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Worked out in terms of W, needs gradients implementing

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Alan Saul 2013-03-19 18:21:57 +00:00
parent 46d59c94b2
commit a9d5555976
3 changed files with 57 additions and 40 deletions
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44
python/examples/laplace_approximations.py
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@ -15,13 +15,13 @@ def student_t_approx():
Y = np.sin(X)
#Add student t random noise to datapoints
deg_free = 2.5
deg_free = 3.5
t_rv = t(deg_free, loc=0, scale=1)
noise = t_rv.rvs(size=Y.shape)
Y += noise
#Add some extreme value noise to some of the datapoints
#percent_corrupted = 0.05
#percent_corrupted = 0.15
#corrupted_datums = int(np.round(Y.shape[0] * percent_corrupted))
#indices = np.arange(Y.shape[0])
#np.random.shuffle(indices)
@ -31,11 +31,11 @@ def student_t_approx():
#Y[corrupted_indices] += noise
# Kernel object
#print X.shape
#kernel = GPy.kern.rbf(X.shape[1])
print X.shape
kernel = GPy.kern.rbf(X.shape[1])
##A GP should completely break down due to the points as they get a lot of weight
## create simple GP model
#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=kernel)
## optimize
@ -46,27 +46,27 @@ def student_t_approx():
#print m
#with a student t distribution, since it has heavy tails it should work well
#likelihood_function = student_t(deg_free, sigma=1)
#lap = Laplace(Y, likelihood_function)
#cov = kernel.K(X)
#lap.fit_full(cov)
likelihood_function = student_t(deg_free, sigma=1)
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()
#import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
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()
import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
# Likelihood object
t_distribution = student_t(deg_free, sigma=1)
stu_t_likelihood = Laplace(Y, t_distribution)
kernel = GPy.kern.rbf(X.shape[1])
kernel = GPy.kern.rbf(X.shape[1]) + GPy.kern.bias(X.shape[1])
m = GPy.models.GP(X, stu_t_likelihood, kernel)
m.ensure_default_constraints()