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So many changes
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Ricardo Andrade
parent
de53917039
commit
182c4c7d64
7 changed files with 118 additions and 139 deletions
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@ -1,7 +1,7 @@
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import numpy as np
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import random
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from scipy import stats, linalg
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from ..core import model
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#from ..core import model
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from ..util.linalg import pdinv,mdot,jitchol
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from ..util.plot import gpplot
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@ -18,6 +18,8 @@ class EP:
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self.likelihood_function = likelihood_function
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self.epsilon = epsilon
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self.eta, self.delta = power_ep
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self.data = data
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self.N = self.data.size
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"""
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Initial values - Likelihood approximation parameters:
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@ -26,6 +28,12 @@ class EP:
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self.tau_tilde = np.zeros(self.N)
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self.v_tilde = np.zeros(self.N)
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#initial values for the GP variables
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self.Y = np.zeros((self.N,1))
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self.variance = np.zeros((self.N,self.N))#np.eye(self.N)
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self.Z = 0
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self.YYT = None
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def predictive_values(self,mu,var):
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return self.likelihood_function.predictive_values(mu,var)
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@ -35,6 +43,8 @@ class EP:
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return []
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def _set_params(self,p):
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pass # TODO: the EP likelihood might want to take some parameters...
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def _gradients(self,partial):
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return np.zeros(0) # TODO: the EP likelihood might want to take some parameters...
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def _compute_GP_variables(self):
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#Variables to be called from GP
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@ -42,7 +52,8 @@ class EP:
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sigma_sum = 1./self.tau_ + 1./self.tau_tilde
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mu_diff_2 = (self.v_/self.tau_ - mu_tilde)**2
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Z_ep = np.sum(np.log(self.Z_hat)) + 0.5*np.sum(np.log(sigma_sum)) + 0.5*np.sum(mu_diff_2/sigma_sum) #Normalization constant
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self.Y, self.beta, self.Z = self.tau_tilde[:,None], mu_tilde[:,None], Z_ep
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self.Y, self.beta, self.Z = mu_tilde[:,None],self.tau_tilde[:,None], Z_ep
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self.variance = np.diag(1./self.beta.flatten())
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def fit_full(self,K):
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"""
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@ -53,7 +64,7 @@ class EP:
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#Initial values - Posterior distribution parameters: q(f|X,Y) = N(f|mu,Sigma)
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self.mu = np.zeros(self.N)
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self.Sigma = K.copy()
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self.Sigma = K.copy() - self.variance.copy()
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"""
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Initial values - Cavity distribution parameters:
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@ -78,14 +89,14 @@ class EP:
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self.np1 = [self.tau_tilde.copy()]
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self.np2 = [self.v_tilde.copy()]
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while epsilon_np1 > self.epsilon or epsilon_np2 > self.epsilon:
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update_order = np.arange(self.N)
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random.shuffle(update_order)
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update_order = np.random.permutation(self.N)
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for i in update_order:
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#Cavity distribution parameters
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self.tau_[i] = 1./self.Sigma[i,i] - self.eta*self.tau_tilde[i]
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self.v_[i] = self.mu[i]/self.Sigma[i,i] - self.eta*self.v_tilde[i]
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print 1./self.Sigma[i,i],self.tau_tilde[i]
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#Marginal moments
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self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.likelihood.moments_match(i,self.tau_[i],self.v_[i])
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self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.likelihood_function.moments_match(self.data[i],self.tau_[i],self.v_[i])
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#Site parameters update
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Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./self.Sigma[i,i])
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Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - self.mu[i]/self.Sigma[i,i])
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@ -96,6 +107,7 @@ class EP:
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self.Sigma = self.Sigma - Delta_tau/(1.+ Delta_tau*self.Sigma[i,i])*np.dot(si,si.T)
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self.mu = np.dot(self.Sigma,self.v_tilde)
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self.iterations += 1
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print self.tau_tilde[i]
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#Sigma recomptutation with Cholesky decompositon
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Sroot_tilde_K = np.sqrt(self.tau_tilde)[:,None]*K
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B = np.eye(self.N) + np.sqrt(self.tau_tilde)[None,:]*Sroot_tilde_K
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@ -116,7 +128,7 @@ class EP:
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For nomenclature see ... 2013.
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"""
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#TODO: this doesn;t work with uncertain inputs!
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#TODO: this doesn;t work with uncertain inputs!
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"""
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Prior approximation parameters:
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@ -251,14 +263,13 @@ class EP:
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self.np1 = [self.tau_tilde.copy()]
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self.np2 = [self.v_tilde.copy()]
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while epsilon_np1 > self.epsilon or epsilon_np2 > self.epsilon:
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update_order = np.arange(self.N)
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random.shuffle(update_order)
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update_order = np.random.permutation(self.N)
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for i in update_order:
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#Cavity distribution parameters
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self.tau_[i] = 1./self.Sigma_diag[i] - self.eta*self.tau_tilde[i]
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self.v_[i] = self.mu[i]/self.Sigma_diag[i] - self.eta*self.v_tilde[i]
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#Marginal moments
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self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.likelihood.moments_match(i,self.tau_[i],self.v_[i])
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self.Z_hat[i], mu_hat[i], sigma2_hat[i] = self.likelihood_function.moments_match(data[i],self.tau_[i],self.v_[i])
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#Site parameters update
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Delta_tau = self.delta/self.eta*(1./sigma2_hat[i] - 1./self.Sigma_diag[i])
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Delta_v = self.delta/self.eta*(mu_hat[i]/sigma2_hat[i] - self.mu[i]/self.Sigma_diag[i])
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@ -39,7 +39,7 @@ class Gaussian:
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_95pc = mean + 2.*np.sqrt(var)
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return mean, _5pc, _95pc
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def fit(self):
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def fit_full(self):
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"""
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No approximations needed
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"""
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@ -7,6 +7,7 @@ from scipy import stats
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import scipy as sp
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import pylab as pb
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from ..util.plot import gpplot
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#from . import EP
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class likelihood:
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"""
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@ -19,7 +20,7 @@ class likelihood:
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self.location = location
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self.scale = scale
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class probit(likelihood):
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class Probit(likelihood):
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"""
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Probit likelihood
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Y is expected to take values in {-1,1}
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@ -28,8 +29,6 @@ class probit(likelihood):
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L(x) = \\Phi (Y_i*f_i)
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$$
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"""
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def __init__(self,location=0,scale=1):
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likelihood.__init__(self,Y,location,scale)
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def moments_match(self,data_i,tau_i,v_i):
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"""
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@ -47,24 +46,18 @@ class probit(likelihood):
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sigma2_hat = 1./tau_i - (phi/((tau_i**2+tau_i)*Z_hat))*(z+phi/Z_hat)
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return Z_hat, mu_hat, sigma2_hat
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def predictive_values(self,mu,var,all=False):
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def predictive_values(self,mu,var):
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"""
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Compute mean, and conficence interval (percentiles 5 and 95) of the prediction
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"""
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mu = mu.flatten()
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var = var.flatten()
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mean = stats.norm.cdf(mu/np.sqrt(1+var))
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if all:
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p_05 = np.zeros([mu.size])
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p_95 = np.ones([mu.size])
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return mean, p_05, p_95
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else:
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return mean
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p_05 = np.zeros([mu.size])
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p_95 = np.ones([mu.size])
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return mean, p_05, p_95
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def _log_likelihood_gradients():
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return np.zeros(0) # there are no parameters of whcih to compute the gradients
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class poisson(likelihood):
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class Poisson(likelihood):
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"""
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Poisson likelihood
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Y is expected to take values in {0,1,2,...}
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@ -73,9 +66,6 @@ class poisson(likelihood):
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L(x) = \exp(\lambda) * \lambda**Y_i / Y_i!
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$$
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"""
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def __init__(self,Y,location=0,scale=1):
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assert len(Y[Y<0]) == 0, "Output cannot have negative values"
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likelihood.__init__(self,Y,location,scale)
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def moments_match(self,i,tau_i,v_i):
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"""
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@ -134,52 +124,12 @@ class poisson(likelihood):
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sigma2_hat = m2 - mu_hat**2 # Second central moment
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return float(Z_hat), float(mu_hat), float(sigma2_hat)
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def predictive_values(self,mu,var,all=False):
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def predictive_values(self,mu,var):
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"""
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Compute mean, and conficence interval (percentiles 5 and 95) of the prediction
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"""
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mean = np.exp(mu*self.scale + self.location)
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if all:
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tmp = stats.poisson.ppf(np.array([.05,.95]),mu)
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p_05 = tmp[:,0]
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p_95 = tmp[:,1]
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return mean,p_05,p_95
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else:
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return mean
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def _log_likelihood_gradients():
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raise NotImplementedError
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def plot(self,X,mu,var,phi,X_obs,Z=None,samples=0):
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assert X_obs.shape[1] == 1, 'Number of dimensions must be 1'
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gpplot(X,phi,phi.flatten())
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pb.plot(X_obs,self.Y,'kx',mew=1.5)
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if samples:
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phi_samples = np.vstack([np.random.poisson(phi.flatten(),phi.size) for s in range(samples)])
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pb.plot(X,phi_samples.T, alpha = 0.4, c='#3465a4', linewidth = 0.8)
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if Z is not None:
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pb.plot(Z,Z*0+pb.ylim()[0],'k|',mew=1.5,markersize=12)
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class gaussian(likelihood):
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"""
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Gaussian likelihood
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Y is expected to take values in (-inf,inf)
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"""
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def moments_match(self,i,tau_i,v_i):
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"""
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Moments match of the marginal approximation in EP algorithm
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:param i: number of observation (int)
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:param tau_i: precision of the cavity distribution (float)
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:param v_i: mean/variance of the cavity distribution (float)
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"""
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mu = v_i/tau_i
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sigma = np.sqrt(1./tau_i)
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s = 1. if self.Y[i] == 0 else 1./self.Y[i]
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sigma2_hat = 1./(1./sigma**2 + 1./s**2)
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mu_hat = sigma2_hat*(mu/sigma**2 + self.Y[i]/s**2)
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Z_hat = 1./np.sqrt(2*np.pi) * 1./np.sqrt(sigma**2+s**2) * np.exp(-.5*(mu-self.Y[i])**2/(sigma**2 + s**2))
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return Z_hat, mu_hat, sigma2_hat
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def _log_likelihood_gradients():
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raise NotImplementedError
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tmp = stats.poisson.ppf(np.array([.05,.95]),mu)
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p_05 = tmp[:,0]
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p_95 = tmp[:,1]
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return mean,p_05,p_95
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