files re-organized

GPy/likelihoods/noise_models/binomial_noise.py

@@ -0,0 +1,111 @@
+# Copyright (c) 2012, 2013 Ricardo Andrade
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+import numpy as np
+from scipy import stats,special
+import scipy as sp
+from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf
+import gp_transformations
+from noise_distributions import NoiseDistribution
+
+class Binomial(NoiseDistribution):
+    """
+    Probit likelihood
+    Y is expected to take values in {-1,1}
+    -----
+    $$
+    L(x) = \\Phi (Y_i*f_i)
+    $$
+    """
+    def __init__(self,gp_link=None,analytical_moments=False):
+        super(Binomial, self).__init__(gp_link,analytical_moments)
+
+    def _preprocess_values(self,Y):
+        """
+        Check if the values of the observations correspond to the values
+        assumed by the likelihood function.
+
+        ..Note:: Binary classification algorithm works better with classes {-1,1}
+        """
+        Y_prep = Y.copy()
+        Y1 = Y[Y.flatten()==1].size
+        Y2 = Y[Y.flatten()==0].size
+        assert Y1 + Y2 == Y.size, 'Binomial likelihood is meant to be used only with outputs in {0,1}.'
+        Y_prep[Y.flatten() == 0] = -1
+        return Y_prep
+
+    def _moments_match_analytical(self,data_i,tau_i,v_i):
+        """
+        Moments match of the marginal approximation in EP algorithm
+
+        :param i: number of observation (int)
+        :param tau_i: precision of the cavity distribution (float)
+        :param v_i: mean/variance of the cavity distribution (float)
+        """
+        z = data_i*v_i/np.sqrt(tau_i**2 + tau_i)
+        Z_hat = std_norm_cdf(z)
+        phi = std_norm_pdf(z)
+        mu_hat = v_i/tau_i + data_i*phi/(Z_hat*np.sqrt(tau_i**2 + tau_i))
+        sigma2_hat = 1./tau_i - (phi/((tau_i**2+tau_i)*Z_hat))*(z+phi/Z_hat)
+        return Z_hat, mu_hat, sigma2_hat
+
+    def _predictive_mean_analytical(self,mu,sigma):
+        return stats.norm.cdf(mu/np.sqrt(1+sigma**2))
+
+    def _mass(self,gp,obs):
+        #NOTE obs must be in {0,1}
+        p = self.gp_link.transf(gp)
+        return p**obs * (1.-p)**(1.-obs)
+
+    def _nlog_mass(self,gp,obs):
+        p = self.gp_link.transf(gp)
+        return obs*np.log(p) + (1.-obs)*np.log(1-p)
+
+    def _dnlog_mass_dgp(self,gp,obs):
+        p = self.gp_link.transf(gp)
+        dp = self.gp_link.dtransf_df(gp)
+        return obs/p * dp - (1.-obs)/(1.-p) * dp
+
+    def _d2nlog_mass_dgp2(self,gp,obs):
+        p = self.gp_link.transf(gp)
+        return (obs/p + (1.-obs)/(1.-p))*self.gp_link.d2transf_df2(gp) + ((1.-obs)/(1.-p)**2-obs/p**2)*self.gp_link.dtransf_df(gp)
+
+    def _mean(self,gp):
+        """
+        Mass (or density) function
+        """
+        return self.gp_link.transf(gp)
+
+    def _dmean_dgp(self,gp):
+        return self.gp_link.dtransf_df(gp)
+
+    def _d2mean_dgp2(self,gp):
+        return self.gp_link.d2transf_df2(gp)
+
+    def _variance(self,gp):
+        """
+        Mass (or density) function
+        """
+        p = self.gp_link.transf(gp)
+        return p*(1-p)
+
+    def _dvariance_dgp(self,gp):
+        return self.gp_link.dtransf_df(gp)*(1. - 2.*self.gp_link.transf(gp))
+
+    def _d2variance_dgp2(self,gp):
+        return self.gp_link.d2transf_df2(gp)*(1. - 2.*self.gp_link.transf(gp)) - 2*self.gp_link.dtransf_df(gp)**2
+
+    """
+    def predictive_values(self,mu,var): #TODO remove
+        mu = mu.flatten()
+        var = var.flatten()
+        #mean = stats.norm.cdf(mu/np.sqrt(1+var))
+        mean = self._predictive_mean_analytical(mu,np.sqrt(var))
+        norm_025 = [stats.norm.ppf(.025,m,v) for m,v in zip(mu,var)]
+        norm_975 = [stats.norm.ppf(.975,m,v) for m,v in zip(mu,var)]
+        #p_025 = stats.norm.cdf(norm_025/np.sqrt(1+var))
+        #p_975 = stats.norm.cdf(norm_975/np.sqrt(1+var))
+        p_025 = self._predictive_mean_analytical(norm_025,np.sqrt(var))
+        p_975 = self._predictive_mean_analytical(norm_975,np.sqrt(var))
+        return mean[:,None], np.nan*var, p_025[:,None], p_975[:,None] # TODO: var
+    """