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Added predicted values for student t, works well

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Alan Saul 2013-04-02 12:33:01 +01:00
parent 15d5c2f22d
commit ffc168c1d2
2 changed files with 53 additions and 36 deletions
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48
python/examples/laplace_approximations.py
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@ -18,7 +18,7 @@ def student_t_approx():
#Y = Y/Y.max()
#Yc[10] += 100
Yc[10] += 100
Yc[25] += 10
Yc[23] += 10
Yc[24] += 10
@ -52,51 +52,30 @@ def student_t_approx():
#A GP should completely break down due to the points as they get a lot of weight
# create simple GP model
m = GPy.models.GP_regression(X, Y, kernel=kernel1)
## optimize
# optimize
m.ensure_default_constraints()
#m.unconstrain('noise')
#m.constrain_fixed('noise', 0.1)
m.optimize()
# plot
plt.subplot(211)
m.plot()
print m
##Corrupt
#Corrupt
print "Corrupt Gaussian"
m = GPy.models.GP_regression(X, Yc, kernel=kernel2)
m.ensure_default_constraints()
#m.unconstrain('noise')
#m.constrain_fixed('noise', 0.1)
m.optimize()
plt.subplot(212)
m.plot()
print m
##with a student t distribution, since it has heavy tails it should work well
##likelihood_function = student_t(deg_free, sigma=real_var)
##lap = Laplace(Y, likelihood_function)
##cov = kernel.K(X)
##lap.fit_full(cov)
##test_range = np.arange(0, 10, 0.1)
##plt.plot(test_range, t_rv.pdf(test_range))
##for i in xrange(X.shape[0]):
##mode = lap.f_hat[i]
##covariance = lap.hess_hat_i[i,i]
##scaling = np.exp(lap.ln_z_hat)
##normalised_approx = norm(loc=mode, scale=covariance)
##print "Normal with mode %f, and variance %f" % (mode, covariance)
##plt.plot(test_range, scaling*normalised_approx.pdf(test_range))
##plt.show()
plt.figure(2)
plt.suptitle('Student-t likelihood')
edited_real_sd = real_sd
# Likelihood object
t_distribution = student_t(deg_free, sigma=edited_real_sd)
stu_t_likelihood = Laplace(Yc, t_distribution)
stu_t_likelihood = Laplace(Y, t_distribution)
print "Clean student t"
m = GPy.models.GP(X, stu_t_likelihood, kernel3)
@ -107,7 +86,7 @@ def student_t_approx():
print(m)
# plot
plt.subplot(211)
m.plot_f()
m.plot()
plt.ylim(-2.5,2.5)
#import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
@ -124,6 +103,23 @@ def student_t_approx():
plt.ylim(-2.5,2.5)
import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
###with a student t distribution, since it has heavy tails it should work well
###likelihood_function = student_t(deg_free, sigma=real_var)
###lap = Laplace(Y, likelihood_function)
###cov = kernel.K(X)
###lap.fit_full(cov)
###test_range = np.arange(0, 10, 0.1)
###plt.plot(test_range, t_rv.pdf(test_range))
###for i in xrange(X.shape[0]):
###mode = lap.f_hat[i]
###covariance = lap.hess_hat_i[i,i]
###scaling = np.exp(lap.ln_z_hat)
###normalised_approx = norm(loc=mode, scale=covariance)
###print "Normal with mode %f, and variance %f" % (mode, covariance)
###plt.plot(test_range, scaling*normalised_approx.pdf(test_range))
###plt.show()
return m