Merge branch 'master' of github.com:SheffieldML/GPy

GPy/examples/BGPLVM_demo.py

@@ -1,37 +0,0 @@
-# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
-# Licensed under the BSD 3-clause license (see LICENSE.txt)
-
-import numpy as np
-import pylab as pb
-import GPy
-np.random.seed(123344)
-
-N = 10
-M = 3
-Q = 2
-D = 4
-#generate GPLVM-like data
-X = np.random.rand(N, Q)
-k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
-K = k.K(X)
-Y = np.random.multivariate_normal(np.zeros(N),K,D).T
-
-k = GPy.kern.linear(Q, ARD = True) + GPy.kern.white(Q)
-# k = GPy.kern.rbf(Q) + GPy.kern.rbf(Q) + GPy.kern.white(Q)
-# k = GPy.kern.rbf(Q) + GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
-# k = GPy.kern.rbf(Q, ARD = False)  + GPy.kern.white(Q, 0.00001)
-
-m = GPy.models.Bayesian_GPLVM(Y, Q, kernel = k,  M=M)
-m.constrain_positive('(rbf|bias|noise|white|S)')
-# m.constrain_fixed('S', 1)
-
-# pb.figure()
-# m.plot()
-# pb.title('PCA initialisation')
-# pb.figure()
-# m.optimize(messages = 1)
-# m.plot()
-# pb.title('After optimisation')
-m.ensure_default_constraints()
-m.randomize()
-m.checkgrad(verbose = 1)

GPy/examples/__init__.py

@@ -1,9 +1,8 @@
 # Copyright (c) 2012, GPy authors (see AUTHORS.txt).
 # Licensed under the BSD 3-clause license (see LICENSE.txt)
 
-# Please don't delete this without explaining to Neil the right way of doing this. I want to be able to run:
-# GPy.examples.regression.toy_rbf_1D() from ipython having imported GPy, and this seems to be the way to do it!
 import classification
 import regression
-import unsupervised
+import dimensionality_reduction
+import non_gaussian
 import tutorials

GPy/examples/classification.py

@@ -107,3 +107,80 @@ def toy_linear_1d_classification(seed=default_seed):
     print(m)
 
     return m
+
+def sparse_toy_linear_1d_classification(seed=default_seed):
+    """
+    Simple 1D classification example
+    :param seed : seed value for data generation (default is 4).
+    :type seed: int
+    """
+
+    data = GPy.util.datasets.toy_linear_1d_classification(seed=seed)
+    Y = data['Y'][:, 0:1]
+    Y[Y == -1] = 0
+
+    # Kernel object
+    kernel = GPy.kern.rbf(1)
+
+    # Likelihood object
+    distribution = GPy.likelihoods.likelihood_functions.probit()
+    likelihood = GPy.likelihoods.EP(Y,distribution)
+
+    Z = np.random.uniform(data['X'].min(),data['X'].max(),(10,1))
+
+    # Model definition
+    m = GPy.models.sparse_GP(data['X'],likelihood=likelihood,kernel=kernel,Z=Z)
+
+    m.ensure_default_constraints()
+    # Optimize
+    m.update_likelihood_approximation()
+    # Parameters optimization:
+    m.optimize()
+    #m.EPEM() #FIXME
+
+    # Plot
+    pb.subplot(211)
+    m.plot_f()
+    pb.subplot(212)
+    m.plot()
+    print(m)
+
+    return m
+
+def sparse_crescent_data(inducing=10, seed=default_seed):
+    """Run a Gaussian process classification on the crescent data. The demonstration calls the basic GP classification model and uses EP to approximate the likelihood.
+
+    :param model_type: type of model to fit ['Full', 'FITC', 'DTC'].
+    :param seed : seed value for data generation.
+    :type seed: int
+    :param inducing : number of inducing variables (only used for 'FITC' or 'DTC').
+    :type inducing: int
+    """
+
+    data = GPy.util.datasets.crescent_data(seed=seed)
+
+    # Kernel object
+    kernel = GPy.kern.rbf(data['X'].shape[1]) + GPy.kern.white(data['X'].shape[1])
+
+    # Likelihood object
+    distribution = GPy.likelihoods.likelihood_functions.probit()
+    likelihood = GPy.likelihoods.EP(data['Y'],distribution)
+
+    sample = np.random.randint(0,data['X'].shape[0],inducing)
+    Z = data['X'][sample,:]
+    #Z = (np.random.random_sample(2*inducing)*(data['X'].max()-data['X'].min())+data['X'].min()).reshape(inducing,-1)
+
+    # create sparse GP EP model
+    m = GPy.models.sparse_GP(data['X'],likelihood=likelihood,kernel=kernel,Z=Z)
+    m.ensure_default_constraints()
+    m.set('len',10.)
+
+    m.update_likelihood_approximation()
+
+    # optimize
+    m.optimize()
+    print(m)
+
+    # plot
+    m.plot()
+    return m

GPy/examples/dimensionality_reduction.py

@@ -0,0 +1,56 @@
+# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+import numpy as np
+import pylab as pb
+import GPy
+
+default_seed = np.random.seed(123344)
+
+def BGPLVM(seed = default_seed):
+    N = 10
+    M = 3
+    Q = 2
+    D = 4
+    #generate GPLVM-like data
+    X = np.random.rand(N, Q)
+    k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
+    K = k.K(X)
+    Y = np.random.multivariate_normal(np.zeros(N),K,D).T
+
+    k = GPy.kern.linear(Q, ARD = True) + GPy.kern.white(Q)
+    # k = GPy.kern.rbf(Q) + GPy.kern.rbf(Q) + GPy.kern.white(Q)
+    # k = GPy.kern.rbf(Q) + GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
+    # k = GPy.kern.rbf(Q, ARD = False)  + GPy.kern.white(Q, 0.00001)
+
+    m = GPy.models.Bayesian_GPLVM(Y, Q, kernel = k,  M=M)
+    m.constrain_positive('(rbf|bias|noise|white|S)')
+    # m.constrain_fixed('S', 1)
+
+    # pb.figure()
+    # m.plot()
+    # pb.title('PCA initialisation')
+    # pb.figure()
+    # m.optimize(messages = 1)
+    # m.plot()
+    # pb.title('After optimisation')
+    m.ensure_default_constraints()
+    m.randomize()
+    m.checkgrad(verbose = 1)
+
+    return m
+
+def GPLVM_oil_100():
+    data = GPy.util.datasets.oil_100()
+
+    # create simple GP model
+    m = GPy.models.GPLVM(data['X'], 2)
+
+
+    # optimize
+    m.ensure_default_constraints()
+    m.optimize()
+
+    # plot
+    print(m)
+    return m

GPy/examples/non_gaussian.py

@@ -11,7 +11,7 @@ import GPy
 
 default_seed=10000
 
-def  toy_1d(seed=default_seed):
+def  toy_poisson_1d(seed=default_seed):
     """
     Simple 1D classification example
     :param seed : seed value for data generation (default is 4).

GPy/examples/oil_flow_demo.py

@@ -1,57 +0,0 @@
-# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
-# Licensed under the BSD 3-clause license (see LICENSE.txt)
-
-
-import cPickle as pickle
-import numpy as np
-import pylab as pb
-import GPy
-import pylab as plt
-np.random.seed(3)
-
-def plot_oil(X, theta, labels, label):
-    plt.figure()
-    X = X[:,np.argsort(theta)[:2]]
-    flow_type = (X[labels[:,0]==1])
-    plt.plot(flow_type[:,0], flow_type[:,1], 'rx')
-    flow_type = (X[labels[:,1]==1])
-    plt.plot(flow_type[:,0], flow_type[:,1], 'gx')
-    flow_type = (X[labels[:,2]==1])
-    plt.plot(flow_type[:,0], flow_type[:,1], 'bx')
-    plt.title(label)
-
-data = pickle.load(open('../../../GPy_assembla/datasets/oil_flow_3classes.pickle', 'r'))
-
-Y = data['DataTrn']
-N, D = Y.shape
-selected = np.random.permutation(N)[:350]
-labels = data['DataTrnLbls'][selected]
-Y = Y[selected]
-N, D = Y.shape
-Y -= Y.mean(axis=0)
-# Y /= Y.std(axis=0)
-
-Q = 5
-k = GPy.kern.linear(Q, ARD = True) + GPy.kern.white(Q)
-m = GPy.models.Bayesian_GPLVM(Y, Q, kernel = k, M = 20)
-m.constrain_positive('(rbf|bias|S|linear|white|noise)')
-
-# m.unconstrain('noise')
-# m.constrain_fixed('noise_precision', 50.0)
-# m.unconstrain('white')
-# m.constrain_bounded('white', 1e-6, 10.0)
-# plot_oil(m.X, np.array([1,1]), labels, 'PCA initialization')
-#m.optimize(messages = True)
-# m.optimize('tnc', messages = True)
-# plot_oil(m.X, m.kern.parts[0].lengthscale, labels, 'B-GPLVM')
-# # pb.figure()
-# m.plot()
-# pb.title('PCA initialisation')
-# pb.figure()
-# m.optimize(messages = 1)
-# m.plot()
-# pb.title('After optimisation')
-# m = GPy.models.GPLVM(Y, Q)
-# m.constrain_positive('(white|rbf|bias|noise)')
-# m.optimize()
-# plot_oil(m.X, np.array([1,1]), labels, 'GPLVM')

GPy/examples/regression.py

@@ -108,9 +108,6 @@ def coregionalisation_toy2():
     pb.plot(X2[:,0],Y2[:,0],'gx',mew=2)
     return m
 
-
-
-
 def coregionalisation_toy():
     """
     A simple demonstration of coregionalisation on two sinusoidal functions
@@ -211,7 +208,7 @@ def multiple_optima(gene_number=937,resolution=80, model_restarts=10, seed=10000
 
     xlim = ax.get_xlim()
     ylim = ax.get_ylim()
-    
+
     # Now run a few optimizations
     models = []
     optim_point_x = np.empty(2)
@@ -219,18 +216,18 @@ def multiple_optima(gene_number=937,resolution=80, model_restarts=10, seed=10000
     np.random.seed(seed=seed)
     for i in range(0, model_restarts):
         kern = GPy.kern.rbf(1, variance=np.random.exponential(1.), lengthscale=np.random.exponential(50.)) + GPy.kern.white(1,variance=np.random.exponential(1.))
-        
+
         m = GPy.models.GP_regression(data['X'],data['Y'], kernel=kern)
         optim_point_x[0] = m.get('rbf_lengthscale')
         optim_point_y[0] = np.log10(m.get('rbf_variance')) - np.log10(m.get('white_variance'));
-        
+
         # optimize
         m.ensure_default_constraints()
         m.optimize(xtol=1e-6,ftol=1e-6)
 
         optim_point_x[1] = m.get('rbf_lengthscale')
         optim_point_y[1] = np.log10(m.get('rbf_variance')) - np.log10(m.get('white_variance'));
-        
+
         pb.arrow(optim_point_x[0], optim_point_y[0], optim_point_x[1]-optim_point_x[0], optim_point_y[1]-optim_point_y[0], label=str(i), head_length=1, head_width=0.5, fc='k', ec='k')
         models.append(m)
 
@@ -264,7 +261,7 @@ def contour_data(data, length_scales, log_SNRs, signal_kernel_call=GPy.kern.rbf)
             total_var = (np.dot(np.dot(data['Y'].T,GPy.util.linalg.pdinv(K)[0]), data['Y'])/data['Y'].shape[0])[0,0]
             noise_var *= total_var
             signal_var *= total_var
-            
+
             kernel = signal_kernel_call(1, variance=signal_var, lengthscale=length_scale) + GPy.kern.white(1, variance=noise_var)
 
             model = GPy.models.GP_regression(data['X'], data['Y'], kernel=kernel)
@@ -273,3 +270,70 @@ def contour_data(data, length_scales, log_SNRs, signal_kernel_call=GPy.kern.rbf)
         lls.append(length_scale_lls)
     return np.array(lls)
 
+def sparse_GP_regression_1D(N = 400, M = 5):
+    """Run a 1D example of a sparse GP regression."""
+    # 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.rbf(1)
+    noise = GPy.kern.white(1)
+    kernel = rbf + noise
+    # create simple GP model
+    m = GPy.models.sparse_GP_regression(X, Y, kernel, M=M)
+
+    m.constrain_positive('(variance|lengthscale|precision)')
+
+    m.checkgrad(verbose=1)
+    m.optimize('tnc', messages = 1)
+    m.plot()
+    return m
+
+def sparse_GP_regression_2D(N = 400, M = 50):
+    """Run a 2D example of a sparse GP regression."""
+    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
+    m = GPy.models.sparse_GP_regression(X,Y,kernel, M = M)
+
+    # contrain all parameters to be positive (but not inducing inputs)
+    m.constrain_positive('(variance|lengthscale|precision)')
+    m.set('len',2.)
+
+    m.checkgrad()
+
+    # optimize and plot
+    pb.figure()
+    m.optimize('tnc', messages = 1)
+    m.plot()
+    print(m)
+    return m
+
+def uncertain_inputs_sparse_regression():
+    """Run a 1D example of a sparse GP regression with uncertain inputs."""
+    # sample inputs and outputs
+    S = np.ones((20,1))
+    X = np.random.uniform(-3.,3.,(20,1))
+    Y = np.sin(X)+np.random.randn(20,1)*0.05
+    likelihood = GPy.likelihoods.Gaussian(Y)
+    Z = np.random.uniform(-3.,3.,(7,1))
+
+    k = GPy.kern.rbf(1) + GPy.kern.white(1)
+
+    # create simple GP model
+    m = GPy.models.sparse_GP(X, likelihood, kernel=k, Z=Z, X_uncertainty=S)
+
+    # contrain all parameters to be positive
+    m.constrain_positive('(variance|prec)')
+
+    # optimize and plot
+    m.optimize('tnc', max_f_eval = 1000, messages=1)
+    m.plot()
+    print(m)
+    return m

GPy/examples/sparse_GPLVM_demo.py

@@ -1,30 +0,0 @@
-# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
-# Licensed under the BSD 3-clause license (see LICENSE.txt)
-
-
-import numpy as np
-import pylab as pb
-import GPy
-np.random.seed(1)
-print "sparse GPLVM with RBF kernel"
-
-N = 100
-M = 8
-Q = 1
-D = 2
-#generate GPLVM-like data
-X = np.random.rand(N, Q)
-k = GPy.kern.rbf(Q, 1.0, 2.0) + GPy.kern.white(Q, 0.00001)
-K = k.K(X)
-Y = np.random.multivariate_normal(np.zeros(N),K,D).T
-
-m = GPy.models.sparse_GPLVM(Y, Q, M=M)
-m.constrain_positive('(rbf|bias|noise|white)')
-
-pb.figure()
-m.plot()
-pb.title('PCA initialisation')
-pb.figure()
-m.optimize(messages = 1)
-m.plot()
-pb.title('After optimisation')

GPy/examples/sparse_GP_regression_demo.py

@@ -1,64 +0,0 @@
-# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
-# Licensed under the BSD 3-clause license (see LICENSE.txt)
-
-
-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 = 400
-M = 5
-
-######################################
-## 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.rbf(1)
-noise = GPy.kern.white(1)
-kernel = rbf + noise
-
-# create simple GP model
-m = GPy.models.sparse_GP_regression(X, Y, kernel, M=M)
-
-m.constrain_positive('(variance|lengthscale|precision)')
-
-m.checkgrad(verbose=1)
-m.optimize('tnc', messages = 1)
-m.plot()
-
-######################################
-## 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)

GPy/examples/sparse_ep_fix.py

@@ -1,95 +0,0 @@
-# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
-# Licensed under the BSD 3-clause license (see LICENSE.txt)
-
-
-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)
-N = 500
-M = 5
-
-default_seed=10000
-
-def crescent_data(inducing=10, seed=default_seed):
-    """Run a Gaussian process classification on the crescent data. The demonstration calls the basic GP classification model and uses EP to approximate the likelihood.
-
-    :param model_type: type of model to fit ['Full', 'FITC', 'DTC'].
-    :param seed : seed value for data generation.
-    :type seed: int
-    :param inducing : number of inducing variables (only used for 'FITC' or 'DTC').
-    :type inducing: int
-    """
-
-    data = GPy.util.datasets.crescent_data(seed=seed)
-
-    # Kernel object
-    kernel = GPy.kern.rbf(data['X'].shape[1]) + GPy.kern.white(data['X'].shape[1])
-
-    # Likelihood object
-    distribution = GPy.likelihoods.likelihood_functions.probit()
-    likelihood = GPy.likelihoods.EP(data['Y'],distribution)
-
-    sample = np.random.randint(0,data['X'].shape[0],inducing)
-    Z = data['X'][sample,:]
-    #Z = (np.random.random_sample(2*inducing)*(data['X'].max()-data['X'].min())+data['X'].min()).reshape(inducing,-1)
-
-    # create sparse GP EP model
-    m = GPy.models.sparse_GP(data['X'],likelihood=likelihood,kernel=kernel,Z=Z)
-    m.ensure_default_constraints()
-
-    m.update_likelihood_approximation()
-    print(m)
-
-    # optimize
-    m.optimize()
-    print(m)
-
-    # plot
-    m.plot()
-    return m
-
-
-def toy_linear_1d_classification(seed=default_seed):
-    """
-    Simple 1D classification example
-    :param seed : seed value for data generation (default is 4).
-    :type seed: int
-    """
-
-    data = GPy.util.datasets.toy_linear_1d_classification(seed=seed)
-    Y = data['Y'][:, 0:1]
-    Y[Y == -1] = 0
-
-    # Kernel object
-    kernel = GPy.kern.rbf(1)
-
-    # Likelihood object
-    distribution = GPy.likelihoods.likelihood_functions.probit()
-    likelihood = GPy.likelihoods.EP(Y,distribution)
-
-    Z = np.random.uniform(data['X'].min(),data['X'].max(),(10,1))
-
-    # Model definition
-    m = GPy.models.sparse_GP(data['X'],likelihood=likelihood,kernel=kernel,Z=Z)
-
-    m.ensure_default_constraints()
-    # Optimize
-    m.update_likelihood_approximation()
-    # Parameters optimization:
-    m.optimize()
-    #m.EPEM() #FIXME
-
-    # Plot
-    pb.subplot(211)
-    m.plot_f()
-    pb.subplot(212)
-    m.plot()
-    print(m)
-
-    return m
-

GPy/examples/uncertain_input_GP_regression_demo.py

@@ -1,27 +0,0 @@
-# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
-# Licensed under the BSD 3-clause license (see LICENSE.txt)
-
-import pylab as pb
-import numpy as np
-import GPy
-pb.ion()
-pb.close('all')
-
-
-# sample inputs and outputs
-S = np.ones((20,1))
-X = np.random.uniform(-3.,3.,(20,1))
-Y = np.sin(X)+np.random.randn(20,1)*0.05
-
-k = GPy.kern.rbf(1) + GPy.kern.white(1)
-
-# create simple GP model
-m = GPy.models.sparse_GP_regression(X,Y,X_uncertainty=S,kernel=k)
-
-# contrain all parameters to be positive
-m.constrain_positive('(variance|prec)')
-
-# optimize and plot
-m.optimize('tnc', max_f_eval = 1000, messages=1)
-m.plot()
-print(m)

GPy/examples/uncollapsed_GP_demo.py

@@ -1,32 +0,0 @@
-# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
-# Licensed under the BSD 3-clause license (see LICENSE.txt)
-
-
-import numpy as np
-"""
-Sparse Gaussian Processes regression with an RBF kernel, 
-using the uncollapsed sparse GP (where the distribution of the 
-inducing points is explicitley represented)
-"""
-import pylab as pb
-import numpy as np
-import GPy
-np.random.seed(2)
-pb.ion()
-N = 500
-M = 20
-
-# sample inputs and outputs
-X = np.random.uniform(-3.,3.,(N,1))
-Y = np.sin(X)+np.random.randn(N,1)*0.05
-
-kernel = GPy.kern.rbf(1) + GPy.kern.white(1)
-
-# create simple GP model
-m = GPy.models.uncollapsed_sparse_GP(X, Y, kernel=kernel, M=M)#, X_uncertainty=np.zeros_like(X)+0.01)
-
-# contrain all parameters to be positive
-m.ensure_default_constraints()
-m.checkgrad()
-# optimize and plot
-m.plot()

GPy/examples/unsupervised.py

@@ -1,25 +0,0 @@
-"""
-Usupervised learning with Gaussian Processes.
-"""
-import pylab as pb
-import numpy as np
-import GPy
-
-
-######################################
-## Oil data subsampled to 100 points.
-def oil_100():
-    data = GPy.util.datasets.oil_100()
-
-    # create simple GP model
-    m = GPy.models.GPLVM(data['X'], 2)
-
-
-    # optimize
-    m.ensure_default_constraints()
-    m.optimize()
-
-    # plot
-    print(m)
-    return m
-