def test2DpyEI(self):
f = lambda x: sum(sin(x))
bounds = [[0., 5.], [0., 5.]]
X = lhcSample(bounds, 5, seed=24)
Y = [f(x) for x in X]
kernel = GaussianKernel_ard(array([1.0, 1.0]))
GP = GaussianProcess(kernel, X, Y)
maxei = maximizeEI(GP, bounds)
if False:
figure(1)
c0 = [(i/50.)*(bounds[0][1]-bounds[0][0])+bounds[0][0] for i in xrange(51)]
c1 = [(i/50.)*(bounds[1][1]-bounds[1][0])+bounds[1][0] for i in xrange(51)]
z = array([[GP.ei(array([i, j])) for i in c0] for j in c1])
ax = plt.subplot(111)
cs = ax.contour(c0, c1, z, 10, alpha=0.5, cmap=cm.Blues_r)
plot([x[0] for x in X], [x[1] for x in X], 'ro')
for i in xrange(len(X)):
annotate('%2f'%Y[i], X[i])
plot(maxei[1][0], maxei[1][1], 'ko')
show()
def test2DpyEI(self):
f = lambda x: sum(sin(x))
bounds = [[0., 5.], [0., 5.]]
X = lhcSample(bounds, 5, seed=24)
Y = [f(x) for x in X]
kernel = GaussianKernel_ard(array([1.0, 1.0]))
GP = GaussianProcess(kernel, X, Y)
maxei = maximizeEI(GP, bounds)
if False:
figure(1)
c0 = [(i / 50.) * (bounds[0][1] - bounds[0][0]) + bounds[0][0]
for i in range(51)]
c1 = [(i / 50.) * (bounds[1][1] - bounds[1][0]) + bounds[1][0]
for i in range(51)]
z = array([[GP.ei(array([i, j])) for i in c0] for j in c1])
ax = plt.subplot(111)
cs = ax.contour(c0, c1, z, 10, alpha=0.5, cmap=cm.Blues_r)
plot([x[0] for x in X], [x[1] for x in X], 'ro')
for i in range(len(X)):
annotate('%2f' % Y[i], X[i])
plot(maxei[1][0], maxei[1][1], 'ko')
show()
def test():
GP = GaussianProcess(GaussianKernel_iso([0.2, 1.0]))
X = array([[0.2], [0.3], [0.5], [1.5]])
Y = [1, 0, 1, 0.75]
GP.addData(X, Y)
figure(1)
A = arange(0, 2, 0.01)
mu = array([GP.mu(x) for x in A])
sig2 = array([GP.posterior(x)[1] for x in A])
Ei = EI(GP)
ei = [-Ei.negf(x) for x in A]
Pi = PI(GP)
pi = [-Pi.negf(x) for x in A]
Ucb = UCB(GP, 1, T=2)
ucb = [-Ucb.negf(x) for x in A]
ax = subplot(1, 1, 1)
ax.plot(A, mu, "k-", lw=2)
xv, yv = poly_between(A, mu - sig2, mu + sig2)
ax.fill(xv, yv, color="#CCCCCC")
ax.plot(A, ei, "g-", lw=2, label="EI")
ax.plot(A, ucb, "g--", lw=2, label="UCB")
ax.plot(A, pi, "g:", lw=2, label="PI")
ax.plot(X, Y, "ro")
ax.legend()
draw()
show()
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 testGDelta(self):
# usually, Gdelta==G
GP = GaussianProcess(GaussianKernel_iso([0.05]))
X = lhcSample([[0., 1.]], 5, seed=10)
Y = [x**2 for x in X]
GP.train(X, Y)
G = (Y[0]-max(Y)) / (Y[0]-1)
self.failUnlessEqual(G, Gdelta(GP, [[0.,1.]], Y[0], 1.0, 0.01))
# sometimes, though, Gdelta > G -- this GP has a very high confidence
# prediction of a very good point at x ~ .65
GP = GaussianProcess(GaussianKernel_iso([0.1]))
X = array([[.5], [.51], [.59], [.6]])
Y = array([1., 2., 2., 1.])
GP.train(X, Y)
# figure(1)
# A = arange(0, 1, 0.01)
# post = [GP.posterior(x) for x in A]
# plot(A, [p[0] for p in post], 'k-')
# plot(A, [p[0]+p[1] for p in post], 'k:')
# show()
G = (Y[0]-max(Y)) / (Y[0]-4.0)
Gd = Gdelta(GP, [[0., 1.]], Y[0], 4.0, 0.01)
self.failUnless(G < Gd)
# however, if there is more variance, we will collapse back to G
GP = GaussianProcess(GaussianKernel_iso([.001]))
GP.train(X, Y)
G = (Y[0]-max(Y)) / (Y[0]-4.0)
self.failUnlessEqual(G, Gdelta(GP, [[0., 1.]], Y[0], 4.0, 0.01))
class Synthetic(TestFunction):
"""
randomly-generated synthetic function
"""
def __init__(self, kernel, bounds, NX, noise=0.05, xstar=None, **kwargs):
super(Synthetic, self).__init__("Synthetic", 0, None, bounds, **kwargs)
self.name += ' %d'%len(bounds)
self.GP = GaussianProcess(kernel)
X = lhcSample(bounds, NX)
self.GP.addData([X[0]], [normal(0, 1)])
if xstar is not None:
ystar = min(self.GP.Y[0]-1.0, -2.0)
self.GP.addData(xstar, ystar)
for x in X[1:]:
mu, sig2 = self.GP.posterior(x)
y = normal(mu, sqrt(sig2)) + normal(0, noise)
# preserve min if necessary
if xstar is not None and y < ystar+.5:
y = ystar+.5
self.GP.addData(x, y)
# now, try minimizing with BFGS
start = self.GP.X[argmin(self.GP.Y)]
xopt = fmin_bfgs(self.GP.mu, start, disp=False)
print "\t[synthetic] optimization started at %s, ended at %s" % (start, xopt)
if xstar is not None:
print '\t[synthetic] realigning minimum'
# now, align minimum with what we specified
for i, (target, origin) in enumerate(zip(xstar, xopt)):
self.GP.X[:,i] += target-origin
xopt = xstar
self.minimum = self.GP.mu(xopt)
self.xstar = xopt
# print self.GP.X
# print self.GP.Y
print '\t[synthetic] x+ = %s, f(x+) = %.3f' % (self.xstar, self.f(self.xstar))
def f(self, x):
y = self.GP.mu(x)
if y < self.minimum:
self.minimum = y
if self.maximize:
return -y
else:
return y
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])
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 testNoise(self):
tf = Branin()
X = lhcSample(tf.bounds, 10, seed=0)
Y = [tf.f(x) for x in X]
GP1 = GaussianProcess(MaternKernel3([1.0, 1.0]), X, Y, noise=1e-4)
self.failUnlessEqual(GP1.noise, 1e-4)
eif1 = EI(GP1)
dopt1, _ = direct(eif1.negf, tf.bounds, maxiter=10)
copt1, _ = cdirect(eif1.negf, tf.bounds, maxiter=10)
mopt1, _ = maximizeEI(GP1, tf.bounds, maxiter=10)
self.failUnlessAlmostEqual(dopt1, copt1, 4)
self.failUnlessAlmostEqual(-dopt1, mopt1, 4)
self.failUnlessAlmostEqual(-copt1, mopt1, 4)
GP2 = GaussianProcess(MaternKernel3([1.0, 1.0]), X, Y, noise=0.01)
self.failUnlessEqual(GP2.noise, 0.01)
eif2 = EI(GP2)
dopt2, _ = direct(eif2.negf, tf.bounds, maxiter=10)
copt2, _ = cdirect(eif2.negf, tf.bounds, maxiter=10)
mopt2, _ = maximizeEI(GP2, tf.bounds, maxiter=10)
self.failUnlessAlmostEqual(dopt2, copt2, 4)
self.failUnlessAlmostEqual(-dopt2, mopt2, 4)
self.failUnlessAlmostEqual(-copt2, mopt2, 4)
self.failIfAlmostEqual(dopt1, dopt2, 4)
self.failIfAlmostEqual(copt1, copt2, 4)
self.failIfAlmostEqual(mopt1, mopt2, 4)
GP3 = GaussianProcess(MaternKernel3([1.0, 1.0]), X, Y, noise=0.1)
self.failUnlessEqual(GP3.noise, 0.1)
eif3 = EI(GP3)
dopt3, _ = direct(eif3.negf, tf.bounds, maxiter=10)
copt3, _ = cdirect(eif3.negf, tf.bounds, maxiter=10)
mopt3, _ = maximizeEI(GP3, tf.bounds, maxiter=10)
self.failUnlessAlmostEqual(dopt3, copt3, 4)
self.failUnlessAlmostEqual(-dopt3, mopt3, 4)
self.failUnlessAlmostEqual(-copt3, mopt3, 4)
self.failIfAlmostEqual(dopt1, dopt3, 4)
self.failIfAlmostEqual(copt1, copt3, 4)
self.failIfAlmostEqual(mopt1, mopt3, 4)
self.failIfAlmostEqual(dopt2, dopt3, 4)
self.failIfAlmostEqual(copt2, copt3, 4)
self.failIfAlmostEqual(mopt2, mopt3, 4)
def testXi(self):
S5 = Shekel5()
GP1 = GaussianProcess(GaussianKernel_iso([.2]))
# self.failUnlessEqual(GP1.xi, 0.0)
X = lhcSample(S5.bounds, 10, seed=0)
Y = [S5.f(x) for x in X]
GP1.addData(X, Y)
eif1 = EI(GP1, xi=0.0)
dopt1, _ = direct(eif1.negf, S5.bounds, maxiter=10)
copt1, _ = cdirect(eif1.negf, S5.bounds, maxiter=10)
mopt1, _ = maximizeEI(GP1, S5.bounds, xi=0.0, maxiter=10)
self.failUnlessAlmostEqual(dopt1, copt1, 4)
self.failUnlessAlmostEqual(-dopt1, mopt1, 4)
self.failUnlessAlmostEqual(-copt1, mopt1, 4)
GP2 = GaussianProcess(GaussianKernel_iso([.3]), X, Y)
eif2 = EI(GP2, xi=0.01)
self.failUnlessEqual(eif2.xi, 0.01)
dopt2, _ = direct(eif2.negf, S5.bounds, maxiter=10)
copt2, _ = cdirect(eif2.negf, S5.bounds, maxiter=10)
mopt2, _ = maximizeEI(GP2, S5.bounds, xi=0.01, maxiter=10)
self.failUnlessAlmostEqual(dopt2, copt2, 4)
self.failUnlessAlmostEqual(-dopt2, mopt2, 4)
self.failUnlessAlmostEqual(-copt2, mopt2, 4)
self.failIfAlmostEqual(dopt1, dopt2, 4)
self.failIfAlmostEqual(copt1, copt2, 4)
self.failIfAlmostEqual(mopt1, mopt2, 4)
GP3 = GaussianProcess(GaussianKernel_iso([.3]), X, Y)
eif3 = EI(GP3, xi=0.1)
dopt3, _ = direct(eif3.negf, S5.bounds, maxiter=10)
copt3, _ = cdirect(eif3.negf, S5.bounds, maxiter=10)
mopt3, _ = maximizeEI(GP3, S5.bounds, xi=0.1, maxiter=10)
self.failUnlessAlmostEqual(dopt3, copt3, 4)
self.failUnlessAlmostEqual(-dopt3, mopt3, 4)
self.failUnlessAlmostEqual(-copt3, mopt3, 4)
self.failIfAlmostEqual(dopt1, dopt3, 4)
self.failIfAlmostEqual(copt1, copt3, 4)
self.failIfAlmostEqual(mopt1, mopt3, 4)
self.failIfAlmostEqual(dopt2, dopt3, 4)
self.failIfAlmostEqual(copt2, copt3, 4)
self.failIfAlmostEqual(mopt2, mopt3, 4)
def testXi(self):
S5 = Shekel5()
GP1 = GaussianProcess(GaussianKernel_iso([.2]))
# self.failUnlessEqual(GP1.xi, 0.0)
X = lhcSample(S5.bounds, 10, seed=0)
Y = [S5.f(x) for x in X]
GP1.addData(X, Y)
ucbf1 = UCB(GP1, len(S5.bounds), scale=0.5)
dopt1, _ = direct(ucbf1.negf, S5.bounds, maxiter=10)
copt1, _ = cdirect(ucbf1.negf, S5.bounds, maxiter=10)
mopt1, _ = maximizeUCB(GP1, S5.bounds, scale=0.5, maxiter=10)
self.failUnlessAlmostEqual(dopt1, copt1, 4)
self.failUnlessAlmostEqual(-dopt1, mopt1, 4)
self.failUnlessAlmostEqual(-copt1, mopt1, 4)
GP2 = GaussianProcess(GaussianKernel_iso([.3]), X, Y)
ucbf2 = UCB(GP2, len(S5.bounds), scale=0.01)
dopt2, _ = direct(ucbf2.negf, S5.bounds, maxiter=10)
copt2, _ = cdirect(ucbf2.negf, S5.bounds, maxiter=10)
mopt2, _ = maximizeUCB(GP2, S5.bounds, scale=.01, maxiter=10)
self.failUnlessAlmostEqual(dopt2, copt2, 4)
self.failUnlessAlmostEqual(-dopt2, mopt2, 4)
self.failUnlessAlmostEqual(-copt2, mopt2, 4)
self.failIfAlmostEqual(dopt1, dopt2, 4)
self.failIfAlmostEqual(copt1, copt2, 4)
self.failIfAlmostEqual(mopt1, mopt2, 4)
GP3 = GaussianProcess(GaussianKernel_iso([.3]), X, Y)
ucbf3 = UCB(GP3, len(S5.bounds), scale=.9)
dopt3, _ = direct(ucbf3.negf, S5.bounds, maxiter=10)
copt3, _ = cdirect(ucbf3.negf, S5.bounds, maxiter=10)
mopt3, _ = maximizeUCB(GP3, S5.bounds, scale=0.9, maxiter=10)
self.failUnlessAlmostEqual(dopt3, copt3, 4)
self.failUnlessAlmostEqual(-dopt3, mopt3, 4)
self.failUnlessAlmostEqual(-copt3, mopt3, 4)
self.failIfAlmostEqual(dopt1, dopt3, 4)
self.failIfAlmostEqual(copt1, copt3, 4)
self.failIfAlmostEqual(mopt1, mopt3, 4)
self.failIfAlmostEqual(dopt2, dopt3, 4)
self.failIfAlmostEqual(copt2, copt3, 4)
self.failIfAlmostEqual(mopt2, mopt3, 4)
def test1DcEI(self):
f = lambda x: float(sin(x*5.))
X = lhcSample([[0., 1.]], 5, seed=22)
Y = [f(x) for x in X]
kernel = GaussianKernel_ard(array([1.0]))
GP = GaussianProcess(kernel)
GP.addData(X, Y)
# should use optimizeGP.cpp
maxei = maximizeEI(GP, [[0., 1.]])
if False:
figure(1)
plot(X, Y, 'ro')
plot([x/100 for x in xrange(100)], [GP.ei(x/100) for x in xrange(100)])
plot(maxei[1][0], maxei[0], 'ko')
show()
def load_results(self, *args):
super(IM_EGO_Test, self).load_results(*args)
from ego.gaussianprocess import GaussianProcess
from ego.gaussianprocess.kernel import GaussianKernel_ard
# Build the gp
kernel = GaussianKernel_ard(self.kernel_hyperparms)
self.gp = GaussianProcess(kernel, noise=self.gp_noise)
for x, y in zip(self.gp_X, self.gp_Y):
self.gp.addData(x, 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)
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 test():
GP = GaussianProcess(GaussianKernel_iso([.2, 1.0]))
X = array([[.2], [.3], [.5], [1.5]])
Y = [1, 0, 1, .75]
GP.addData(X, Y)
figure(1)
A = arange(0, 2, 0.01)
mu = array([GP.mu(x) for x in A])
sig2 = array([GP.posterior(x)[1] for x in A])
Ei = EI(GP)
ei = [-Ei.negf(x) for x in A]
Pi = PI(GP)
pi = [-Pi.negf(x) for x in A]
Ucb = UCB(GP, 1, T=2)
ucb = [-Ucb.negf(x) for x in A]
ax = subplot(1, 1, 1)
ax.plot(A, mu, 'k-', lw=2)
xv, yv = poly_between(A, mu - sig2, mu + sig2)
ax.fill(xv, yv, color="#CCCCCC")
ax.plot(A, ei, 'g-', lw=2, label='EI')
ax.plot(A, ucb, 'g--', lw=2, label='UCB')
ax.plot(A, pi, 'g:', lw=2, label='PI')
ax.plot(X, Y, 'ro')
ax.legend()
draw()
show()
def test1DcUCB(self):
f = lambda x: float(sin(x * 5.))
X = lhcSample([[0., 1.]], 5, seed=22)
Y = [f(x) for x in X]
kernel = GaussianKernel_ard(array([1.0]))
GP = GaussianProcess(kernel)
GP.addData(X, Y)
# should use optimizeGP.cpp
ucbf = UCB(GP, 1)
dopt, doptx = direct(ucbf.negf, [[0., 1.]], maxiter=10)
copt, coptx = cdirect(ucbf.negf, [[0., 1.]], maxiter=10)
mopt, moptx = maximizeUCB(GP, [[0., 1.]], 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)
def test1DcUCB(self):
f = lambda x: float(sin(x*5.))
X = lhcSample([[0., 1.]], 5, seed=22)
Y = [f(x) for x in X]
kernel = GaussianKernel_ard(array([1.0]))
GP = GaussianProcess(kernel)
GP.addData(X, Y)
# should use optimizeGP.cpp
ucbf = UCB(GP, 1)
dopt, doptx = direct(ucbf.negf, [[0., 1.]], maxiter=10)
copt, coptx = cdirect(ucbf.negf, [[0., 1.]], maxiter=10)
mopt, moptx = maximizeUCB(GP, [[0., 1.]], 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)
def load_results(self, *args):
super(SARD_EGO_Test, self).load_results(*args)
from ego.gaussianprocess import GaussianProcess
from ego.gaussianprocess.kernel import GaussianKernel_ard
# Build the gp
kernel = GaussianKernel_ard(self.kernel_hyperparms)
self.gp = GaussianProcess(kernel, noise=self.gp_noise)
for x, y in zip(self.gp_X, self.gp_Y):
self.gp.addData(x, y)
print shape(self.S_end)
print shape(self.E_samples)
print shape(self.MH_ratios)
print shape(self.E_proposeds)
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 testXi(self):
S5 = Shekel5()
GP1 = GaussianProcess(GaussianKernel_iso([.2]))
# self.failUnlessEqual(GP1.xi, 0.0)
X = lhcSample(S5.bounds, 10, seed=0)
Y = [S5.f(x) for x in X]
GP1.addData(X, Y)
eif1 = EI(GP1, xi=0.0)
dopt1, _ = direct(eif1.negf, S5.bounds, maxiter=10)
copt1, _ = cdirect(eif1.negf, S5.bounds, maxiter=10)
mopt1, _ = maximizeEI(GP1, S5.bounds, xi=0.0, maxiter=10)
self.failUnlessAlmostEqual(dopt1, copt1, 4)
self.failUnlessAlmostEqual(-dopt1, mopt1, 4)
self.failUnlessAlmostEqual(-copt1, mopt1, 4)
GP2 = GaussianProcess(GaussianKernel_iso([.3]), X, Y)
eif2 = EI(GP2, xi=0.01)
self.failUnlessEqual(eif2.xi, 0.01)
dopt2, _ = direct(eif2.negf, S5.bounds, maxiter=10)
copt2, _ = cdirect(eif2.negf, S5.bounds, maxiter=10)
mopt2, _ = maximizeEI(GP2, S5.bounds, xi=0.01, maxiter=10)
self.failUnlessAlmostEqual(dopt2, copt2, 4)
self.failUnlessAlmostEqual(-dopt2, mopt2, 4)
self.failUnlessAlmostEqual(-copt2, mopt2, 4)
self.failIfAlmostEqual(dopt1, dopt2, 4)
self.failIfAlmostEqual(copt1, copt2, 4)
self.failIfAlmostEqual(mopt1, mopt2, 4)
GP3 = GaussianProcess(GaussianKernel_iso([.3]), X, Y)
eif3 = EI(GP3, xi=0.1)
dopt3, _ = direct(eif3.negf, S5.bounds, maxiter=10)
copt3, _ = cdirect(eif3.negf, S5.bounds, maxiter=10)
mopt3, _ = maximizeEI(GP3, S5.bounds, xi=0.1, maxiter=10)
self.failUnlessAlmostEqual(dopt3, copt3, 4)
self.failUnlessAlmostEqual(-dopt3, mopt3, 4)
self.failUnlessAlmostEqual(-copt3, mopt3, 4)
self.failIfAlmostEqual(dopt1, dopt3, 4)
self.failIfAlmostEqual(copt1, copt3, 4)
self.failIfAlmostEqual(mopt1, mopt3, 4)
self.failIfAlmostEqual(dopt2, dopt3, 4)
self.failIfAlmostEqual(copt2, copt3, 4)
self.failIfAlmostEqual(mopt2, mopt3, 4)
def testXi(self):
S5 = Shekel5()
GP1 = GaussianProcess(GaussianKernel_iso([.2]))
# self.failUnlessEqual(GP1.xi, 0.0)
X = lhcSample(S5.bounds, 10, seed=0)
Y = [S5.f(x) for x in X]
GP1.addData(X, Y)
ucbf1 = UCB(GP1, len(S5.bounds), scale=0.5)
dopt1, _ = direct(ucbf1.negf, S5.bounds, maxiter=10)
copt1, _ = cdirect(ucbf1.negf, S5.bounds, maxiter=10)
mopt1, _ = maximizeUCB(GP1, S5.bounds, scale=0.5, maxiter=10)
self.failUnlessAlmostEqual(dopt1, copt1, 4)
self.failUnlessAlmostEqual(-dopt1, mopt1, 4)
self.failUnlessAlmostEqual(-copt1, mopt1, 4)
GP2 = GaussianProcess(GaussianKernel_iso([.3]), X, Y)
ucbf2 = UCB(GP2, len(S5.bounds), scale=0.01)
dopt2, _ = direct(ucbf2.negf, S5.bounds, maxiter=10)
copt2, _ = cdirect(ucbf2.negf, S5.bounds, maxiter=10)
mopt2, _ = maximizeUCB(GP2, S5.bounds, scale=.01, maxiter=10)
self.failUnlessAlmostEqual(dopt2, copt2, 4)
self.failUnlessAlmostEqual(-dopt2, mopt2, 4)
self.failUnlessAlmostEqual(-copt2, mopt2, 4)
self.failIfAlmostEqual(dopt1, dopt2, 4)
self.failIfAlmostEqual(copt1, copt2, 4)
self.failIfAlmostEqual(mopt1, mopt2, 4)
GP3 = GaussianProcess(GaussianKernel_iso([.3]), X, Y)
ucbf3 = UCB(GP3, len(S5.bounds), scale=.9)
dopt3, _ = direct(ucbf3.negf, S5.bounds, maxiter=10)
copt3, _ = cdirect(ucbf3.negf, S5.bounds, maxiter=10)
mopt3, _ = maximizeUCB(GP3, S5.bounds, scale=0.9, maxiter=10)
self.failUnlessAlmostEqual(dopt3, copt3, 4)
self.failUnlessAlmostEqual(-dopt3, mopt3, 4)
self.failUnlessAlmostEqual(-copt3, mopt3, 4)
self.failIfAlmostEqual(dopt1, dopt3, 4)
self.failIfAlmostEqual(copt1, copt3, 4)
self.failIfAlmostEqual(mopt1, mopt3, 4)
self.failIfAlmostEqual(dopt2, dopt3, 4)
self.failIfAlmostEqual(copt2, copt3, 4)
self.failIfAlmostEqual(mopt2, mopt3, 4)
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 fastUCBGallery(GP, bounds, N, useBest=True, samples=300, useCDIRECT=True, xi=0, passback={}):
"""
Use UCB to generate a gallery of N instances using Monte Carlo to
approximate the optimization of the utility function.
"""
gallery = []
if len(GP.X) > 0:
if useBest:
# find best sample already seen, that lies within the bounds
bestY = -inf
bestX = None
for x, y in zip(GP.X, GP.Y):
if y > bestY:
for v, b in zip(x, bounds):
if v < b[0] or v > b[1]:
break
else:
bestY = y
bestX = x
if bestX is not None:
gallery.append(bestX)
# create a "fake" GP from the GP that was passed in (can't just copy
# b/c original could have been PrefGP)
hallucGP = GaussianProcess(deepcopy(GP.kernel), deepcopy(GP.X), deepcopy(GP.Y), prior=GP.prior)
elif GP.prior is None:
# if we have no data and no prior, start in the center
x = array([(b[0]+b[1])/2. for b in bounds])
gallery.append(x)
hallucGP = GaussianProcess(deepcopy(GP.kernel), [x], [0.0], prior=GP.prior)
else:
# optimize from prior
if DEBUG: print 'GET DATA FROM PRIOR'
bestmu = -inf
bestX = None
for m in GP.prior.means:
argmin = fmin_bfgs(GP.negmu, m, disp=False)
if DEBUG: print argmin,
for i in xrange(len(argmin)):
argmin[i] = clip(argmin[i], bounds[i][0], bounds[i][1])
# if DEBUG: print 'converted to', argmin
if GP.mu(argmin) > bestmu:
bestX = argmin
bestmu = GP.mu(argmin)
if DEBUG: print '***** bestmu =', bestmu
if DEBUG: print '***** bestX =', bestX
gallery.append(bestX)
hallucGP = GaussianProcess(deepcopy(GP.kernel), bestX, bestmu, prior=GP.prior)
while len(gallery) < N:
if DEBUG: print '\n\n\thave %d data for gallery' % len(gallery)
bestUCB = -inf
bestX = None
# ut = UCB(hallucGP, len(bounds), N)
ut = EI(hallucGP, xi=xi)
if DEBUG: print '\tget with max EI'
opt, optx = maximizeEI(hallucGP, bounds, xi=xi, useCDIRECT=useCDIRECT)
#if len(gallery)==0 or min(norm(optx-gx) for gx in gallery) > .5:
# if DEBUG: print '\tgot one'
bestUCB = opt
bestX = optx
#else:
# if DEBUG: print '\ttoo close to existing'
'''
# try some random samples
if DEBUG: print '\ttry random samples'
for x in lhcSample(bounds, samples):
u = -ut.negf(x)
if u > bestUCB and min(norm(x-gx) for gx in gallery) > .5:
'\they, this one is even better!'
bestUCB = u
bestX = x
passback['found_random'] = 1
# now try the prior means
if hallucGP.prior is not None:
if DEBUG: print '\ttry prior means (bestUCB = %f)'%bestUCB
for x in hallucGP.prior.means:
x = array([clip(x[i], bounds[i][0], bounds[i][1]) for i in xrange(len(x))])
x = x * hallucGP.prior.width + hallucGP.prior.lowerb
u = -ut.negf(x)
# if DEBUG: print 'u = %f', u
if u > bestUCB:
if len(gallery)==0 or min(norm(x-gx) for gx in gallery) > .5:
if DEBUG: print '\tthis one is even better! prior mean %s has u = %f' % (x, u)
bestUCB = u
bestX = x
passback['found_prior'] = 1
'''
gallery.append(bestX)
if len(gallery) < N-1:
hallucGP.addData(bestX, hallucGP.mu(bestX))
# these can be optionally passed back if the caller passes in its own dict
passback['hallucGP'] = hallucGP
passback['utility'] = ut
return gallery
def demoObservations():
"""
Simple demo for a scenario where we have direct observations (ie ratings
or responses) with noise. The model has three parameters, but after
initial training, we fix one to be 1.0 and optimize the other two. At
each step, we visualize the posterior mean, variance and expected
improvement. We then find the point of maximum expected improvement and
ask the user for the scalar response value.
To see how the model adapts to inputs, try rating the first few values
higher or lower than predicted and see what happens to the visualizations.
"""
# the kernel parameters control the impact of different values on the
# parameters. we are defining a model with three parameters
kernel = GaussianKernel_ard(array([.5, .5, .3]))
# we want to allow some noise in the observations -- the noise parameter
# is the variance of the additive Gaussian noise Y + N(0, noise)
noise = 0.1
# create the Gaussian Process using the kernel we've just defined
GP = GaussianProcess(kernel, noise=noise)
# add some data to the model. the data must have the same dimensionality
# as the kernel
X = [array([1, 1.5, 0.9]),
array([.8, -.2, -0.1]),
array([2, .8, -.2]),
array([0, 0, .5])]
Y = [1, .7, .6, -.1]
print 'adding data to model'
for x, y in zip(X, Y):
print '\tx = %s, y = %.1f' % (x, y)
GP.addData(X, Y)
# the GP.posterior(x) function returns, for x, the posterior distribution
# at x, characterized as a normal distribution with mean mu, variance
# sigma^2
testX = [array([1, 1.45, 1.0]),
array([-10, .5, -10])]
for tx in testX:
mu, sig2 = GP.posterior(tx)
print 'the posterior of %s is a normal distribution N(%.3f, %.3f)' % (tx, mu, sig2)
# now, let's find the best points to evaluate next. we fix the first
# dimension to be 1 and for the others, we search the range [-2, 2]
bound = [[1, 1], [-1.99, 1.98], [-1.99, 1.98]]
figure(1, figsize=(5, 10))
while True:
_, optx = maximizeEI(GP, bound, xi=.1, useCDIRECT=False)
print "X"
# visualize the mean, variance and expected improvement functions on
# the free parameters
x1 = arange(bound[1][0], bound[1][1], 0.1)
x2 = arange(bound[2][0], bound[2][1], 0.1)
X1, X2 = meshgrid(x1, x2)
ei = zeros_like(X1)
m = zeros_like(X1)
v = zeros_like(X1)
for i in xrange(X1.shape[0]):
for j in xrange(X1.shape[1]):
z = array([1.0, X1[i,j], X2[i,j]])
ei[i,j] = -EI(GP).negf(z)
m[i,j], v[i,j] = GP.posterior(z)
clf()
for i, (func, title) in enumerate(([m, 'prediction (posterior mean)'], [v, 'uncertainty (posterior variance)'], [ei, 'utility (expected improvement)'])):
ax = subplot(3, 1, i+1)
cs = ax.contourf(X1, X2, func, 20)
ax.plot(optx[1], optx[2], 'wo')
colorbar(cs)
ax.set_title(title)
ax.set_xlabel('x[1]')
ax.set_ylabel('x[2]')
ax.set_xticks([-2,0,2])
ax.set_yticks([-2,0,2])
m, v = GP.posterior(optx)
try:
response = input('\nmaximum expected improvement is at parameters x = [%.3f, %.3f, %.3f], where mean is %.3f, variance is %.3f. \nwhat is the value there (non-numeric to quit)? ' % (optx[0], optx[1], optx[2], m, v))
except:
break
GP.addData(optx, response)
print 'updating model.'
class SARD_EGO_Test(SARD_Test):
name = "SARD_EGO"
nadapted_moves = None
nruns_per_param_update = None
nadaptations = None
saved_res_fields = \
set(['nadapted_moves', 'nruns_per_param_update',
'nadaptations', 'gp_X', 'gp_Y', 'rewards',
'kernel_hyperparms', 'gp_noise', 'policy']) | \
SARD_Test.saved_res_fields
def __init__(self, graph,
nmoves, nadaptations, nruns_per_param_update,
policy_size,
gamma_hi_bounds, gamma_lo_bounds,
iters_per_move_bounds, strategy, exp_temp, MH_rate,
max_SAW_length_bounds, min_SAW_length_bounds,
S_in=None, return_samples=1):
super(SARD_EGO_Test, self).__init__\
(graph, nmoves, gamma_hi_bounds, gamma_lo_bounds,
iters_per_move_bounds,
max_SAW_length_bounds, min_SAW_length_bounds, S_in)
self.max_SAW_length_bounds = [self.max_SAW_length_bounds[i] - \
self.min_SAW_length_bounds[i] for i in range(len(self.min_SAW_length_bounds))]
self.gamma_hi_bounds = [self.gamma_hi_bounds[i] - \
self.gamma_lo_bounds[i] for i in range(len(self.gamma_lo_bounds))]
self.policy_size = policy_size
self.hdf5_base_loc += "/p" + str(self.policy_size)
self.nadapted_moves = \
array([get_num_adapted_moves(nruns_per_param_update,
nadaptations)])
self.nadaptations = nadaptations
self.nruns_per_param_update = nruns_per_param_update
h_effective_in = self.graph.get_effective_fields(self.S_in)
self.sampler_fn = \
lambda : sard.SARDRun_EGO \
(self.graph.nbrs_list_i, self.graph.incident_edge_list_i,
self.graph.edges_i, self.graph.J, self.graph.h,
self.S_in, h_effective_in, self.graph.beta_true,
self.gamma_hi_bounds, self.gamma_lo_bounds,
self.iters_per_move_bounds,
self.max_SAW_length_bounds, self.min_SAW_length_bounds,
self.nmoves, self.nadaptations,
self.nruns_per_param_update, self.policy_size, strategy, exp_temp, MH_rate, return_samples)
def make_policy_dict(self):
reshaped = self.policy.reshape(8, self.policy_size)
policy = map(lambda x, y: (round(x[0],0), round(y[0], 0)),
self.policy[1::8], self.policy[1::8]+self.policy[2::8])
policy_dict = {}
for x in policy:
policy_dict[x] = policy_dict.get(x, 0) + 1
return policy_dict
def plot_policy_as_histogram(self):
plot_name = "policy_histogram"
import matplotlib.pyplot as plt
xpos = []
ypos = []
dz = []
policy_dict = self.make_policy_dict()
for k, v in policy_dict.iteritems():
xpos.append(k[0])
ypos.append(k[1])
dz.append(v)
dx_size = (self.min_SAW_length_bounds[1] - self.min_SAW_length_bounds[0])/200
dy_size = (self.max_SAW_length_bounds[1] - self.max_SAW_length_bounds[0])/200 + dx_size
zpos = zeros_like(xpos)
dx = dx_size * ones_like(xpos)
dy = dy_size * ones_like(ypos)
colour_max = max(dz)
colours = map(lambda x: plt.cm.jet(x / colour_max), dz)
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
fig = plt.figure()
ax = Axes3D(fig, elev=70)
ax.w_zaxis.set_major_locator(LinearLocator(10))
ax.w_zaxis.set_major_formatter(FormatStrFormatter('%.03f'))
ax.bar3d(xpos, ypos, zpos, dx, dy, dz,
edgecolors=(0.0, 0.0, 0.0, 0.0),
color=colours)
ax.set_xlim3d(self.min_SAW_length_bounds[0], self.min_SAW_length_bounds[1])
ax.set_ylim3d(self.min_SAW_length_bounds[0] + self.max_SAW_length_bounds[0], self.min_SAW_length_bounds[1] + self.max_SAW_length_bounds[1])
self.save_current_plot(plot_name)
def run(self):
self.S_end, self.E_samples, self.E_proposeds, \
self.log_f_fwds, self.log_f_revs, \
self.MH_ratios, self.move_types, \
self.used_sigma_lengths, self.used_rho_lengths, \
self.used_iters_per_move, \
self.used_gammas_his, self.used_gammas_los, \
self.used_P_LL, self.used_P_LH, self.used_P_HL, \
self.rewards, gp, self.policy, self.samples \
= self.sampler_fn()
self.gp_X = gp.X
self.gp_Y = gp.Y
self.kernel_hyperparms = gp.kernel.getHyperparams()
self.gp_noise = gp.noise
def load_results(self, *args):
super(SARD_EGO_Test, self).load_results(*args)
from ego.gaussianprocess import GaussianProcess
from ego.gaussianprocess.kernel import GaussianKernel_ard
# Build the gp
kernel = GaussianKernel_ard(self.kernel_hyperparms)
self.gp = GaussianProcess(kernel, noise=self.gp_noise)
for x, y in zip(self.gp_X, self.gp_Y):
self.gp.addData(x, y)
print shape(self.S_end)
print shape(self.E_samples)
print shape(self.MH_ratios)
print shape(self.E_proposeds)
def testGDelta(self):
# usually, Gdelta==G
GP = GaussianProcess(GaussianKernel_iso([0.05]))
X = lhcSample([[0., 1.]], 5, seed=10)
Y = [x**2 for x in X]
GP.train(X, Y)
G = (Y[0] - max(Y)) / (Y[0] - 1)
self.failUnlessEqual(G, Gdelta(GP, [[0., 1.]], Y[0], 1.0, 0.01))
# sometimes, though, Gdelta > G -- this GP has a very high confidence
# prediction of a very good point at x ~ .65
GP = GaussianProcess(GaussianKernel_iso([0.1]))
X = array([[.5], [.51], [.59], [.6]])
Y = array([1., 2., 2., 1.])
GP.train(X, Y)
# figure(1)
# A = arange(0, 1, 0.01)
# post = [GP.posterior(x) for x in A]
# plot(A, [p[0] for p in post], 'k-')
# plot(A, [p[0]+p[1] for p in post], 'k:')
# show()
G = (Y[0] - max(Y)) / (Y[0] - 4.0)
Gd = Gdelta(GP, [[0., 1.]], Y[0], 4.0, 0.01)
self.failUnless(G < Gd)
# however, if there is more variance, we will collapse back to G
GP = GaussianProcess(GaussianKernel_iso([.001]))
GP.train(X, Y)
G = (Y[0] - max(Y)) / (Y[0] - 4.0)
self.failUnlessEqual(G, Gdelta(GP, [[0., 1.]], Y[0], 4.0, 0.01))
class IM_EGO_Test(IM_Test):
name = "IM_EGO"
nadapted_moves = None
nruns_per_param_update = None
nadaptations = None
gamma_min = None
gamma_max = None
saved_res_fields = \
set(['nadapted_moves', 'nruns_per_param_update',
'nadaptations', 'gp_X', 'gp_Y', 'rewards',
'kernel_hyperparms', 'gp_noise',
'gamma_min', 'gamma_max', 'policy']) | \
IM_Test.saved_res_fields
def __init__(self, graph,
nmoves, nadaptations, nruns_per_param_update,
policy_size,
SAW_length_min, SAW_length_max, strategy, exp_temp,
MH_rate, S_ref=None, S_in=None):
super(IM_EGO_Test, self).__init__\
(graph, nmoves,
SAW_length_min, SAW_length_max, S_ref, S_in)
self.exp_temp = exp_temp
self.MH_rate = MH_rate
self.strategy = strategy
self.policy_size = policy_size
self.hdf5_base_loc += "/p" + str(self.policy_size)
self.nadapted_moves = \
array([get_num_adapted_moves(nruns_per_param_update,
nadaptations)])
self.nadaptations = nadaptations
self.nruns_per_param_update = nruns_per_param_update
self.gammas = arange(0,2.0001,0.2) * self.graph.beta_true
self.h_effective_in = self.graph.get_effective_fields(self.S_in)
self.sampler_fn = \
lambda : im.IMRun_EGO\
(self.graph.nbrs_list_i, self.graph.incident_edge_list_i,
self.graph.edges_i, self.graph.J, self.graph.h,
self.S_ref, self.S_in, self.h_effective_in,
self.graph.beta_true, self.gammas,
self.SAW_length_min, self.SAW_length_max,
self.nmoves, self.nadaptations,
self.nruns_per_param_update, self.policy_size,
self.strategy, self.exp_temp, self.MH_rate)
def run(self):
self.S_end, self.E_samples, self.E_proposeds, \
self.log_f_fwds, self.log_f_revs, \
self.MH_ratios, self.SAW_lengths, self.used_gammas, \
self.rewards, gp, self.gamma_min, self.gamma_max, \
self.policy \
= self.sampler_fn()
self.gp_X = gp.X
self.gp_Y = gp.Y
self.kernel_hyperparms = gp.kernel.getHyperparams()
self.gp_noise = gp.noise
def load_results(self, *args):
super(IM_EGO_Test, self).load_results(*args)
from ego.gaussianprocess import GaussianProcess
from ego.gaussianprocess.kernel import GaussianKernel_ard
# Build the gp
kernel = GaussianKernel_ard(self.kernel_hyperparms)
self.gp = GaussianProcess(kernel, noise=self.gp_noise)
for x, y in zip(self.gp_X, self.gp_Y):
self.gp.addData(x, y)
def save_current_plot(self, plot_name):
plot_dir = "plots/%s" % (self.graph.name)
plot_fn = "%s/%s_%s_p%d_r%d.pdf" % \
(plot_dir, plot_name, self.name,
self.policy_size, self.res_num)
self.save_current_plot_to_file(plot_fn)
def compute_gp_posterior_over_grid(self):
x1 = arange(self.SAW_length_min, self.SAW_length_max, 1, dtype=float)
x2 = arange(self.gamma_min, self.gamma_max,
(self.gamma_max - self.gamma_min) / 100,
dtype=float)
X1, X2 = meshgrid(x1, x2)
m = zeros_like(X1)
v = zeros_like(X1)
for i in xrange(X1.shape[0]):
for j in xrange(X1.shape[1]):
z = array([X1[i, j], X2[i, j]])
res = self.gp.posterior(z)
m[i, j] = res[0]
v[i, j] = res[1]
return X1, X2, m, v
def plot_surface_on_grid(self, X1, X2, s):
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
fig = plt.figure()
ax = Axes3D(fig, elev=70)
surf = ax.plot_surface(X1, X2, s, rstride=1, cstride=1, cmap=cm.jet,
linewidth=0, antialiased=True)
ax.set_zlim3d(-1.01, 1.01)
ax.w_zaxis.set_major_locator(LinearLocator(10))
ax.w_zaxis.set_major_formatter(FormatStrFormatter('%.03f'))
fig.colorbar(surf, shrink=0.5, aspect=5)
def plot_gp_mean(self):
plot_name = "gp_mean"
X1, X2, m, _ = self.compute_gp_posterior_over_grid()
self.plot_surface_on_grid(X1, X2, m)
self.save_current_plot(plot_name)
def plot_flat_gp_mean(self):
plot_name = "flat_gp_mean"
import matplotlib.pyplot as plt
from matplotlib import cm
_, _, m, _ = self.compute_gp_posterior_over_grid()
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.imshow(m, cmap=cm.jet, interpolation='nearest', origin='lower',
extent=[self.SAW_length_min, self.SAW_length_max,
self.gamma_min, self.gamma_max],
aspect=self.SAW_length_max/self.gamma_max)
ax.set_xlabel('SAW length $k$')
ax.set_ylabel('Energy-biasing parameter $\gamma$')
self.save_current_plot(plot_name)
def plot_average_gp_mean(self):
plot_name = "average_gp_mean"
nresults = self.get_num_results()
X1 = None
X2 = None
m_avg = None
if self.res_num is not None:
old_res_num = self.res_num
else:
old_res_num = 0
for i in xrange(nresults):
self.load_results(i)
X1, X2, m, _ = self.compute_gp_posterior_over_grid()
if m_avg is None:
m_avg = m
else:
m_avg += m
m_avg /= nresults
self.plot_surface_on_grid(X1, X2, m_avg)
self.save_current_plot(plot_name)
self.load_results(old_res_num)
def plot_flat_average_gp_mean(self):
plot_name = "flat_average_gp_mean"
import matplotlib.pyplot as plt
from matplotlib import cm
nresults = self.get_num_results()
m_avg = None
if self.res_num is not None:
old_res_num = self.res_num
else:
old_res_num = 0
for i in xrange(nresults):
self.load_results(i)
_, _, m, _ = self.compute_gp_posterior_over_grid()
if m_avg is None:
m_avg = m
else:
m_avg += m
m_avg /= nresults
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.imshow(m_avg, cmap=cm.jet, interpolation='nearest', origin='lower',
extent=[self.SAW_length_min, self.SAW_length_max,
self.gamma_min, self.gamma_max],
aspect=self.SAW_length_max/self.gamma_max)
ax.set_xlabel('SAW length $k$')
ax.set_ylabel('Energy-biasing parameter $\gamma$')
self.save_current_plot(plot_name)
self.load_results(old_res_num)
def plot_gp_var(self):
plot_name = "gp_var"
X1, X2, _, v = self.compute_gp_posterior_over_grid()
self.plot_surface_on_grid(X1, X2, v)
self.save_current_plot(plot_name)
def plot_gp_query_points(self):
plot_name = "gp_query_points"
import matplotlib.pyplot as plt
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.scatter(self.gp.X[:, 0], self.gp.X[:, 1], c=self.gp.Y)
self.save_current_plot(plot_name)
def plot_parameter_cdf(self):
pass
def make_policy_dict(self):
policy = map(lambda x, y: (round(x[0],3), round(y[0], 3)),
self.policy[::2], self.policy[1::2])
policy_dict = {}
for x in policy:
policy_dict[x] = policy_dict.get(x, 0) + 1
return policy_dict
def plot_policy_as_histogram(self):
plot_name = "policy_histogram"
import matplotlib.pyplot as plt
xpos = []
ypos = []
dz = []
policy_dict = self.make_policy_dict()
for k, v in policy_dict.iteritems():
xpos.append(k[0])
ypos.append(k[1])
dz.append(v)
dy_size = (self.gammas[-1] - self.gammas[0]) / 100
zpos = zeros_like(xpos)
dx = ones_like(xpos)
dy = dy_size * ones_like(ypos)
colour_max = max(dz)
colours = map(lambda x: plt.cm.jet(x / colour_max), dz)
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
from matplotlib.ticker import LinearLocator, FormatStrFormatter
fig = plt.figure()
ax = Axes3D(fig, elev=70)
ax.w_zaxis.set_major_locator(LinearLocator(10))
ax.w_zaxis.set_major_formatter(FormatStrFormatter('%.03f'))
ax.bar3d(xpos, ypos, zpos, dx, dy, dz,
edgecolors=(0.0, 0.0, 0.0, 0.0),
color=colours)
ax.set_xlim3d(self.SAW_length_min, self.SAW_length_max)
ax.set_ylim3d(self.gammas[0], self.gammas[-1])
self.save_current_plot(plot_name)
def plot_policy_as_flat_surface():
plot_name = 'flat_policy'
def demoObservations():
"""
Simple demo for a scenario where we have direct observations (ie ratings
or responses) with noise. The model has three parameters, but after
initial training, we fix one to be 1.0 and optimize the other two. At
each step, we visualize the posterior mean, variance and expected
improvement. We then find the point of maximum expected improvement and
ask the user for the scalar response value.
To see how the model adapts to inputs, try rating the first few values
higher or lower than predicted and see what happens to the visualizations.
"""
# the kernel parameters control the impact of different values on the
# parameters. we are defining a model with three parameters
kernel = GaussianKernel_ard(array([.5, .5, .3]))
# we want to allow some noise in the observations -- the noise parameter
# is the variance of the additive Gaussian noise Y + N(0, noise)
noise = 0.1
# create the Gaussian Process using the kernel we've just defined
GP = GaussianProcess(kernel, noise=noise)
# add some data to the model. the data must have the same dimensionality
# as the kernel
X = [
array([1, 1.5, 0.9]),
array([.8, -.2, -0.1]),
array([2, .8, -.2]),
array([0, 0, .5])
]
Y = [1, .7, .6, -.1]
print 'adding data to model'
for x, y in zip(X, Y):
print '\tx = %s, y = %.1f' % (x, y)
GP.addData(X, Y)
# the GP.posterior(x) function returns, for x, the posterior distribution
# at x, characterized as a normal distribution with mean mu, variance
# sigma^2
testX = [array([1, 1.45, 1.0]), array([-10, .5, -10])]
for tx in testX:
mu, sig2 = GP.posterior(tx)
print 'the posterior of %s is a normal distribution N(%.3f, %.3f)' % (
tx, mu, sig2)
# now, let's find the best points to evaluate next. we fix the first
# dimension to be 1 and for the others, we search the range [-2, 2]
bound = [[1, 1], [-1.99, 1.98], [-1.99, 1.98]]
figure(1, figsize=(5, 10))
while True:
_, optx = maximizeEI(GP, bound, xi=.1)
# visualize the mean, variance and expected improvement functions on
# the free parameters
x1 = arange(bound[1][0], bound[1][1], 0.1)
x2 = arange(bound[2][0], bound[2][1], 0.1)
X1, X2 = meshgrid(x1, x2)
ei = zeros_like(X1)
m = zeros_like(X1)
v = zeros_like(X1)
for i in xrange(X1.shape[0]):
for j in xrange(X1.shape[1]):
z = array([1.0, X1[i, j], X2[i, j]])
ei[i, j] = -EI(GP).negf(z)
m[i, j], v[i, j] = GP.posterior(z)
clf()
for i, (func, title) in enumerate(
([m, 'prediction (posterior mean)'
], [v, 'uncertainty (posterior variance)'],
[ei, 'utility (expected improvement)'])):
ax = subplot(3, 1, i + 1)
cs = ax.contourf(X1, X2, func, 20)
ax.plot(optx[1], optx[2], 'wo')
colorbar(cs)
ax.set_title(title)
ax.set_xlabel('x[1]')
ax.set_ylabel('x[2]')
ax.set_xticks([-2, 0, 2])
ax.set_yticks([-2, 0, 2])
show()
m, v = GP.posterior(optx)
try:
response = input(
'\nmaximum expected improvement is at parameters x = [%.3f, %.3f, %.3f], where mean is %.3f, variance is %.3f. \nwhat is the value there (non-numeric to quit)? '
% (optx[0], optx[1], optx[2], m, v))
except:
break
GP.addData(optx, response)
print 'updating model.'
def fastUCBGallery(GP, bounds, N, useBest=True, samples=300, useCDIRECT=True):
"""
Use UCB to generate a gallery of N instances using Monte Carlo to
approximate the optimization of the utility function.
"""
gallery = []
if len(GP.X) > 0:
if useBest:
# find best sample already seen, that lies within the bounds
bestY = -inf
bestX = None
for x, y in zip(GP.X, GP.Y):
if y > bestY:
for v, b in zip(x, bounds):
if v < b[0] or v > b[1]:
break
else:
bestY = y
bestX = x
if bestX is not None:
gallery.append(bestX)
# create a "fake" GP from the GP that was passed in (can't just copy
# b/c original could have been PrefGP)
hallucGP = GaussianProcess(deepcopy(GP.kernel),
deepcopy(GP.X),
deepcopy(GP.Y),
prior=GP.prior)
elif GP.prior is None:
# if we have no data and no prior, start in the center
x = array([(b[0] + b[1]) / 2. for b in bounds])
gallery.append(x)
hallucGP = GaussianProcess(deepcopy(GP.kernel), [x], [0.0],
prior=GP.prior)
else:
# optimize from prior
bestmu = -inf
bestX = None
for m in GP.prior.means:
argmin = fmin_bfgs(GP.negmu, m, disp=False)
if GP.mu(argmin) > bestmu:
bestX = argmin
bestmu = GP.mu(argmin)
gallery.append(bestX)
hallucGP = GaussianProcess(deepcopy(GP.kernel),
bestX,
bestmu,
prior=GP.prior)
while len(gallery) < N:
bestUCB = -inf
bestX = None
# ut = UCB(hallucGP, len(bounds), N)
ut = EI(hallucGP, xi=.4)
opt, optx = maximizeEI(hallucGP, bounds, xi=.3, useCDIRECT=useCDIRECT)
if len(gallery) == 0 or min(norm(optx - gx) for gx in gallery) > .5:
bestUCB = opt
bestX = optx
# try some random samples
for x in lhcSample(bounds, samples):
u = -ut.negf(x)
if u > bestUCB and min(norm(x - gx) for gx in gallery) > .5:
'\they, this one is even better!'
bestUCB = u
bestX = x
# now try the prior means
if hallucGP.prior is not None:
for x in hallucGP.prior.means:
x = array([
clip(x[i], bounds[i][0], bounds[i][1])
for i in xrange(len(x))
])
x = x * hallucGP.prior.width + hallucGP.prior.lowerb
u = -ut.negf(x)
if u > bestUCB:
if len(gallery) == 0 or min(
norm(x - gx) for gx in gallery) > .5:
bestUCB = u
bestX = x
gallery.append(bestX)
hallucGP.addData(bestX, hallucGP.mu(bestX))
return gallery
