Initial commit, setting up the laplace approximation for a student t

python/likelihoods/Laplace.py

@@ -0,0 +1,54 @@
+import nump as np
+import GPy
+from GPy.util.linalg import jitchol
+
+class Laplace(GPy.likelihoods.likelihood):
+    """Laplace approximation to a posterior"""
+
+    def __init__(self,data,likelihood_function):
+        """
+        Laplace Approximation
+
+        First find the moments \hat{f} and the hessian at this point (using Newton-Raphson)
+        then find the z^{prime} which allows this to be a normalised gaussian instead of a
+        non-normalized gaussian
+
+        Finally we must compute the GP variables (i.e. generate some Y^{squiggle} and z^{squiggle}
+        which makes a gaussian the same as the laplace approximation
+
+        Arguments
+        ---------
+
+        :data: @todo
+        :likelihood_function: @todo
+
+        """
+        GPy.likelihoods.likelihood.__init__(self)
+
+        self.data = data
+        self.likelihood_function = likelihood_function
+
+        #Inital values
+        self.N, self.D = self.data.shape
+
+    def _compute_GP_variables(self):
+        """
+        Generates data Y which would give the normal distribution identical to the laplace approximation
+
+        GPy expects a likelihood to be gaussian, so need to caluclate the points Y^{squiggle} and Z^{squiggle}
+        that makes the posterior match that found by a laplace approximation to a non-gaussian likelihood
+        """
+        raise NotImplementedError
+
+    def fit_full(self, K):
+        """
+        The laplace approximation algorithm
+        For nomenclature see Rasmussen & Williams 2006
+        :K: Covariance matrix
+        """
+        self.f = np.zeros(self.N)
+
+        #Find \hat(f) using a newton raphson optimizer for example
+
+        #At this point get the hessian matrix
+