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Changed more examples to accept optimize and plot

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Alan Saul 2013-11-29 14:40:31 +00:00
parent 0a36d98a71
commit 98074e1e6c
3 changed files with 144 additions and 113 deletions
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40
GPy/examples/non_gaussian.py
View file

@ -263,24 +263,24 @@ def boston_example(optimize=True, plot=True):
ax.set_axisbelow(True) ax.set_axisbelow(True)
return mstu_t return mstu_t
def precipitation_example(): #def precipitation_example():
import sklearn #import sklearn
from sklearn.cross_validation import KFold #from sklearn.cross_validation import KFold
data = datasets.boston_housing() #data = datasets.boston_housing()
X = data['X'].copy() #X = data['X'].copy()
Y = data['Y'].copy() #Y = data['Y'].copy()
X = X-X.mean(axis=0) #X = X-X.mean(axis=0)
X = X/X.std(axis=0) #X = X/X.std(axis=0)
Y = Y-Y.mean() #Y = Y-Y.mean()
Y = Y/Y.std() #Y = Y/Y.std()
import ipdb; ipdb.set_trace() # XXX BREAKPOINT #import ipdb; ipdb.set_trace() # XXX BREAKPOINT
num_folds = 10 #num_folds = 10
kf = KFold(len(Y), n_folds=num_folds, indices=True) #kf = KFold(len(Y), n_folds=num_folds, indices=True)
score_folds = np.zeros((4, num_folds)) #score_folds = np.zeros((4, num_folds))
def rmse(Y, Ystar): #def rmse(Y, Ystar):
return np.sqrt(np.mean((Y-Ystar)**2)) #return np.sqrt(np.mean((Y-Ystar)**2))
#for train, test in kf: ##for train, test in kf:
for n, (train, test) in enumerate(kf): #for n, (train, test) in enumerate(kf):
X_train, X_test, Y_train, Y_test = X[train], X[test], Y[train], Y[test] #X_train, X_test, Y_train, Y_test = X[train], X[test], Y[train], Y[test]
print "Fold {}".format(n) #print "Fold {}".format(n)

138
GPy/examples/regression.py
View file

@ -101,9 +101,7 @@ def coregionalization_sparse(optimize=True, plot=True):
return m return m
def epomeo_gpx(max_iters=200, optimize=True, plot=True):
def epomeo_gpx(optimize=True, plot=True):
""" """
Perform Gaussian process regression on the latitude and longitude data Perform Gaussian process regression on the latitude and longitude data
from the Mount Epomeo runs. Requires gpxpy to be installed on your system from the Mount Epomeo runs. Requires gpxpy to be installed on your system
@ -141,8 +139,7 @@ def epomeo_gpx(optimize=True, plot=True):
return m return m
def multiple_optima(gene_number=937, resolution=80, model_restarts=10, seed=10000, max_iters=300, optimize=True, plot=True):
def multiple_optima(gene_number=937, resolution=80, model_restarts=10, seed=10000, max_iters=300):
""" """
Show an example of a multimodal error surface for Gaussian process Show an example of a multimodal error surface for Gaussian process
regression. Gene 939 has bimodal behaviour where the noisy mode is regression. Gene 939 has bimodal behaviour where the noisy mode is
@ -160,13 +157,14 @@ def multiple_optima(gene_number=937, resolution=80, model_restarts=10, seed=1000
data['Y'] = data['Y'] - np.mean(data['Y']) data['Y'] = data['Y'] - np.mean(data['Y'])
lls = GPy.examples.regression._contour_data(data, length_scales, log_SNRs, GPy.kern.rbf) lls = GPy.examples.regression._contour_data(data, length_scales, log_SNRs, GPy.kern.rbf)
pb.contour(length_scales, log_SNRs, np.exp(lls), 20, cmap=pb.cm.jet) if plot:
ax = pb.gca() pb.contour(length_scales, log_SNRs, np.exp(lls), 20, cmap=pb.cm.jet)
pb.xlabel('length scale') ax = pb.gca()
pb.ylabel('log_10 SNR') pb.xlabel('length scale')
pb.ylabel('log_10 SNR')
xlim = ax.get_xlim() xlim = ax.get_xlim()
ylim = ax.get_ylim() ylim = ax.get_ylim()
# Now run a few optimizations # Now run a few optimizations
models = [] models = []
@ -183,16 +181,19 @@ def multiple_optima(gene_number=937, resolution=80, model_restarts=10, seed=1000
optim_point_y[0] = np.log10(m['rbf_variance']) - np.log10(m['noise_variance']); optim_point_y[0] = np.log10(m['rbf_variance']) - np.log10(m['noise_variance']);
# optimize # optimize
m.optimize('scg', xtol=1e-6, ftol=1e-6, max_iters=max_iters) if optimize:
m.optimize('scg', xtol=1e-6, ftol=1e-6, max_iters=max_iters)
optim_point_x[1] = m['rbf_lengthscale'] optim_point_x[1] = m['rbf_lengthscale']
optim_point_y[1] = np.log10(m['rbf_variance']) - np.log10(m['noise_variance']); optim_point_y[1] = np.log10(m['rbf_variance']) - np.log10(m['noise_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') if plot:
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) models.append(m)
ax.set_xlim(xlim) if plot:
ax.set_ylim(ylim) ax.set_xlim(xlim)
ax.set_ylim(ylim)
return m # (models, lls) return m # (models, lls)
def _contour_data(data, length_scales, log_SNRs, kernel_call=GPy.kern.rbf): def _contour_data(data, length_scales, log_SNRs, kernel_call=GPy.kern.rbf):
@ -295,6 +296,7 @@ def toy_poisson_rbf_1d(optimize=True, plot=True):
def toy_poisson_rbf_1d_laplace(optimize=True, plot=True): def toy_poisson_rbf_1d_laplace(optimize=True, plot=True):
"""Run a simple demonstration of a standard Gaussian process fitting it to data sampled from an RBF covariance.""" """Run a simple demonstration of a standard Gaussian process fitting it to data sampled from an RBF covariance."""
optimizer='scg'
x_len = 30 x_len = 30
X = np.linspace(0, 10, x_len)[:, None] X = np.linspace(0, 10, x_len)[:, None]
f_true = np.random.multivariate_normal(np.zeros(x_len), GPy.kern.rbf(1).K(X)) f_true = np.random.multivariate_normal(np.zeros(x_len), GPy.kern.rbf(1).K(X))
@ -307,7 +309,7 @@ def toy_poisson_rbf_1d_laplace(optimize=True, plot=True):
m = GPy.models.GPRegression(X, Y, likelihood=likelihood) m = GPy.models.GPRegression(X, Y, likelihood=likelihood)
if optimize: if optimize:
m.optimize(optimizer, max_f_eval=max_nb_eval_optim) m.optimize(optimizer)
if plot: if plot:
m.plot() m.plot()
# plot the real underlying rate function # plot the real underlying rate function
@ -315,9 +317,7 @@ def toy_poisson_rbf_1d_laplace(optimize=True, plot=True):
return m return m
def toy_ARD(max_iters=1000, kernel_type='linear', num_samples=300, D=4, optimize=True, plot=True):
def toy_ARD(max_iters=1000, kernel_type='linear', num_samples=300, D=4):
# Create an artificial dataset where the values in the targets (Y) # Create an artificial dataset where the values in the targets (Y)
# only depend in dimensions 1 and 3 of the inputs (X). Run ARD to # only depend in dimensions 1 and 3 of the inputs (X). Run ARD to
# see if this dependency can be recovered # see if this dependency can be recovered
@ -347,13 +347,16 @@ def toy_ARD(max_iters=1000, kernel_type='linear', num_samples=300, D=4):
# len_prior = GPy.priors.inverse_gamma(1,18) # 1, 25 # len_prior = GPy.priors.inverse_gamma(1,18) # 1, 25
# m.set_prior('.*lengthscale',len_prior) # m.set_prior('.*lengthscale',len_prior)
m.optimize(optimizer='scg', max_iters=max_iters, messages=1) if optimize:
m.optimize(optimizer='scg', max_iters=max_iters, messages=1)
m.kern.plot_ARD() if plot:
print(m) m.kern.plot_ARD()
print m
return m return m
def toy_ARD_sparse(max_iters=1000, kernel_type='linear', num_samples=300, D=4): def toy_ARD_sparse(max_iters=1000, kernel_type='linear', num_samples=300, D=4, optimize=True, plot=True):
# Create an artificial dataset where the values in the targets (Y) # Create an artificial dataset where the values in the targets (Y)
# only depend in dimensions 1 and 3 of the inputs (X). Run ARD to # only depend in dimensions 1 and 3 of the inputs (X). Run ARD to
# see if this dependency can be recovered # see if this dependency can be recovered
@ -384,13 +387,16 @@ def toy_ARD_sparse(max_iters=1000, kernel_type='linear', num_samples=300, D=4):
# len_prior = GPy.priors.inverse_gamma(1,18) # 1, 25 # len_prior = GPy.priors.inverse_gamma(1,18) # 1, 25
# m.set_prior('.*lengthscale',len_prior) # m.set_prior('.*lengthscale',len_prior)
m.optimize(optimizer='scg', max_iters=max_iters, messages=1) if optimize:
m.optimize(optimizer='scg', max_iters=max_iters, messages=1)
m.kern.plot_ARD() if plot:
print(m) m.kern.plot_ARD()
print m
return m return m
def robot_wireless(max_iters=100, kernel=None): def robot_wireless(max_iters=100, kernel=None, optimize=True, plot=True):
"""Predict the location of a robot given wirelss signal strength readings.""" """Predict the location of a robot given wirelss signal strength readings."""
data = GPy.util.datasets.robot_wireless() data = GPy.util.datasets.robot_wireless()
@ -398,20 +404,24 @@ def robot_wireless(max_iters=100, kernel=None):
m = GPy.models.GPRegression(data['Y'], data['X'], kernel=kernel) m = GPy.models.GPRegression(data['Y'], data['X'], kernel=kernel)
# optimize # optimize
m.optimize(messages=True, max_iters=max_iters) if optimize:
m.optimize(messages=True, max_iters=max_iters)
Xpredict = m.predict(data['Ytest'])[0] Xpredict = m.predict(data['Ytest'])[0]
pb.plot(data['Xtest'][:, 0], data['Xtest'][:, 1], 'r-') if plot:
pb.plot(Xpredict[:, 0], Xpredict[:, 1], 'b-') pb.plot(data['Xtest'][:, 0], data['Xtest'][:, 1], 'r-')
pb.axis('equal') pb.plot(Xpredict[:, 0], Xpredict[:, 1], 'b-')
pb.title('WiFi Localization with Gaussian Processes') pb.axis('equal')
pb.legend(('True Location', 'Predicted Location')) pb.title('WiFi Localization with Gaussian Processes')
pb.legend(('True Location', 'Predicted Location'))
sse = ((data['Xtest'] - Xpredict)**2).sum() sse = ((data['Xtest'] - Xpredict)**2).sum()
print(m)
print m
print('Sum of squares error on test data: ' + str(sse)) print('Sum of squares error on test data: ' + str(sse))
return m return m
def silhouette(max_iters=100): def silhouette(max_iters=100, optimize=True, plot=True):
"""Predict the pose of a figure given a silhouette. This is a task from Agarwal and Triggs 2004 ICML paper.""" """Predict the pose of a figure given a silhouette. This is a task from Agarwal and Triggs 2004 ICML paper."""
data = GPy.util.datasets.silhouette() data = GPy.util.datasets.silhouette()
@ -419,12 +429,13 @@ def silhouette(max_iters=100):
m = GPy.models.GPRegression(data['X'], data['Y']) m = GPy.models.GPRegression(data['X'], data['Y'])
# optimize # optimize
m.optimize(messages=True, max_iters=max_iters) if optimize:
m.optimize(messages=True, max_iters=max_iters)
print(m) print m
return m return m
def sparse_GP_regression_1D(num_samples=400, num_inducing=5, max_iters=100): def sparse_GP_regression_1D(num_samples=400, num_inducing=5, max_iters=100, optimize=True, plot=True):
"""Run a 1D example of a sparse GP regression.""" """Run a 1D example of a sparse GP regression."""
# sample inputs and outputs # sample inputs and outputs
X = np.random.uniform(-3., 3., (num_samples, 1)) X = np.random.uniform(-3., 3., (num_samples, 1))
@ -433,14 +444,17 @@ def sparse_GP_regression_1D(num_samples=400, num_inducing=5, max_iters=100):
rbf = GPy.kern.rbf(1) rbf = GPy.kern.rbf(1)
# create simple GP Model # create simple GP Model
m = GPy.models.SparseGPRegression(X, Y, kernel=rbf, num_inducing=num_inducing) m = GPy.models.SparseGPRegression(X, Y, kernel=rbf, num_inducing=num_inducing)
m.checkgrad(verbose=1) m.checkgrad(verbose=1)
m.optimize('tnc', messages=1, max_iters=max_iters)
m.plot() if optimize:
m.optimize('tnc', messages=1, max_iters=max_iters)
if plot:
m.plot()
return m return m
def sparse_GP_regression_2D(num_samples=400, num_inducing=50, max_iters=100): def sparse_GP_regression_2D(num_samples=400, num_inducing=50, max_iters=100, optimize=True, plot=True):
"""Run a 2D example of a sparse GP regression.""" """Run a 2D example of a sparse GP regression."""
X = np.random.uniform(-3., 3., (num_samples, 2)) X = np.random.uniform(-3., 3., (num_samples, 2))
Y = np.sin(X[:, 0:1]) * np.sin(X[:, 1:2]) + np.random.randn(num_samples, 1) * 0.05 Y = np.sin(X[:, 0:1]) * np.sin(X[:, 1:2]) + np.random.randn(num_samples, 1) * 0.05
@ -456,13 +470,18 @@ def sparse_GP_regression_2D(num_samples=400, num_inducing=50, max_iters=100):
m.checkgrad() m.checkgrad()
# optimize and plot # optimize
m.optimize('tnc', messages=1, max_iters=max_iters) if optimize:
m.plot() m.optimize('tnc', messages=1, max_iters=max_iters)
print(m)
# plot
if plot:
m.plot()
print m
return m return m
def uncertain_inputs_sparse_regression(optimize=True, plot=True): def uncertain_inputs_sparse_regression(max_iters=200, optimize=True, plot=True):
"""Run a 1D example of a sparse GP regression with uncertain inputs.""" """Run a 1D example of a sparse GP regression with uncertain inputs."""
fig, axes = pb.subplots(1, 2, figsize=(12, 5)) fig, axes = pb.subplots(1, 2, figsize=(12, 5))
@ -477,18 +496,23 @@ def uncertain_inputs_sparse_regression(optimize=True, plot=True):
# create simple GP Model - no input uncertainty on this one # create simple GP Model - no input uncertainty on this one
m = GPy.models.SparseGPRegression(X, Y, kernel=k, Z=Z) m = GPy.models.SparseGPRegression(X, Y, kernel=k, Z=Z)
m.optimize('scg', messages=1, max_iters=max_iters)
m.plot(ax=axes[0])
axes[0].set_title('no input uncertainty')
if optimize:
m.optimize('scg', messages=1, max_iters=max_iters)
if plot:
m.plot(ax=axes[0])
axes[0].set_title('no input uncertainty')
print m
# the same Model with uncertainty # the same Model with uncertainty
m = GPy.models.SparseGPRegression(X, Y, kernel=k, Z=Z, X_variance=S) m = GPy.models.SparseGPRegression(X, Y, kernel=k, Z=Z, X_variance=S)
m.optimize('scg', messages=1, max_iters=max_iters) if optimize:
m.plot(ax=axes[1]) m.optimize('scg', messages=1, max_iters=max_iters)
axes[1].set_title('with input uncertainty') if plot:
print(m) m.plot(ax=axes[1])
axes[1].set_title('with input uncertainty')
fig.canvas.draw() fig.canvas.draw()
print m
return m return m

79
GPy/examples/tutorials.py
View file

@ -11,7 +11,7 @@ pb.ion()
import numpy as np import numpy as np
import GPy import GPy
def tuto_GP_regression(): def tuto_GP_regression(optimize=True, plot=True):
"""The detailed explanations of the commands used in this file can be found in the tutorial section""" """The detailed explanations of the commands used in this file can be found in the tutorial section"""
X = np.random.uniform(-3.,3.,(20,1)) X = np.random.uniform(-3.,3.,(20,1))
@ -22,7 +22,8 @@ def tuto_GP_regression():
m = GPy.models.GPRegression(X, Y, kernel) m = GPy.models.GPRegression(X, Y, kernel)
print m print m
m.plot() if plot:
m.plot()
m.constrain_positive('') m.constrain_positive('')
@ -31,9 +32,9 @@ def tuto_GP_regression():
m.constrain_bounded('.*lengthscale',1.,10. ) m.constrain_bounded('.*lengthscale',1.,10. )
m.constrain_fixed('.*noise',0.0025) m.constrain_fixed('.*noise',0.0025)
m.optimize() if optimize:
m.optimize()
m.optimize_restarts(num_restarts = 10) m.optimize_restarts(num_restarts = 10)
####################################################### #######################################################
####################################################### #######################################################
@ -51,22 +52,26 @@ def tuto_GP_regression():
m.constrain_positive('') m.constrain_positive('')
# optimize and plot # optimize and plot
m.optimize('tnc', max_f_eval = 1000) if optimize:
m.plot() m.optimize('tnc', max_f_eval = 1000)
print(m) if plot:
m.plot()
print m
return(m) return(m)
def tuto_kernel_overview(): def tuto_kernel_overview(optimize=True, plot=True):
"""The detailed explanations of the commands used in this file can be found in the tutorial section""" """The detailed explanations of the commands used in this file can be found in the tutorial section"""
ker1 = GPy.kern.rbf(1) # Equivalent to ker1 = GPy.kern.rbf(input_dim=1, variance=1., lengthscale=1.) ker1 = GPy.kern.rbf(1) # Equivalent to ker1 = GPy.kern.rbf(input_dim=1, variance=1., lengthscale=1.)
ker2 = GPy.kern.rbf(input_dim=1, variance = .75, lengthscale=2.) ker2 = GPy.kern.rbf(input_dim=1, variance = .75, lengthscale=2.)
ker3 = GPy.kern.rbf(1, .5, .5) ker3 = GPy.kern.rbf(1, .5, .5)
print ker2 print ker2
ker1.plot() if plot:
ker2.plot() ker1.plot()
ker3.plot() ker2.plot()
ker3.plot()
k1 = GPy.kern.rbf(1,1.,2.) k1 = GPy.kern.rbf(1,1.,2.)
k2 = GPy.kern.Matern32(1, 0.5, 0.2) k2 = GPy.kern.Matern32(1, 0.5, 0.2)
@ -77,8 +82,8 @@ def tuto_kernel_overview():
# Sum of kernels # Sum of kernels
k_add = k1.add(k2) # By default, tensor=False k_add = k1.add(k2) # By default, tensor=False
k_addtens = k1.add(k2,tensor=True) k_addtens = k1.add(k2,tensor=True)
k1 = GPy.kern.rbf(1,1.,2) k1 = GPy.kern.rbf(1,1.,2)
k2 = GPy.kern.periodic_Matern52(1,variance=1e3, lengthscale=1, period = 1.5, lower=-5., upper = 5) k2 = GPy.kern.periodic_Matern52(1,variance=1e3, lengthscale=1, period = 1.5, lower=-5., upper = 5)
@ -102,7 +107,7 @@ def tuto_kernel_overview():
k.unconstrain('white') k.unconstrain('white')
k.constrain_bounded('white',lower=1e-5,upper=.5) k.constrain_bounded('white',lower=1e-5,upper=.5)
print k print k
k_cst = GPy.kern.bias(1,variance=1.) k_cst = GPy.kern.bias(1,variance=1.)
k_mat = GPy.kern.Matern52(1,variance=1., lengthscale=3) k_mat = GPy.kern.Matern52(1,variance=1., lengthscale=3)
Kanova = (k_cst + k_mat).prod(k_cst + k_mat,tensor=True) Kanova = (k_cst + k_mat).prod(k_cst + k_mat,tensor=True)
@ -114,30 +119,32 @@ def tuto_kernel_overview():
# Create GP regression model # Create GP regression model
m = GPy.models.GPRegression(X, Y, Kanova) m = GPy.models.GPRegression(X, Y, Kanova)
fig = pb.figure(figsize=(5,5))
ax = fig.add_subplot(111) if plot:
m.plot(ax=ax) fig = pb.figure(figsize=(5,5))
ax = fig.add_subplot(111)
pb.figure(figsize=(20,3)) m.plot(ax=ax)
pb.subplots_adjust(wspace=0.5)
axs = pb.subplot(1,5,1) pb.figure(figsize=(20,3))
m.plot(ax=axs) pb.subplots_adjust(wspace=0.5)
pb.subplot(1,5,2) axs = pb.subplot(1,5,1)
pb.ylabel("= ",rotation='horizontal',fontsize='30') m.plot(ax=axs)
axs = pb.subplot(1,5,3) pb.subplot(1,5,2)
m.plot(ax=axs, which_parts=[False,True,False,False]) pb.ylabel("= ",rotation='horizontal',fontsize='30')
pb.ylabel("cst +",rotation='horizontal',fontsize='30') axs = pb.subplot(1,5,3)
axs = pb.subplot(1,5,4) m.plot(ax=axs, which_parts=[False,True,False,False])
m.plot(ax=axs, which_parts=[False,False,True,False]) pb.ylabel("cst +",rotation='horizontal',fontsize='30')
pb.ylabel("+ ",rotation='horizontal',fontsize='30') axs = pb.subplot(1,5,4)
axs = pb.subplot(1,5,5) m.plot(ax=axs, which_parts=[False,False,True,False])
pb.ylabel("+ ",rotation='horizontal',fontsize='30') pb.ylabel("+ ",rotation='horizontal',fontsize='30')
m.plot(ax=axs, which_parts=[False,False,False,True]) axs = pb.subplot(1,5,5)
pb.ylabel("+ ",rotation='horizontal',fontsize='30')
m.plot(ax=axs, which_parts=[False,False,False,True])
return(m) return(m)
def model_interaction(): def model_interaction(optimize=True, plot=True):
X = np.random.randn(20,1) X = np.random.randn(20,1)
Y = np.sin(X) + np.random.randn(*X.shape)*0.01 + 5. Y = np.sin(X) + np.random.randn(*X.shape)*0.01 + 5.
k = GPy.kern.rbf(1) + GPy.kern.bias(1) k = GPy.kern.rbf(1) + GPy.kern.bias(1)