examples

GPy/examples/sparse_GP_regression_demo.py

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+import numpy as np
+"""
+Sparse Gaussian Processes regression with an RBF kernel
+"""
+import pylab as pb
+import numpy as np
+import GPy
+np.random.seed(2)
+pb.ion()
+N = 500
+
+######################################
+## 1 dimensional example
+
+# sample inputs and outputs
+X = np.random.uniform(-3.,3.,(N,1))
+Y = np.sin(X)+np.random.randn(N,1)*0.05
+
+# construct kernel
+rbf =  GPy.kern.Matern52(1)
+noise = GPy.kern.white(1)
+kernel = rbf + noise
+
+# create simple GP model
+m1 = GPy.models.sparse_GP_regression(X,Y,kernel, M = 10)
+
+# contrain all parameters to be positive
+m1.constrain_positive('(variance|lengthscale|precision)')
+#m1.constrain_positive('(variance|lengthscale)')
+#m1.constrain_fixed('prec',10.)
+
+
+#check gradient FIXME unit test please
+m1.checkgrad()
+# optimize and plot
+m1.optimize('bfgs', messages = 1)
+m1.plot()
+# print(m1)
+
+######################################
+## 2 dimensional example
+
+# # sample inputs and outputs
+# X = np.random.uniform(-3.,3.,(N,2))
+# Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(N,1)*0.05
+
+# # construct kernel
+# rbf =  GPy.kern.rbf(2)
+# noise = GPy.kern.white(2)
+# kernel = rbf + noise
+
+# # create simple GP model
+# m2 = GPy.models.sparse_GP_regression(X,Y,kernel, M = 50)
+# create simple GP model
+
+# # contrain all parameters to be positive (but not inducing inputs)
+# m2.constrain_positive('(variance|lengthscale|precision)')
+
+# #check gradient FIXME unit test please
+# m2.checkgrad()
+
+# # optimize and plot
+# pb.figure()
+# m2.optimize('tnc', messages = 1)
+# m2.plot()
+# print(m2)