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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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72
python/likelihoods/likelihood_function.py
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@ -1,4 +1,5 @@
from scipy.special import gammaln
from scipy.special import gammaln, gamma
from scipy import integrate
import numpy as np
from GPy.likelihoods.likelihood_functions import likelihood_function
from scipy import stats
@ -79,9 +80,68 @@ class student_t(likelihood_function):
def predictive_values(self, mu, var):
"""
Compute mean, and conficence interval (percentiles 5 and 95) of the prediction
"""
mean = np.exp(mu)
p_025 = stats.t.ppf(.025, mean)
p_975 = stats.t.ppf(.975, mean)
return mean, np.nan*mean, p_025, p_975
Need to find what the variance is at the latent points for a student t*normal
(((g((v+1)/2))/(g(v/2)*s*sqrt(v*pi)))*(1+(1/v)*((y-f)/s)^2)^(-(v+1)/2))*((1/(s*sqrt(2*pi)))*exp(-(1/(2*(s^2)))*((y-f)^2)))
(((g((v+1)/2))/(g(v/2)*s*sqrt(v*pi)))*(1+(1/v)*((y-f)/s)^2)^(-(v+1)/2))
*((1/(s*sqrt(2*pi)))*exp(-(1/(2*(s^2)))*((y-f)^2)))
"""
#p_025 = stats.t.ppf(.025, mu)
#p_975 = stats.t.ppf(.975, mu)
num_test_points = mu.shape[0]
#Each mu is the latent point f* at the test point x*,
#and the var is the gaussian variance at this point
#Take lots of samples from this, so we have lots of possible values
#for latent point f* for each test point x* weighted by how likely we were to pick it
print "Taking %d samples of f*".format(num_test_points)
num_f_samples = 10
num_y_samples = 10
student_t_means = np.random.normal(loc=mu, scale=np.sqrt(var), size=(num_test_points, num_f_samples))
print "Student t means shape: ", student_t_means.shape
#Now we have lots of f*, lets work out the likelihood of getting this by sampling
#from a student t centred on this point, sample many points from this distribution
#centred on f*
#for test_point, f in enumerate(student_t_means):
#print test_point
#print f.shape
#student_t_samples = stats.t.rvs(self.v, loc=f[:,None],
#scale=self.sigma,
#size=(num_f_samples, num_y_samples))
#print student_t_samples.shape
student_t_samples = stats.t.rvs(self.v, loc=student_t_means[:,None],
scale=self.sigma,
size=(num_test_points, num_y_samples, num_f_samples))
student_t_samples = np.reshape(student_t_samples,
(num_test_points, num_y_samples*num_f_samples))
#Now take the 97.5 and 0.25 percentile of these points
p_025 = stats.scoreatpercentile(student_t_samples, .025, axis=1)[:, None]
p_975 = stats.scoreatpercentile(student_t_samples, .975, axis=1)[:, None]
p_025 = 1+p_025
p_975 = 1+p_975
##Alernenately we could sample from int p(y|f*)p(f*|x*) df*
def t_gaussian(f, mu, var):
return (((gamma((self.v+1)*0.5)) / (gamma(self.v*0.5)*self.sigma*np.sqrt(self.v*np.pi))) * ((1+(1/self.v)*(((mu-f)/self.sigma)**2))**(-(self.v+1)*0.5))
* ((1/(np.sqrt(2*np.pi*var)))*np.exp(-(1/(2*var)) *((mu-f)**2)))
)
def t_gauss_int(mu, var):
print "Mu: ", mu
print "var: ", var
result = integrate.quad(t_gaussian, -np.inf, 0.975, args=(mu, var))
print "Result: ", result
return result[0]
vec_t_gauss_int = np.vectorize(t_gauss_int)
p_025 = vec_t_gauss_int(mu, var)
p_975 = vec_t_gauss_int(mu, var)
import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
return mu, np.nan*mu, p_025, p_975