.variance, model_gpflow2.likelihood.variance]
gp_mean_params = [model_gpflow.kernel.lengthscales, model_gpflow.kernel.variance, model_gpflow.likelihood.variance]
return mu, cov, gp_var_params, gp_mean_params, prediction_times, optimization_times, R, Rs