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Changing definitions again...

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Alan Saul 2013-03-21 14:00:22 +00:00
parent a9d5555976
commit 474d5484b0
3 changed files with 43 additions and 26 deletions
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15
python/examples/laplace_approximations.py
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@ -15,8 +15,9 @@ def student_t_approx():
Y = np.sin(X) Y = np.sin(X)
#Add student t random noise to datapoints #Add student t random noise to datapoints
deg_free = 3.5 deg_free = 100000.5
t_rv = t(deg_free, loc=0, scale=1) real_var = 4
t_rv = t(deg_free, loc=0, scale=real_var)
noise = t_rv.rvs(size=Y.shape) noise = t_rv.rvs(size=Y.shape)
Y += noise Y += noise
@ -46,7 +47,7 @@ def student_t_approx():
#print m #print m
#with a student t distribution, since it has heavy tails it should work well #with a student t distribution, since it has heavy tails it should work well
likelihood_function = student_t(deg_free, sigma=1) likelihood_function = student_t(deg_free, sigma=real_var)
lap = Laplace(Y, likelihood_function) lap = Laplace(Y, likelihood_function)
cov = kernel.K(X) cov = kernel.K(X)
lap.fit_full(cov) lap.fit_full(cov)
@ -64,7 +65,7 @@ def student_t_approx():
import ipdb; ipdb.set_trace() ### XXX BREAKPOINT import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
# Likelihood object # Likelihood object
t_distribution = student_t(deg_free, sigma=1) t_distribution = student_t(deg_free, sigma=real_var)
stu_t_likelihood = Laplace(Y, t_distribution) stu_t_likelihood = Laplace(Y, t_distribution)
kernel = GPy.kern.rbf(X.shape[1]) + GPy.kern.bias(X.shape[1]) kernel = GPy.kern.rbf(X.shape[1]) + GPy.kern.bias(X.shape[1])
@ -77,12 +78,16 @@ def student_t_approx():
# optimize # optimize
#m.optimize() #m.optimize()
print(m) #print(m)
# plot # plot
m.plot() m.plot()
import ipdb; ipdb.set_trace() ### XXX BREAKPOINT import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
m.optimize()
print(m)
import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
return m return m

44
python/likelihoods/Laplace.py
View file

@ -1,7 +1,7 @@
import numpy as np import numpy as np
import scipy as sp import scipy as sp
import GPy import GPy
from scipy.linalg import cholesky, eig, inv from scipy.linalg import cholesky, eig, inv, det
from functools import partial from functools import partial
from GPy.likelihoods.likelihood import likelihood from GPy.likelihoods.likelihood import likelihood
from GPy.util.linalg import pdinv,mdot from GPy.util.linalg import pdinv,mdot
@ -43,8 +43,10 @@ class Laplace(likelihood):
self.Z = 0 self.Z = 0
self.YYT = None self.YYT = None
def predictive_values(self,mu,var): def predictive_values(self, mu, var, full_cov):
return self.likelihood_function.predictive_values(mu,var) if full_cov:
raise NotImplementedError("Cannot make correlated predictions with an EP likelihood")
return self.likelihood_function.predictive_values(mu, var)
def _get_params(self): def _get_params(self):
return np.zeros(0) return np.zeros(0)
@ -52,10 +54,10 @@ class Laplace(likelihood):
def _get_param_names(self): def _get_param_names(self):
return [] return []
def _set_params(self,p): def _set_params(self, p):
pass # TODO: Laplace likelihood might want to take some parameters... pass # TODO: Laplace likelihood might want to take some parameters...
def _gradients(self,partial): def _gradients(self, partial):
return np.zeros(0) # TODO: Laplace likelihood might want to take some parameters... return np.zeros(0) # TODO: Laplace likelihood might want to take some parameters...
raise NotImplementedError raise NotImplementedError
@ -83,7 +85,13 @@ class Laplace(likelihood):
and $$\ln \tilde{z} = \ln z + \frac{N}{2}\ln 2\pi + \frac{1}{2}\tilde{Y}\tilde{\Sigma}^{-1}\tilde{Y}$$ and $$\ln \tilde{z} = \ln z + \frac{N}{2}\ln 2\pi + \frac{1}{2}\tilde{Y}\tilde{\Sigma}^{-1}\tilde{Y}$$
""" """
self.Sigma_tilde_i = self.hess_hat_i #self.W #self.hess_hat_i - self.Ki self.Sigma_tilde_i = self.W #self.hess_hat_i
#Check it isn't singular!
epsilon = 1e-2
"""
if np.abs(det(self.Sigma_tilde_i)) < epsilon:
raise ValueError("inverse covariance must be non-singular to inverse!")
"""
#Do we really need to inverse Sigma_tilde_i? :( #Do we really need to inverse Sigma_tilde_i? :(
if self.likelihood_function.log_concave: if self.likelihood_function.log_concave:
(self.Sigma_tilde, _, _, _) = pdinv(self.Sigma_tilde_i) (self.Sigma_tilde, _, _, _) = pdinv(self.Sigma_tilde_i)
@ -91,12 +99,17 @@ class Laplace(likelihood):
self.Sigma_tilde = inv(self.Sigma_tilde_i) self.Sigma_tilde = inv(self.Sigma_tilde_i)
#f_hat? should be f but we must have optimized for them I guess? #f_hat? should be f but we must have optimized for them I guess?
Y_tilde = mdot(self.Sigma_tilde, self.hess_hat, self.f_hat) Y_tilde = mdot(self.Sigma_tilde, self.hess_hat, self.f_hat)
self.Z_tilde = np.exp(self.ln_z_hat - self.NORMAL_CONST #Z_tilde = (self.ln_z_hat - self.NORMAL_CONST
- 0.5*mdot(self.f_hat, self.hess_hat, self.f_hat) #- 0.5*mdot(self.f_hat, self.hess_hat, self.f_hat)
+ 0.5*mdot(Y_tilde.T, (self.Sigma_tilde_i, Y_tilde)) #+ 0.5*mdot(Y_tilde.T, (self.Sigma_tilde_i, Y_tilde))
) #)
Z_tilde = (self.ln_z_hat - self.NORMAL_CONST
+ 0.5*self.log_hess_hat_det
+ 0.5*mdot(self.f_hat, self.Ki , self.f_hat)
+ 0.5*mdot(Y_tilde.T, (self.Sigma_tilde_i, Y_tilde))
)
self.Z = self.Z_tilde self.Z = Z_tilde
self.Y = Y_tilde self.Y = Y_tilde
self.covariance_matrix = self.Sigma_tilde self.covariance_matrix = self.Sigma_tilde
self.precision = 1 / np.diag(self.Sigma_tilde)[:, None] self.precision = 1 / np.diag(self.Sigma_tilde)[:, None]
@ -128,7 +141,7 @@ class Laplace(likelihood):
return np.squeeze(res) return np.squeeze(res)
def obj_hess(f): def obj_hess(f):
res = -1 * (-np.diag(self.likelihood_function.link_hess(self.data[:, 0], f)) - self.Ki) res = -1 * (--np.diag(self.likelihood_function.link_hess(self.data[:, 0], f)) - self.Ki)
return np.squeeze(res) return np.squeeze(res)
self.f_hat = sp.optimize.fmin_ncg(obj, f, fprime=obj_grad, fhess=obj_hess) self.f_hat = sp.optimize.fmin_ncg(obj, f, fprime=obj_grad, fhess=obj_hess)
@ -153,7 +166,10 @@ class Laplace(likelihood):
#the area of p(f)p(y|f) we do this by matching the height of the distributions at the mode #the area of p(f)p(y|f) we do this by matching the height of the distributions at the mode
#z_hat = -0.5*ln|H| - 0.5*ln|K| - 0.5*f_hat*K^{-1}*f_hat \sum_{n} ln p(y_n|f_n) #z_hat = -0.5*ln|H| - 0.5*ln|K| - 0.5*f_hat*K^{-1}*f_hat \sum_{n} ln p(y_n|f_n)
#Unsure whether its log_hess or log_hess_i #Unsure whether its log_hess or log_hess_i
self.ln_z_hat = -0.5*np.log(self.log_hess_hat_det) - 0.5*self.log_Kdet + -1*self.likelihood_function.link_function(self.data[:,0], self.f_hat) - mdot(self.f_hat.T, (self.Ki, self.f_hat)) self.ln_z_hat = (-0.5*self.log_hess_hat_det
import ipdb; ipdb.set_trace() ### XXX BREAKPOINT - 0.5*self.log_Kdet
-1*self.likelihood_function.link_function(self.data[:,0], self.f_hat)
- mdot(self.f_hat.T, (self.Ki, self.f_hat))
)
return self._compute_GP_variables() return self._compute_GP_variables()

10
python/likelihoods/likelihood_function.py
View file

@ -81,11 +81,7 @@ class student_t(likelihood_function):
Compute mean, and conficence interval (percentiles 5 and 95) of the prediction Compute mean, and conficence interval (percentiles 5 and 95) of the prediction
""" """
mean = np.exp(mu) mean = np.exp(mu)
p_025 = stats.t.ppf(025,mean) p_025 = stats.t.ppf(.025, mean)
p_975 = stats.t.ppf(975,mean) p_975 = stats.t.ppf(.975, mean)
#p_025 = tmp[:,0]
#p_975 = tmp[:,1]
import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
return mean,p_025,p_975
return mean, np.nan*mean, p_025, p_975