def testRBFN_1D(self):
# sample from a synthetic function and see how much we improve the
# error by using the prior function
def foo(x):
return sum(sin(x*20))
X = lhcSample([[0., 1.]], 50, seed=3)
Y = [foo(x) for x in X]
prior = RBFNMeanPrior()
prior.train(X, Y, [[0., 1.]], k=10, seed=100)
# See how well we fit the function by getting the average squared error
# over 100 samples of the function. Baseline foo(x)=0 MSE is 0.48.
# We will aim for MSE < 0.05.
S = arange(0, 1, .01)
error = mean([foo(x)-prior.mu(x) for x in S])
self.failUnless(error < 0.05)
# for debugging
if False:
figure(1)
plot(S, [foo(x) for x in S], 'b-')
plot(S, [prior.mu(x) for x in S], 'k-')
show()
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)
X = lhcSample(S5.bounds, 10, seed=9)
Y = [S5.f(x) for x in X]
hv = .1
hyper = [hv, hv, hv, hv]
gkernel = GaussianKernel_ard(hyper)
priorGP = GaussianProcess(gkernel, X, Y, prior=prior)
nopriorGP = GaussianProcess(gkernel, X, Y)
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 testPriorAndPrefs(self):
S5 = Shekel5()
pX = lhcSample(S5.bounds, 100, seed=13)
pY = [S5.f(x) for x in pX]
prior = RBFNMeanPrior()
prior.train(pX, pY, S5.bounds, k=10)
hv = .1
hyper = [hv, hv, hv, hv]
gkernel = GaussianKernel_ard(hyper)
GP = PrefGaussianProcess(gkernel, prior=prior)
X = [array([i+.5]*4) for i in xrange(5)]
valX = [x.copy() for x in X]
prefs = []
for i in xrange(len(X)):
for j in xrange(i):
if S5.f(X[i]) > S5.f(X[j]):
prefs.append((X[i], X[j], 0))
else:
prefs.append((X[j], X[i], 0))
GP.addPreferences(prefs)
opt, optx = maximizeEI(GP, S5.bounds)
def _testKernelMaxEI(self):
# test different methods of optimizing kernel
S5 = Shekel5()
hv = 0.1
testkernels = [GaussianKernel_iso([hv]),
GaussianKernel_ard([hv, hv, hv, hv]),
MaternKernel3([hv, 1.0])]
# MaternKernel5([hv, 1.0])]
for kernel in testkernels:
# print
# print kernel.__class__
# train GPs
X = lhcSample(S5.bounds, 10, seed=0)
Y = [S5.f(x) for x in X]
GP = GaussianProcess(kernel, X, Y)
eif = EI(GP)
dopt, doptx = direct(eif.negf, S5.bounds, maxiter=10)
copt, coptx = cdirect(eif.negf, S5.bounds, maxiter=10)
mopt, moptx = maximizeEI(GP, S5.bounds, maxiter=10)
# print dopt, doptx
# print copt, coptx
# print mopt, moptx
self.failUnlessAlmostEqual(dopt, copt, 4)
self.failUnlessAlmostEqual(-dopt, mopt, 4)
self.failUnlessAlmostEqual(-copt, mopt, 4)
self.failUnless(sum(abs(doptx-coptx)) < .01)
self.failUnless(sum(abs(moptx-coptx)) < .01)
self.failUnless(sum(abs(moptx-doptx)) < .01)
# train GP w/prior
pX = lhcSample(S5.bounds, 100, seed=101)
pY = [S5.f(x) for x in pX]
prior = RBFNMeanPrior()
prior.train(pX, pY, bounds=S5.bounds, k=10, seed=102)
GP = GaussianProcess(kernel, X, Y, prior=prior)
eif = EI(GP)
pdopt, pdoptx = direct(eif.negf, S5.bounds, maxiter=10)
pcopt, pcoptx = cdirect(eif.negf, S5.bounds, maxiter=10)
pmopt, pmoptx = maximizeEI(GP, S5.bounds, maxiter=10)
self.failIfAlmostEqual(pdopt, dopt, 3)
self.failUnlessAlmostEqual(pdopt, pcopt, 4)
self.failUnlessAlmostEqual(-pdopt, pmopt, 4)
self.failUnlessAlmostEqual(-pcopt, pmopt, 4)
self.failUnless(sum(abs(pdoptx-pcoptx)) < .01)
self.failUnless(sum(abs(pmoptx-pcoptx)) < .01)
self.failUnless(sum(abs(pmoptx-pdoptx)) < .01)
def _testKernelMaxEI(self):
# test different methods of optimizing kernel
S5 = Shekel5()
hv = 0.1
testkernels = [
GaussianKernel_iso([hv]),
GaussianKernel_ard([hv, hv, hv, hv]),
MaternKernel3([hv, 1.0])
]
# MaternKernel5([hv, 1.0])]
for kernel in testkernels:
# train GPs
X = lhcSample(S5.bounds, 10, seed=0)
Y = [S5.f(x) for x in X]
GP = GaussianProcess(kernel, X, Y)
eif = EI(GP)
dopt, doptx = direct(eif.negf, S5.bounds, maxiter=10)
copt, coptx = cdirect(eif.negf, S5.bounds, maxiter=10)
mopt, moptx = maximizeEI(GP, S5.bounds, maxiter=10)
self.failUnlessAlmostEqual(dopt, copt, 4)
self.failUnlessAlmostEqual(-dopt, mopt, 4)
self.failUnlessAlmostEqual(-copt, mopt, 4)
self.failUnless(sum(abs(doptx - coptx)) < .01)
self.failUnless(sum(abs(moptx - coptx)) < .01)
self.failUnless(sum(abs(moptx - doptx)) < .01)
# train GP w/prior
pX = lhcSample(S5.bounds, 100, seed=101)
pY = [S5.f(x) for x in pX]
prior = RBFNMeanPrior()
prior.train(pX, pY, bounds=S5.bounds, k=10, seed=102)
GP = GaussianProcess(kernel, X, Y, prior=prior)
eif = EI(GP)
pdopt, pdoptx = direct(eif.negf, S5.bounds, maxiter=10)
pcopt, pcoptx = cdirect(eif.negf, S5.bounds, maxiter=10)
pmopt, pmoptx = maximizeEI(GP, S5.bounds, maxiter=10)
self.failIfAlmostEqual(pdopt, dopt, 3)
self.failUnlessAlmostEqual(pdopt, pcopt, 4)
self.failUnlessAlmostEqual(-pdopt, pmopt, 4)
self.failUnlessAlmostEqual(-pcopt, pmopt, 4)
self.failUnless(sum(abs(pdoptx - pcoptx)) < .01)
self.failUnless(sum(abs(pmoptx - pcoptx)) < .01)
self.failUnless(sum(abs(pmoptx - pdoptx)) < .01)
def testMaxEIPrior(self):
# make sure that the prior works with the different methods of EI
# maximization
S5 = Shekel5()
pX = lhcSample(S5.bounds, 100, seed=511)
pY = [S5.f(x) for x in pX]
prior = RBFNMeanPrior()
prior.train(pX, pY, bounds=S5.bounds, k=10, seed=504)
hv = .1
hyper = [hv, hv, hv, hv]
kernel = GaussianKernel_ard(hyper)
# train GPs
X = lhcSample(S5.bounds, 10, seed=512)
Y = [S5.f(x) for x in X]
# validation
valX = list(x.copy() for x in X)
valY = copy(Y)
GP = GaussianProcess(kernel, X, Y, prior=prior)
eif = EI(GP)
copt, _ = cdirect(eif.negf, S5.bounds, maxiter=20)
mopt, _ = maximizeEI(GP, S5.bounds, maxiter=20)
self.failUnlessAlmostEqual(-copt, mopt, 2)
for i in xrange(len(GP.X)):
self.failUnless(all(valX[i]==GP.X[i]))
self.failUnless(valY[i]==GP.Y[i])
GP.prior.mu(GP.X[0])
self.failUnless(all(valX[0]==GP.X[0]))
# print GP.X
for i in xrange(len(GP.X)):
self.failUnless(all(valX[i]==GP.X[i]))
self.failUnless(valY[i]==GP.Y[i])
GP.prior.mu(GP.X[0])
self.failUnless(all(valX[0]==GP.X[0]))
def testRNFN_10D(self):
# as above, but with a 10D test function and more data
def foo(x):
return sum(sin(x * 2))
bounds = [[0., 1.]] * 10
X = lhcSample(bounds, 100, seed=4)
Y = [foo(x) for x in X]
prior = RBFNMeanPrior()
prior.train(X, Y, bounds, k=20, seed=5)
S = lhcSample(bounds, 100, seed=6)
RBNError = mean([(foo(x) - prior.mu(x))**2 for x in S])
baselineError = mean([foo(x)**2 for x in S])
self.failUnless(RBNError < baselineError)
def testRNFN_10D(self):
# as above, but with a 10D test function and more data
def foo(x):
return sum(sin(x*2))
bounds = [[0., 1.]]*10
X = lhcSample(bounds, 100, seed=4)
Y = [foo(x) for x in X]
prior = RBFNMeanPrior()
prior.train(X, Y, bounds, k=20, seed=5)
S = lhcSample(bounds, 100, seed=6)
RBNError = mean([(foo(x)-prior.mu(x))**2 for x in S])
baselineError = mean([foo(x)**2 for x in S])
# print '\nRBN err =', RBNError
# print 'baseline =', baselineError
self.failUnless(RBNError < baselineError)
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 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)
X = lhcSample(S5.bounds, 10, seed=9)
Y = [S5.f(x) for x in X]
hv = .1
hyper = [hv, hv, hv, hv]
gkernel = GaussianKernel_ard(hyper)
priorGP = GaussianProcess(gkernel, X, Y, prior=prior)
nopriorGP = GaussianProcess(gkernel, X, Y)
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])
self.failUnless(priorErr < nopriorErr * .8)