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Working laplace, just needs predictive values

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Alan Saul 2013-03-28 17:42:42 +00:00
parent 7b0d0550cb
commit 15d5c2f22d
3 changed files with 121 additions and 46 deletions
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80
python/examples/laplace_approximations.py
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@ -10,20 +10,23 @@ def student_t_approx():
"""
Example of regressing with a student t likelihood
"""
real_var = 0.1
#Start a function, any function
X = np.linspace(0.0, 10.0, 100)[:, None]
Y = np.sin(X) + np.random.randn(*X.shape)*0.1
X = np.linspace(0.0, 10.0, 30)[:, None]
Y = np.sin(X) + np.random.randn(*X.shape)*real_var
Yc = Y.copy()
Y = Y/Y.max()
#Y = Y/Y.max()
Yc[10] += 5
Yc[15] += 20
Yc = Yc/Yc.max()
#Yc[10] += 100
Yc[25] += 10
Yc[23] += 10
Yc[24] += 10
#Yc = Yc/Yc.max()
#Add student t random noise to datapoints
deg_free = 1000000 #100000.5
real_var = 0.1
deg_free = 20 #100000.5
real_sd = np.sqrt(real_var)
#t_rv = t(deg_free, loc=0, scale=real_var)
#noise = t_rvrvs(size=Y.shape)
#Y += noise
@ -38,36 +41,37 @@ def student_t_approx():
#noise = t_rv.rvs(size=(len(corrupted_indices), 1))
#Y[corrupted_indices] += noise
plt.figure(1)
plt.suptitle('Gaussian likelihood')
# Kernel object
kernel1 = GPy.kern.rbf(X.shape[1])
kernel2 = kernel1.copy()
kernel3 = kernel1.copy()
kernel4 = kernel1.copy()
#print "Clean Gaussian"
##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
#m.ensure_default_constraints()
##m.unconstrain('noise')
##m.constrain_fixed('noise', 0.1)
#m.optimize()
## plot
#plt.subplot(221)
#m.plot()
#print m
print "Clean Gaussian"
#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
m.ensure_default_constraints()
#m.unconstrain('noise')
#m.constrain_fixed('noise', 0.1)
m.optimize()
# plot
plt.subplot(211)
m.plot()
print m
##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(222)
#m.plot()
#print m
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)
@ -86,9 +90,13 @@ def student_t_approx():
##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=np.sqrt(real_var))
stu_t_likelihood = Laplace(Y, t_distribution)
t_distribution = student_t(deg_free, sigma=edited_real_sd)
stu_t_likelihood = Laplace(Yc, t_distribution)
print "Clean student t"
m = GPy.models.GP(X, stu_t_likelihood, kernel3)
@ -100,9 +108,11 @@ def student_t_approx():
# plot
plt.subplot(211)
m.plot_f()
plt.ylim(-2.5,2.5)
#import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
print "Corrupt student t"
t_distribution = student_t(deg_free, sigma=np.sqrt(real_var))
t_distribution = student_t(deg_free, sigma=edited_real_sd)
corrupt_stu_t_likelihood = Laplace(Yc, t_distribution)
m = GPy.models.GP(X, corrupt_stu_t_likelihood, kernel4)
m.ensure_default_constraints()
@ -110,8 +120,8 @@ def student_t_approx():
m.optimize()
print(m)
plt.subplot(212)
m.plot_f()
m.plot()
plt.ylim(-2.5,2.5)
import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
return m