some more messing with the likelihood directory

GPy/likelihoods/link_functions.py

@@ -0,0 +1,158 @@
+# Copyright (c) 2012, 2013 The GPy authors
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+import numpy as np
+from scipy import stats
+import scipy as sp
+import pylab as pb
+from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf,inv_std_norm_cdf
+
+class GPTransformation(object):
+    """
+    Link function class for doing non-Gaussian likelihoods approximation
+
+    :param Y: observed output (Nx1 numpy.darray)
+
+    .. note:: Y values allowed depend on the likelihood_function used
+
+    """
+    def __init__(self):
+        pass
+
+    def transf(self,f):
+        """
+        Gaussian process tranformation function, latent space -> output space
+        """
+        raise NotImplementedError
+
+    def dtransf_df(self,f):
+        """
+        derivative of transf(f) w.r.t. f
+        """
+        raise NotImplementedError
+
+    def d2transf_df2(self,f):
+        """
+        second derivative of transf(f) w.r.t. f
+        """
+        raise NotImplementedError
+
+    def d3transf_df3(self,f):
+        """
+        third derivative of transf(f) w.r.t. f
+        """
+        raise NotImplementedError
+
+class Identity(GPTransformation):
+    """
+    .. math::
+
+        g(f) = f
+
+    """
+    def transf(self,f):
+        return f
+
+    def dtransf_df(self,f):
+        return np.ones_like(f)
+
+    def d2transf_df2(self,f):
+        return np.zeros_like(f)
+
+    def d3transf_df3(self,f):
+        return np.zeros_like(f)
+
+
+class Probit(GPTransformation):
+    """
+    .. math::
+
+        g(f) = \\Phi^{-1} (mu)
+
+    """
+    def transf(self,f):
+        return std_norm_cdf(f)
+
+    def dtransf_df(self,f):
+        return std_norm_pdf(f)
+
+    def d2transf_df2(self,f):
+        #FIXME
+        return -f * std_norm_pdf(f)
+
+    def d3transf_df3(self,f):
+        #FIXME
+        f2 = f**2
+        return -(1/(np.sqrt(2*np.pi)))*np.exp(-0.5*(f2))*(1-f2)
+
+class Log(GPTransformation):
+    """
+    .. math::
+
+        g(f) = \\log(\\mu)
+
+    """
+    def transf(self,f):
+        return np.exp(f)
+
+    def dtransf_df(self,f):
+        return np.exp(f)
+
+    def d2transf_df2(self,f):
+        return np.exp(f)
+
+    def d3transf_df3(self,f):
+        return np.exp(f)
+
+class Log_ex_1(GPTransformation):
+    """
+    .. math::
+
+        g(f) = \\log(\\exp(\\mu) - 1)
+
+    """
+    def transf(self,f):
+        return np.log(1.+np.exp(f))
+
+    def dtransf_df(self,f):
+        return np.exp(f)/(1.+np.exp(f))
+
+    def d2transf_df2(self,f):
+        aux = np.exp(f)/(1.+np.exp(f))
+        return aux*(1.-aux)
+
+    def d3transf_df3(self,f):
+        aux = np.exp(f)/(1.+np.exp(f))
+        daux_df = aux*(1.-aux)
+        return daux_df - (2.*aux*daux_df)
+
+class Reciprocal(GPTransformation):
+    def transf(self,f):
+        return 1./f
+
+    def dtransf_df(self,f):
+        return -1./(f**2)
+
+    def d2transf_df2(self,f):
+        return 2./(f**3)
+
+    def d3transf_df3(self,f):
+        return -6./(f**4)
+
+class Heaviside(GPTransformation):
+    """
+
+    .. math::
+
+        g(f) = I_{x \\in A}
+
+    """
+    def transf(self,f):
+        #transformation goes here
+        return np.where(f>0, 1, 0)
+
+    def dtransf_df(self,f):
+        raise NotImplementedError, "This function is not differentiable!"
+
+    def d2transf_df2(self,f):
+        raise NotImplementedError, "This function is not differentiable!"