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Added sampling to student_t noise distribution, very slow

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and is possible to speed up. predictive mean analytical and
variance need checking
This commit is contained in:
Alan Saul 2013-10-28 16:17:17 +00:00
parent fc59ef4baf
commit df9a546c73
1 changed files with 10 additions and 67 deletions
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77
GPy/likelihoods/noise_models/student_t_noise.py
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@ -241,92 +241,35 @@ class StudentT(NoiseDistribution):
*((1/(s*sqrt(2*pi)))*exp(-(1/(2*(s^2)))*((y-f)^2))) *((1/(s*sqrt(2*pi)))*exp(-(1/(2*(s^2)))*((y-f)^2)))
""" """
#FIXME: Not correct
#We want the variance around test points y which comes from int p(y*|f*)p(f*) df* #We want the variance around test points y which comes from int p(y*|f*)p(f*) df*
#Var(y*) = Var(E[y*|f*]) + E[Var(y*|f*)] #Var(y*) = Var(E[y*|f*]) + E[Var(y*|f*)]
#Since we are given f* (mu) which is our mean (expected) value of y*|f* then the variance is the variance around this #Since we are given f* (mu) which is our mean (expected) value of y*|f* then the variance is the variance around this
#Which was also given to us as (var) #Which was also given to us as (var)
#We also need to know the expected variance of y* around samples f*, this is the variance of the student t distribution #We also need to know the expected variance of y* around samples f*, this is the variance of the student t distribution
#However the variance of the student t distribution is not dependent on f, only on sigma and the degrees of freedom #However the variance of the student t distribution is not dependent on f, only on sigma and the degrees of freedom
true_var = sigma**2 + self.variance true_var = 1/(1/sigma**2 + 1/self.variance)
return true_var return true_var
def _predictive_mean_analytical(self, mu, var): def _predictive_mean_analytical(self, mu, sigma):
""" """
Compute mean of the prediction Compute mean of the prediction
""" """
#FIXME: Not correct
return mu return mu
def sample_predicted_values(self, mu, var):
""" Experimental sample approches and numerical integration """
raise NotImplementedError
#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]
##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, 0.025, 0.975, args=(mu, var))
print "Result: ", result
return result[0]
vec_t_gauss_int = np.vectorize(t_gauss_int)
p = vec_t_gauss_int(mu, var)
p_025 = mu - p
p_975 = mu + p
return mu, np.nan*mu, p_025, p_975
def samples(self, gp): def samples(self, gp):
""" """
Returns a set of samples of observations based on a given value of the latent variable. Returns a set of samples of observations based on a given value of the latent variable.
:param size: number of samples to compute
:param gp: latent variable :param gp: latent variable
""" """
orig_shape = gp.shape orig_shape = gp.shape
gp = gp.flatten() gp = gp.flatten()
f = self.gp_link.transf(gp) #FIXME: Very slow as we are computing a new random variable per input!
#student_t_samples = stats.t.rvs(self.v, loc=f, #Can't get it to sample all at the same time
#scale=np.sqrt(self.sigma2), student_t_samples = np.array([stats.t.rvs(self.v, self.gp_link.transf(gpj),scale=np.sqrt(self.sigma2), size=1) for gpj in gp])
#size=(num_test_points, num_y_samples, num_f_samples)) #student_t_samples = stats.t.rvs(self.v, loc=self.gp_link.transf(gp),
#Ysim = np.array([np.random.binomial(1,self.gp_link.transf(gpj),size=1) for gpj in gp]) #scale=np.sqrt(self.sigma2))
return Ysim.reshape(orig_shape) return student_t_samples.reshape(orig_shape)