def testShekelClass(self):
S = Shekel5()
# get 50 latin hypercube samples
X = lhcSample(S.bounds, 50, seed=2)
Y = [S.f(x) for x in X]
hyper = [.2, .2, .2, .2]
noise = 0.1
gkernel = GaussianKernel_ard(hyper)
# print gkernel.sf2
GP = GaussianProcess(gkernel, X, Y, noise=noise)
# let's take a look at the trained GP. first, make sure variance at
# the samples is determined by noise
mu, sig2 = GP.posteriors(X)
for m, s, y in zip(mu, sig2, Y):
# print m, s
self.failUnless(s < 1/(1+noise))
self.failUnless(abs(m-y) < 2*noise)
# now get some test samples and see how well we are fitting the function
testX = lhcSample(S.bounds, 50, seed=3)
testY = [S.f(x) for x in X]
for tx, ty in zip(testX, testY):
m, s = GP.posterior(tx)
# prediction should be within one stdev of mean
self.failUnless(abs(ty-m)/sqrt(s) < 1)
def testShekelClass(self):
S = Shekel5()
# get 50 latin hypercube samples
X = lhcSample(S.bounds, 50, seed=2)
Y = [S.f(x) for x in X]
hyper = [.2, .2, .2, .2]
noise = 0.1
gkernel = GaussianKernel_ard(hyper)
# print gkernel.sf2
GP = GaussianProcess(gkernel, X, Y, noise=noise)
# let's take a look at the trained GP. first, make sure variance at
# the samples is determined by noise
mu, sig2 = GP.posteriors(X)
for m, s, y in zip(mu, sig2, Y):
# print m, s
self.failUnless(s < 1 / (1 + noise))
self.failUnless(abs(m - y) < 2 * noise)
# now get some test samples and see how well we are fitting the function
testX = lhcSample(S.bounds, 50, seed=3)
testY = [S.f(x) for x in X]
for tx, ty in zip(testX, testY):
m, s = GP.posterior(tx)
# prediction should be within one stdev of mean
self.failUnless(abs(ty - m) / sqrt(s) < 1)
def testShekelGPPrior(self):
# see how the GP works on the Shekel function
S5 = Shekel5()
pX = lhcSample(S5.bounds, 100, seed=8)
pY = [S5.f(x) for x in pX]
prior = RBFNMeanPrior()
prior.train(pX, pY, S5.bounds, k=10, seed=103)
hv = .1
hyper = [hv, hv, hv, hv]
gkernel = GaussianKernel_ard(hyper)
X = lhcSample(S5.bounds, 10, seed=9)
Y = [S5.f(x) for x in X]
priorGP = GaussianProcess(gkernel, X, Y, prior=prior)
nopriorGP = GaussianProcess(gkernel, X, Y, prior=None)
S = lhcSample(S5.bounds, 1000, seed=10)
nopriorErr = mean([(S5.f(x)-nopriorGP.mu(x))**2 for x in S])
priorErr = mean([(S5.f(x)-priorGP.mu(x))**2 for x in S])
# print '\nno prior Err =', nopriorErr
# print 'prior Err =', priorErr
self.failUnless(priorErr < nopriorErr*.8)
def testFromEmptyGP(self):
# test a GP that has no data to start
f = lambda x: float(sin(x*10)+x)
kernel = GaussianKernel_iso(array([1.0]))
GP = GaussianProcess(kernel)
for x in arange(0., 1., .1):
GP.addData(array([x]), f(x))
for x in arange(1., 2., .1):
GP.addData(array([x]), f(x))
self.failUnlessEqual(len(GP.X), 20)
def test1DGP(self):
f = lambda x: float(sin(x * 5.))
X = lhcSample([[0., 1.]], 5, seed=25)
Y = [f(x) for x in X]
kernel = GaussianKernel_ard(array([1.0, 1.0]))
GP = GaussianProcess(kernel, X=X, Y=Y)
def testShekelGPPrior(self):
# see how the GP works on the Shekel function
S5 = Shekel5()
pX = lhcSample(S5.bounds, 100, seed=8)
pY = [S5.f(x) for x in pX]
prior = RBFNMeanPrior()
prior.train(pX, pY, S5.bounds, k=10, seed=103)
hv = .1
hyper = [hv, hv, hv, hv]
gkernel = GaussianKernel_ard(hyper)
X = lhcSample(S5.bounds, 10, seed=9)
Y = [S5.f(x) for x in X]
priorGP = GaussianProcess(gkernel, X, Y, prior=prior)
nopriorGP = GaussianProcess(gkernel, X, Y, prior=None)
S = lhcSample(S5.bounds, 1000, seed=10)
nopriorErr = mean([(S5.f(x) - nopriorGP.mu(x))**2 for x in S])
priorErr = mean([(S5.f(x) - priorGP.mu(x))**2 for x in S])
# print '\nno prior Err =', nopriorErr
# print 'prior Err =', priorErr
self.failUnless(priorErr < nopriorErr * .8)
def testFromEmptyGP(self):
# test a GP that has no data to start
f = lambda x: float(sin(x * 10) + x)
kernel = GaussianKernel_iso(array([1.0]))
GP = GaussianProcess(kernel)
for x in arange(0., 1., .1):
GP.addData(array([x]), f(x))
for x in arange(1., 2., .1):
GP.addData(array([x]), f(x))
self.failUnlessEqual(len(GP.X), 20)
def testGPPrior(self):
# see how GP works with the dataprior...
def foo(x):
return sum(sin(x * 20))
bounds = [[0., 1.]]
# train prior
pX = lhcSample([[0., 1.]], 100, seed=6)
pY = [foo(x) for x in pX]
prior = RBFNMeanPrior()
prior.train(pX, pY, bounds, k=10, seed=102)
X = lhcSample([[0., 1.]], 2, seed=7)
Y = [foo(x) for x in X]
kernel = GaussianKernel_ard(array([.1]))
GP = GaussianProcess(kernel, X, Y, prior=prior)
GPnoprior = GaussianProcess(kernel, X, Y)
S = arange(0, 1, .01)
nopriorErr = mean([(foo(x) - GPnoprior.mu(x))**2 for x in S])
priorErr = mean([(foo(x) - GP.mu(x))**2 for x in S])
# print '\nno prior Err =', nopriorErr
# print 'prior Err =', priorErr
self.failUnless(priorErr < nopriorErr * .5)
if False:
figure(1)
clf()
plot(S, [prior.mu(x) for x in S], 'g-', alpha=0.3)
plot(S, [GPnoprior.mu(x) for x in S], 'b-', alpha=0.3)
plot(S, [GP.mu(x) for x in S], 'k-', lw=2)
plot(X, Y, 'ko')
show()
def testGPPrior(self):
# see how GP works with the dataprior...
def foo(x):
return sum(sin(x*20))
bounds = [[0., 1.]]
# train prior
pX = lhcSample([[0., 1.]], 100, seed=6)
pY = [foo(x) for x in pX]
prior = RBFNMeanPrior()
prior.train(pX, pY, bounds, k=10, seed=102)
X = lhcSample([[0., 1.]], 2, seed=7)
Y = [foo(x) for x in X]
kernel = GaussianKernel_ard(array([.1]))
GP = GaussianProcess(kernel, X, Y, prior=prior)
GPnoprior = GaussianProcess(kernel, X, Y)
S = arange(0, 1, .01)
nopriorErr = mean([(foo(x)-GPnoprior.mu(x))**2 for x in S])
priorErr = mean([(foo(x)-GP.mu(x))**2 for x in S])
# print '\nno prior Err =', nopriorErr
# print 'prior Err =', priorErr
self.failUnless(priorErr < nopriorErr*.5)
if False:
figure(1)
clf()
plot(S, [prior.mu(x) for x in S], 'g-', alpha=0.3)
plot(S, [GPnoprior.mu(x) for x in S], 'b-', alpha=0.3)
plot(S, [GP.mu(x) for x in S], 'k-', lw=2)
plot(X, Y, 'ko')
show()
def testTraining(self):
# test that sequential training gives the same result as batch
tf = Shekel5()
X = lhcSample(tf.bounds, 25, seed=1)
Y = [tf.f(x) for x in X]
# GP1 adds all data during initialization
GP1 = GaussianProcess(GaussianKernel_iso([.1]), X, Y, noise=.2)
# GP2 adds data one at a time
GP2 = GaussianProcess(GaussianKernel_iso([.1]), noise=.2)
# GP3 uses addData()
GP3 = GaussianProcess(GaussianKernel_iso([.1]), noise=.2)
# GP4 adds using various methods
GP4 = GaussianProcess(GaussianKernel_iso([.1]),
X[:10],
Y[:10],
noise=.2)
for x, y in zip(X, Y):
GP2.addData(x, y)
for i in xrange(0, 25, 5):
GP3.addData(X[i:i + 5], Y[i:i + 5])
GP4.addData(X[10], Y[10])
GP4.addData(X[11:18], Y[11:18])
for i in xrange(18, 25):
GP4.addData(X[i], Y[i])
self.failUnless(all(GP1.R == GP2.R))
self.failUnless(all(GP1.R == GP3.R))
self.failUnless(all(GP1.R == GP4.R))
testX = lhcSample(tf.bounds, 25, seed=2)
for x in testX:
mu1, s1 = GP1.posterior(x)
mu2, s2 = GP2.posterior(x)
mu3, s3 = GP3.posterior(x)
mu4, s4 = GP4.posterior(x)
self.failUnlessEqual(mu1, mu2)
self.failUnlessEqual(mu1, mu3)
self.failUnlessEqual(mu1, mu4)
self.failUnlessEqual(s1, s2)
self.failUnlessEqual(s1, s3)
self.failUnlessEqual(s1, s4)
def testTraining(self):
# test that sequential training gives the same result as batch
tf = Shekel5()
X = lhcSample(tf.bounds, 25, seed=1)
Y = [tf.f(x) for x in X]
# GP1 adds all data during initialization
GP1 = GaussianProcess(GaussianKernel_iso([.1]), X, Y, noise=.2)
# GP2 adds data one at a time
GP2 = GaussianProcess(GaussianKernel_iso([.1]), noise=.2)
# GP3 uses addData()
GP3 = GaussianProcess(GaussianKernel_iso([.1]), noise=.2)
# GP4 adds using various methods
GP4 = GaussianProcess(GaussianKernel_iso([.1]), X[:10], Y[:10], noise=.2)
for x, y in zip(X, Y):
GP2.addData(x, y)
for i in xrange(0, 25, 5):
GP3.addData(X[i:i+5], Y[i:i+5])
GP4.addData(X[10], Y[10])
GP4.addData(X[11:18], Y[11:18])
for i in xrange(18, 25):
GP4.addData(X[i], Y[i])
self.failUnless(all(GP1.R==GP2.R))
self.failUnless(all(GP1.R==GP3.R))
self.failUnless(all(GP1.R==GP4.R))
testX = lhcSample(tf.bounds, 25, seed=2)
for x in testX:
mu1, s1 = GP1.posterior(x)
mu2, s2 = GP2.posterior(x)
mu3, s3 = GP3.posterior(x)
mu4, s4 = GP4.posterior(x)
self.failUnlessEqual(mu1, mu2)
self.failUnlessEqual(mu1, mu3)
self.failUnlessEqual(mu1, mu4)
self.failUnlessEqual(s1, s2)
self.failUnlessEqual(s1, s3)
self.failUnlessEqual(s1, s4)
