Got most of laplace approximation working

python/examples/laplace_approximations.py

@@ -1,8 +1,9 @@
 import GPy
 import numpy as np
-import scipy as sp
-import scipy.stats
 import matplotlib.pyplot as plt
+from scipy.stats import t
+from coxGP.python.likelihoods.Laplace import Laplace
+from coxGP.python.likelihoods.likelihood_function import student_t
 
 
 def student_t_approx():
@@ -13,6 +14,41 @@ def student_t_approx():
     X = np.sort(np.random.uniform(0, 15, 70))[:, None]
     Y = np.sin(X)
 
+    #Add student t random noise to datapoints
+    deg_free = 1
+    noise = t.rvs(deg_free, loc=1.8, scale=1, size=Y.shape)
+    Y += noise
+
+    # Kernel object
+    print X.shape
+    kernel = GPy.kern.rbf(X.shape[1])
+
+    #A GP should completely break down due to the points as they get a lot of weight
+    # create simple GP model
+    m = GPy.models.GP_regression(X, Y, kernel=kernel)
+
+    # optimize
+    m.ensure_default_constraints()
+    m.optimize()
+    # plot
+    #m.plot()
+    print m
+
+    #with a student t distribution, since it has heavy tails it should work well
+    likelihood_function = student_t(deg_free, sigma=1)
+    lap = Laplace(Y, likelihood_function)
+    cov = kernel.K(X)
+    lap.fit_full(cov)
+
+
+def noisy_laplace_approx():
+    """
+    Example of regressing with a student t likelihood
+    """
+    #Start a function, any function
+    X = np.sort(np.random.uniform(0, 15, 70))[:, None]
+    Y = np.sin(X)
+
     #Add some extreme value noise to some of the datapoints
     percent_corrupted = 0.05
     corrupted_datums = int(np.round(Y.shape[0] * percent_corrupted))
@@ -20,12 +56,12 @@ def student_t_approx():
     np.random.shuffle(indices)
     corrupted_indices = indices[:corrupted_datums]
     print corrupted_indices
-    noise = np.random.uniform(-10,10,(len(corrupted_indices), 1))
+    noise = np.random.uniform(-10, 10, (len(corrupted_indices), 1))
     Y[corrupted_indices] += noise
 
     #A GP should completely break down due to the points as they get a lot of weight
     # create simple GP model
-    m = GPy.models.GP_regression(X,Y)
+    m = GPy.models.GP_regression(X, Y)
 
     # optimize
     m.ensure_default_constraints()