Added binomial likelihood

Also some changes to pass through Y_metadata, where it had previously
been (errorneously) omitted.

GPy/inference/latent_function_inference/svgp.py

@@ -43,7 +43,7 @@ class SVGP(LatentFunctionInference):
 
 
         #quadrature for the likelihood
-        F, dF_dmu, dF_dv, dF_dthetaL = likelihood.variational_expectations(Y, mu, v)
+        F, dF_dmu, dF_dv, dF_dthetaL = likelihood.variational_expectations(Y, mu, v, Y_metadata=Y_metadata)
 
         #rescale the F term if working on a batch
         F, dF_dmu, dF_dv =  F*batch_scale, dF_dmu*batch_scale, dF_dv*batch_scale

GPy/likelihoods/__init__.py

@@ -6,3 +6,4 @@ from poisson import Poisson
 from student_t import StudentT
 from likelihood import Likelihood
 from mixed_noise import MixedNoise
+from binomial import Binomial

GPy/likelihoods/binomial.py

@@ -0,0 +1,125 @@
+# Copyright (c) 2012-2014 The GPy authors (see AUTHORS.txt)
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+import numpy as np
+from ..util.univariate_Gaussian import std_norm_pdf, std_norm_cdf
+import link_functions
+from likelihood import Likelihood
+from scipy import special
+
+class Binomial(Likelihood):
+    """
+    Binomial likelihood
+
+    .. math::
+        p(y_{i}|\\lambda(f_{i})) = \\lambda(f_{i})^{y_{i}}(1-f_{i})^{1-y_{i}}
+
+    .. Note::
+        Y takes values in either {-1, 1} or {0, 1}.
+        link function should have the domain [0, 1], e.g. probit (default) or Heaviside
+
+    .. See also::
+        likelihood.py, for the parent class
+    """
+    def __init__(self, gp_link=None):
+        if gp_link is None:
+            gp_link = link_functions.Probit()
+
+        super(Binomial, self).__init__(gp_link, 'Binomial')
+
+    def conditional_mean(self, gp, Y_metadata):
+        return self.gp_link(gp)*Y_metadata['trials']
+
+    def pdf_link(self, inv_link_f, y, Y_metadata):
+        """
+        Likelihood function given inverse link of f.
+
+        .. math::
+            p(y_{i}|\\lambda(f_{i})) = \\lambda(f_{i})^{y_{i}}(1-f_{i})^{1-y_{i}}
+
+        :param inv_link_f: latent variables inverse link of f.
+        :type inv_link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata must contain 'trials'
+        :returns: likelihood evaluated for this point
+        :rtype: float
+
+        .. Note:
+            Each y_i must be in {0, 1}
+        """
+        return np.exp(self.logpdf_link(inv_link_f, y, Y_metadata))
+
+    def logpdf_link(self, inv_link_f, y, Y_metadata=None):
+        """
+        Log Likelihood function given inverse link of f.
+
+        .. math::
+            \\ln p(y_{i}|\\lambda(f_{i})) = y_{i}\\log\\lambda(f_{i}) + (1-y_{i})\\log (1-f_{i})
+
+        :param inv_link_f: latent variables inverse link of f.
+        :type inv_link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata must contain 'trials'
+        :returns: log likelihood evaluated at points inverse link of f.
+        :rtype: float
+        """
+        N = Y_metadata['trials']
+        nchoosey = special.gammaln(N+1) - special.gammaln(y+1) - special.gammaln(N-y+1)
+
+        return nchoosey + y*np.log(inv_link_f) + (N-y)*np.log(1.-inv_link_f)
+
+    def dlogpdf_dlink(self, inv_link_f, y, Y_metadata=None):
+        """
+        Gradient of the pdf at y, given inverse link of f w.r.t inverse link of f.
+
+        :param inv_link_f: latent variables inverse link of f.
+        :type inv_link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata must contain 'trials'
+        :returns: gradient of log likelihood evaluated at points inverse link of f.
+        :rtype: Nx1 array
+        """
+        N = Y_metadata['trials']
+        return y/inv_link_f - (N-y)/(1-inv_link_f)
+
+    def d2logpdf_dlink2(self, inv_link_f, y, Y_metadata=None):
+        """
+        Hessian at y, given inv_link_f, w.r.t inv_link_f the hessian will be 0 unless i == j
+        i.e. second derivative logpdf at y given inverse link of f_i and inverse link of f_j  w.r.t inverse link of f_i and inverse link of f_j.
+
+
+        .. math::
+            \\frac{d^{2}\\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)^{2}} = \\frac{-y_{i}}{\\lambda(f)^{2}} - \\frac{(1-y_{i})}{(1-\\lambda(f))^{2}}
+
+        :param inv_link_f: latent variables inverse link of f.
+        :type inv_link_f: Nx1 array
+        :param y: data
+        :type y: Nx1 array
+        :param Y_metadata: Y_metadata not used in binomial
+        :returns: Diagonal of log hessian matrix (second derivative of log likelihood evaluated at points inverse link of f.
+        :rtype: Nx1 array
+
+        .. Note::
+            Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
+            (the distribution for y_i depends only on inverse link of f_i not on inverse link of f_(j!=i)
+        """
+        N = Y_metadata['trials']
+        return -y/np.square(inv_link_f) - (N-y)/np.square(1-inv_link_f)
+
+    def samples(self, gp, Y_metadata=None):
+        """
+        Returns a set of samples of observations based on a given value of the latent variable.
+
+        :param gp: latent variable
+        """
+        orig_shape = gp.shape
+        gp = gp.flatten()
+        N = Y_metadata['trials']
+        Ysim = np.random.binomial(N, self.gp_link.transf(gp))
+        return Ysim.reshape(orig_shape)
+
+    def exact_inference_gradients(self, dL_dKdiag,Y_metadata=None):
+        pass

GPy/likelihoods/likelihood.py

@@ -131,7 +131,7 @@ class Likelihood(Parameterized):
 
         return z, mean, variance
 
-    def variational_expectations(self, Y, m, v, gh_points=None):
+    def variational_expectations(self, Y, m, v, gh_points=None, Y_metadata=None):
         """
         Use Gauss-Hermite Quadrature to compute
 
@@ -158,9 +158,9 @@ class Likelihood(Parameterized):
 
         #evaluate the likelhood for the grid. First ax indexes the data (and mu, var) and the second indexes the grid.
         # broadcast needs to be handled carefully.
-        logp = self.logpdf(X,Y[:,None])
+        logp = self.logpdf(X,Y[:,None], Y_metadata=Y_metadata)
-        dlogp_dx = self.dlogpdf_df(X, Y[:,None])
+        dlogp_dx = self.dlogpdf_df(X, Y[:,None], Y_metadata=Y_metadata)
-        d2logp_dx2 = self.d2logpdf_df2(X, Y[:,None])
+        d2logp_dx2 = self.d2logpdf_df2(X, Y[:,None], Y_metadata=Y_metadata)
 
         #clipping for numerical stability
         #logp = np.clip(logp,-1e9,1e9)

GPy/likelihoods/poisson.py

@@ -64,8 +64,7 @@ class Poisson(Likelihood):
         :rtype: float
 
         """
-        assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
+        return -link_f + y*np.log(link_f) - special.gammaln(y+1)
-        return np.sum(-link_f + y*np.log(link_f) - special.gammaln(y+1))
 
     def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
         """
@@ -83,7 +82,6 @@ class Poisson(Likelihood):
         :rtype: Nx1 array
 
         """
-        assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
         return y/link_f - 1
 
     def d2logpdf_dlink2(self, link_f, y, Y_metadata=None):
@@ -107,12 +105,7 @@ class Poisson(Likelihood):
             Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
             (the distribution for y_i depends only on link(f_i) not on link(f_(j!=i))
         """
-        assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
+        return -y/(link_f**2) 
-        hess = -y/(link_f**2)
-        return hess
-        #d2_df = self.gp_link.d2transf_df2(gp)
-        #transf = self.gp_link.transf(gp)
-        #return obs * ((self.gp_link.dtransf_df(gp)/transf)**2 - d2_df/transf) + d2_df
 
     def d3logpdf_dlink3(self, link_f, y, Y_metadata=None):
         """