inference

GPy/inference/likelihoods.py

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+import numpy as np
+from scipy import stats
+import scipy as sp
+import pylab as pb
+from ..util.plot import gpplot
+
+class likelihood:
+    def __init__(self,Y):
+        """
+        Likelihood class for doing Expectation propagation
+
+        :param Y: observed output (Nx1 numpy.darray)
+        ..Note:: Y values allowed depend on the likelihood used
+        """
+        self.Y = Y
+        self.N = self.Y.shape[0]
+
+    def plot1Da(self,X_new,Mean_new,Var_new,X_u,Mean_u,Var_u):
+        """
+        Plot the predictive distribution of the GP model for 1-dimensional inputs
+
+        :param X_new: The points at which to make a prediction
+        :param Mean_new: mean values at X_new
+        :param Var_new: variance values at X_new
+        :param X_u: input (inducing)  points used to train the model
+        :param Mean_u: mean values at X_u
+        :param Var_new: variance values at X_u
+        """
+        assert X_new.shape[1] == 1, 'Number of dimensions must be 1'
+        gpplot(X_new,Mean_new,Var_new)
+        pb.errorbar(X_u,Mean_u,2*np.sqrt(Var_u),fmt='r+')
+        pb.plot(X_u,Mean_u,'ro')
+
+    def plot2D(self,X,X_new,F_new,U=None):
+        """
+        Predictive distribution of the fitted GP model for 2-dimensional inputs
+
+        :param X_new: The points at which to make a prediction
+        :param Mean_new: mean values at X_new
+        :param Var_new: variance values at X_new
+        :param X_u: input points used to train the model
+        :param Mean_u: mean values at X_u
+        :param Var_new: variance values at X_u
+        """
+        N,D = X_new.shape
+        assert D == 2, 'Number of dimensions must be 2'
+        n = np.sqrt(N)
+        x1min = X_new[:,0].min()
+        x1max = X_new[:,0].max()
+        x2min = X_new[:,1].min()
+        x2max = X_new[:,1].max()
+        pb.imshow(F_new.reshape(n,n),extent=(x1min,x1max,x2max,x2min),vmin=0,vmax=1)
+        pb.colorbar()
+        C1 = np.arange(self.N)[self.Y.flatten()==1]
+        C2 = np.arange(self.N)[self.Y.flatten()==-1]
+        [pb.plot(X[i,0],X[i,1],'ro') for i in C1]
+        [pb.plot(X[i,0],X[i,1],'bo') for i in C2]
+        pb.xlim(x1min,x1max)
+        pb.ylim(x2min,x2max)
+        if U is not None:
+            [pb.plot(a,b,'wo') for a,b in U]
+
+class probit(likelihood):
+    """
+    Probit likelihood
+    Y is expected to take values in {-1,1}
+    -----
+    $$
+    L(x) = \\Phi (Y_i*f_i)
+    $$
+    """
+    def moments_match(self,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 = self.Y[i]*v_i/np.sqrt(tau_i**2 + tau_i)
+        Z_hat = stats.norm.cdf(z)
+        phi = stats.norm.pdf(z)
+        mu_hat = v_i/tau_i + self.Y[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 plot1Db(self,X,X_new,F_new,U=None):
+        assert X.shape[1] == 1, 'Number of dimensions must be 1'
+        gpplot(X_new,F_new,np.zeros(X_new.shape[0]))
+        pb.plot(X,(self.Y+1)/2,'kx',mew=1.5)
+        pb.ylim(-0.2,1.2)
+        if U is not None:
+            pb.plot(U,U*0+.5,'r|',mew=1.5,markersize=12)
+
+    def predictive_mean(self,mu,variance):
+        return stats.norm.cdf(mu/np.sqrt(1+variance))
+
+    def log_likelihood_gradients():
+        raise NotImplementedError
+