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

python/examples/laplace_approximations.py

@@ -0,0 +1,37 @@
+import GPy
+import numpy as np
+import scipy as sp
+import scipy.stats
+import matplotlib.pyplot as plt
+
+
+def student_t_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))
+    indices = np.arange(Y.shape[0])
+    np.random.shuffle(indices)
+    corrupted_indices = indices[:corrupted_datums]
+    print corrupted_indices
+    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)
+
+    # 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