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4_TPR.py
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4_TPR.py
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# import required packages/modules
import numpy as np
import os
import tensorflow.compat.v2 as tf
import tensorflow_probability as tfp
from CustomCauchyKernel import CustomCauchy # kernel not defined in TensorFlow, so we define it manually
# define required parts of tensorflow_probability
tfb = tfp.bijectors
tfd = tfp.distributions
tfk = tfp.math.psd_kernels
tf.enable_v2_behavior()
# define list of priors, covariance functions, and datasets
priornames = ['NoPrior', 'Riess', 'TRGB', 'H0LiCOW', 'CM', 'Planck', 'DES']
priorvals = [None, 74.22, 69.8, 73.3, 75.35, 67.4, 67.4]
priorsdevs = [None, 1.82, 1.9, 1.7, 1.68, 0.5, 1.1]
covnames = ['Squex', 'DoubleSquex', 'RatQuadratic', 'Matern32', 'Matern52', 'Matern72', 'Matern92', 'Cauchy']
datanames = ['CC', 'CC+SN', 'CC+SN+BAO']
os.chdir("~/GaPP_27/Application/4_TP/files/")
for i in range(len(datanames)):
dataname = datanames[i]
for j in range(len(covnames)):
covname = covnames[j]
for k in range(len(priornames)):
print()
print(i, j, k)
priorname = priornames[k]
# prepare the data
(z, H, sigmaH) = np.loadtxt("~/GaPP_27/Application/data/Hdata_" + dataname + ".txt", unpack=True)
# append prior (at z=0) if applicable
if priorname != 'NoPrior':
z = np.insert(z, 0, 0, axis=0)
H = np.insert(H, 0, priorvals[k], axis=0)
sigmaH = np.insert(sigmaH, 0, priorsdevs[k], axis=0)
# X = redshift value
z = np.asarray(z).reshape(-1, 1)
# y = corresponding value of H(z)
H = np.asarray(H).astype(np.float32)
# define kernel and list of hyperparameters
# double square exponential only
def build_tp_doublesquex(sigmaf1, l1, sigmaf2, l2, sigmaH, nu):
k = tfp.math.psd_kernels.ExponentiatedQuadratic(amplitude=sigmaf1,
length_scale=l1) + tfp.math.psd_kernels.ExponentiatedQuadratic(
amplitude=sigmaf2, length_scale=l2)
return tfd.StudentTProcess(kernel=k, index_points=z, observation_noise_variance=sigmaH, df=nu)
# rational quadratic only
def build_tp_ratquad(sigmaf, l, alpha, sigmaH, nu):
k = tfp.math.psd_kernels.RationalQuadratic(amplitude=sigmaf, length_scale=l, scale_mixture_rate=alpha)
return tfd.StudentTProcess(kernel=k, index_points=z, observation_noise_variance=sigmaH, df=nu)
# all other kernels
def build_tp_others(sigmaf, l, sigmaH, nu):
# define kernel
if covname == "Squex":
k = tfp.math.psd_kernels.ExponentiatedQuadratic(amplitude=sigmaf, length_scale=l)
elif covname == "Matern32":
k = tfp.math.psd_kernels.MaternThreeHalves(amplitude=sigmaf, length_scale=l)
elif covname == "Matern52":
k = tfp.math.psd_kernels.MaternFiveHalves(amplitude=sigmaf, length_scale=l)
elif covname == "Matern72":
k = tfp.math.psd_kernels.GeneralizedMatern(df=3.5, amplitude=sigmaf, length_scale=l)
elif covname == "Matern92":
k = tfp.math.psd_kernels.GeneralizedMatern(df=4.5, amplitude=sigmaf, length_scale=l)
elif covname == "Cauchy":
k = CustomCauchy(amplitude=sigmaf, length_scale=l)
# define Student's t-process prior
return tfd.StudentTProcess(kernel=k, index_points=z, observation_noise_variance=sigmaH, df=nu)
# function to return uniform tensor distribution
def up(a, b):
return tfd.Uniform(np.float64(a), np.float64(b))
# define uninformative uniform priors on kernel hyperparameters
if covname == "DoubleSquex":
tp_joint_model = tfd.JointDistributionNamed({
'sigmaf1': up(0, 100),
'l1': up(0, 100),
'sigmaf2': up(0, 100),
'l2': up(0, 100),
'nu': up(30, 100),
'sigmaH': up(0, 0.01),
'obs': build_tp_doublesquex,
})
elif covname == "RatQuadratic":
tp_joint_model = tfd.JointDistributionNamed({
'sigmaf': up(0, 100),
'l': up(0, 100),
'alpha': up(0, 1),
'nu': up(0, 100),
'sigmaH': up(0, 0.01),
'obs': build_tp_ratquad,
})
else:
tp_joint_model = tfd.JointDistributionNamed({
'sigmaf': up(0, 100),
'l': up(0, 100),
'nu': up(30, 100),
'sigmaH': up(0, 0.01),
'obs': build_tp_others,
})
# constrain all parameters to positive and define initial values
constrain_positive = tfb.Shift(np.finfo(np.float64).tiny)(tfb.Exp())
# function to define parameters
def defineParameter(init, name):
return tfp.util.TransformedVariable(initial_value=init, bijector=constrain_positive, name=name,
dtype=np.float64)
sigmafvar = defineParameter(50., 'sigmaf') # not used for double squex
lvar = defineParameter(1., 'l') # not used for double squex
sigmaf1var = defineParameter(50., 'sigmaf1') # only used for double squex
l1var = defineParameter(1., 'l1') # only used for double squex
sigmaf2var = defineParameter(50., 'sigmaf2') # only used for double squex
l2var = defineParameter(1., 'l2') # only used for double squex
alphavar = defineParameter(0.5, 'alpha') # only used for rational quadratic
nuvar = defineParameter(20., 'nu') # degrees of freedom
sigmaHvar = defineParameter(0.01, 'sigmaH') # observation noise variance
# list of hyperparameters
if covname == "DoubleSquex":
varlist = [sigmaf1var, l1var, sigmaf2var, l2var, nuvar, sigmaHvar]
elif covname == "RatQuadratic":
varlist = [sigmafvar, lvar, alphavar, nuvar, sigmaHvar]
elif covname == "Squex" or covname == "Cauchy":
varlist = [sigmafvar, lvar, nuvar, sigmaHvar]
else:
varlist = [lvar, nuvar, sigmaHvar]
trainablevariables = [v.trainable_variables[0] for v in varlist]
# define target log probability to be minimised
def target_log_prob(sigmaf, l, sigmaf1, l1, sigmaf2, l2, alpha, nu, sigmaH):
if covname == "DoubleSquex":
return tp_joint_model.log_prob(
{'sigmaf1': sigmaf1, 'l1': l1, 'sigmaf2': sigmaf2, 'l2': l2, 'nu': nu, 'sigmaH': sigmaH,
'obs': H})
elif covname == "RatQuadratic":
return tp_joint_model.log_prob(
{'sigmaf': sigmaf, 'l': l, 'alpha': alpha, 'nu': nu, 'sigmaH': sigmaH, 'obs': H})
else:
return tp_joint_model.log_prob({'sigmaf': sigmaf, 'l': l, 'nu': nu, 'sigmaH': sigmaH, 'obs': H})
# define number of optimisers and learning rate
num_iters = 10000
optimizer = tf.optimizers.Adam(learning_rate=.001)
# optimise loglikelihood
@tf.function(autograph=False, jit_compile=False)
def train_model():
with tf.GradientTape() as tape:
logl = -target_log_prob(sigmafvar, lvar, sigmaf1var, l1var, sigmaf2var, l2var, alphavar, nuvar,
sigmaHvar)
grads = tape.gradient(logl, trainablevariables)
optimizer.apply_gradients(zip(grads, trainablevariables))
return logl
# store value of loglikelihood at each iteration for plot
lls_ = np.zeros(num_iters, np.float64)
for ii in range(num_iters):
logl = train_model()
lls_[ii] = logl
# print optimised parameter values
with open("opt_para_" + dataname + "_" + covname + "_" + priorname + ".txt", "w") as f:
f.write('Trained parameters:' + "\n")
if covname == "Squex" or covname == "Cauchy" or covname == "RatQuadratic":
f.write('sigmaf: {}'.format(sigmafvar._value().numpy()) + "\n")
if covname != "DoubleSquex":
f.write('l: {}'.format(lvar._value().numpy()) + "\n")
if covname == "DoubleSquex":
f.write('sigmaf1: {}'.format(sigmaf1var._value().numpy()) + "\n")
f.write('l1: {}'.format(l1var._value().numpy()) + "\n")
f.write('sigmaf2: {}'.format(sigmaf2var._value().numpy()) + "\n")
f.write('l2: {}'.format(l2var._value().numpy()) + "\n")
if covname == "RatQuadratic":
f.write('alpha: {}'.format(alphavar._value().numpy()) + "\n")
f.write('nu: {}'.format(nuvar._value().numpy()) + "\n")
f.write('sigmaH: {}'.format(sigmaHvar._value().numpy()) + "\n")
zmin = 0.0
zmax = 2.5 if dataname == "CC+SN+BAO" else 2.0
nstar = 100
# reshape to [100, 1] -- 1 is the dimensionality of the feature space.
Xstar = np.linspace(zmin, zmax, nstar, dtype=np.float64)
Xstar = Xstar[..., np.newaxis]
# kernel function with optimised parameters
if covname == "Squex":
kopt = tfp.math.psd_kernels.ExponentiatedQuadratic(amplitude=sigmafvar, length_scale=lvar)
elif covname == "DoubleSquex":
kopt = tfp.math.psd_kernels.ExponentiatedQuadratic(amplitude=sigmaf1var,
length_scale=l1var) + tfp.math.psd_kernels.ExponentiatedQuadratic(
amplitude=sigmaf2var, length_scale=l2var)
elif covname == "RatQuadratic":
kopt = tfp.math.psd_kernels.RationalQuadratic(amplitude=sigmafvar, length_scale=lvar,
scale_mixture_rate=alphavar)
elif covname == "Matern32":
kopt = tfp.math.psd_kernels.MaternThreeHalves(amplitude=sigmafvar, length_scale=lvar)
elif covname == "Matern52":
kopt = tfp.math.psd_kernels.MaternFiveHalves(amplitude=sigmafvar, length_scale=lvar)
elif covname == "Matern72":
kopt = tfp.math.psd_kernels.GeneralizedMatern(df=3.5, amplitude=sigmafvar, length_scale=lvar)
elif covname == "Matern92":
kopt = tfp.math.psd_kernels.GeneralizedMatern(df=4.5, amplitude=sigmafvar, length_scale=lvar)
elif covname == "Cauchy":
kopt = CustomCauchy(amplitude=sigmafvar, length_scale=lvar)
# function to return TP posterior predictive function
tprm = tfd.StudentTProcessRegressionModel(kernel=kopt, df=nuvar, index_points=np.float64(Xstar),
observation_index_points=np.float64(z),
observations=np.float64(H),
observation_noise_variance=np.float64(sigmaHvar),
predictive_noise_variance=np.float64(0.))
# create 500 samples, each of size [nrow(Xstar), 1]
num_samples = 500
samples = tprm.sample(num_samples)
# get sample mean and variance
samplemean = tf.math.reduce_mean(samples, axis=0)
samplevar = tf.math.reduce_variance(samples, axis=0)
# reconstruction
rec = np.zeros((len(Xstar), 3))
rec[:, 0] = Xstar.ravel()
rec[:, 1] = samplemean.numpy()
rec[:, 2] = np.sqrt(samplevar.numpy())
np.savetxt("H_" + dataname + "_" + covname + "_" + priorname + ".txt", rec)
# plot the observations and posterior samples
# similarly to what was done in GPR
import plottingfunction
plotname = "plot_" + dataname + "_" + covname + "_" + priorname
plottitle = dataname + "/" + covname + "/" + priorname
print("Plotting " + plottitle)
plottingfunction.plot(z, H, sigmaH, rec, zmin, zmax, plotname, plottitle)