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This commit is contained in:
Alan Saul 2013-03-14 15:30:22 +00:00
parent 3f114aa020
commit f9535c858a
3 changed files with 52 additions and 32 deletions
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22
python/examples/laplace_approximations.py
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@ -1,7 +1,7 @@
import GPy
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import t
from scipy.stats import t, norm
from coxGP.python.likelihoods.Laplace import Laplace
from coxGP.python.likelihoods.likelihood_function import student_t
@ -11,12 +11,13 @@ def student_t_approx():
Example of regressing with a student t likelihood
"""
#Start a function, any function
X = np.sort(np.random.uniform(0, 15, 70))[:, None]
X = np.sort(np.random.uniform(0, 15, 100))[:, None]
Y = np.sin(X)
#Add student t random noise to datapoints
deg_free = 1
noise = t.rvs(deg_free, loc=1.8, scale=1, size=Y.shape)
deg_free = 2.5
t_rv = t(deg_free, loc=5, scale=1)
noise = t_rv.rvs(size=Y.shape)
Y += noise
# Kernel object
@ -39,6 +40,19 @@ def student_t_approx():
lap = Laplace(Y, likelihood_function)
cov = kernel.K(X)
lap.fit_full(cov)
#Get one sample (just look at a single Y
mode = float(lap.f_hat[0])
variance = float((deg_free/(deg_free-2))) #BUG: Not convinced this is giving reasonable variables
#variance = float((deg_free/(deg_free-2)) + np.diagonal(lap.hess_hat)[0]) #BUG: Not convinced this is giving reasonable variables
normalised_approx = norm(loc=mode, scale=variance)
print "Normal with mode %f, and variance %f" % (mode, variance)
print lap.height_unnormalised
test_range = np.arange(0, 10, 0.1)
print np.diagonal(lap.hess_hat)
plt.plot(test_range, t_rv.pdf(test_range))
plt.plot(test_range, normalised_approx.pdf(test_range))
plt.show()
def noisy_laplace_approx():