n,D = x.shape
## DEFINE parameterized covariance function
covfunc = [ ['kernels.covSum'], [ ['kernels.covSEiso'],[['kernels.covProd'],[['kernels.covPeriodic'],['kernels.covSEiso']]],\
['kernels.covRQiso'],['kernels.covSEiso'],['kernels.covNoise'] ] ]
## DEFINE parameterized mean function
meanfunc = [ ['means.meanZero'] ]
## DEFINE parameterized inference and liklihood functions
inffunc = ['inf.infExact']
likfunc = ['lik.likGauss']
## SET (hyper)parameters
hyp = hyperParameters()
## SET (hyper)parameters for covariance and mean
hyp.cov = np.array([np.log(67.), np.log(66.), np.log(1.3), np.log(1.0), np.log(2.4), np.log(90.), np.log(2.4), \
np.log(1.2), np.log(0.66), np.log(0.78), np.log(1.6/12.), np.log(0.18), np.log(0.19)])
hyp.mean = np.array([])
sn = 0.1
hyp.lik = np.array([np.log(sn)])
##----------------------------------------------------------##
## STANDARD GP (prediction) ##
##----------------------------------------------------------##
xs = np.arange(2004+1./24.,2024-1./24.,1./12.) # TEST POINTS
xs = xs.reshape(len(xs),1)
def train_cross(self):
## not sure how importatn this crap is..
## SET (hyper)parameters
n_iters = len(self.training_set) * 5
hyp = hyperParameters()
sn = 0.001; hyp.lik = array([log(sn)])
conf = self.conf
dimensions = len(self.training_set[0])
hyp.mean = [0.5 for d in xrange(dimensions)]
hyp.mean.append(1.0)
hyp.mean = array(hyp.mean)
hyp.mean = array([])
# Scale inputs and particles?
self.input_scaler = preprocessing.StandardScaler().fit(self.training_set)
self.scaled_training_set = self.input_scaler.transform(self.training_set)
# Scale training data
if self.transLog:
self.output_scaler = preprocessing.StandardScaler(with_std=False).fit(log(self.training_fitness - self.shift_by()))
self.adjusted_training_fitness = self.output_scaler.transform(log(self.training_fitness - self.shift_by()))
else:
self.output_scaler = preprocessing.StandardScaler(with_std=False).fit(self.training_fitness)
self.adjusted_training_fitness = self.output_scaler.transform(self.training_fitness)
## retrain a number of times and pick best likelihood
press_best = None
best_hyp = None
i = 0
index_array = ShuffleSplit(len(self.scaled_training_set), n_iter=n_iters, train_size=0.8, test_size=0.2) ##we use 10% of example to evaluate our
while i < conf.random_start:
if conf.corr == "isotropic":
self.covfunc = [['kernels.covSum'], [['kernels.covSEiso'],['kernels.covNoise']]]
hyp.cov = [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(2)]
elif conf.corr == "anisotropic":
self.covfunc = [['kernels.covSum'], [['kernels.covSEard'],['kernels.covNoise']]]
hyp.cov = [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(dimensions+1)]
elif conf.corr == "anirat": ## todo
self.covfunc = [['kernels.covSum'], [['kernels.covRQard'],['kernels.covNoise']]]
hyp.cov = [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(dimensions)]
hyp.cov.append(log(uniform(low=conf.thetaL, high=conf.thetaU)))
hyp.cov.append(log(uniform(low=conf.thetaL, high=conf.thetaU)))
elif conf.corr == "matern3":
self.covfunc = [['kernels.covSum'], [['kernels.covMatern'],['kernels.covNoise']]]
hyp.cov = [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(2)]
hyp.cov.append(log(3))
elif conf.corr == "matern5":
self.covfunc = [['kernels.covSum'], [['kernels.covMatern'],['kernels.covNoise']]]
hyp.cov = [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(2)]
hyp.cov.append(log(5))
elif conf.corr == "rqard":
self.covfunc = [['kernels.covSum'], [['kernels.covRQard'],['kernels.covNoise']]]
hyp.cov = [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(dimensions+2)]
elif conf.corr == "special":
self.covfunc = [['kernels.covSum'], [['kernels.covSEiso'],['kernels.covMatern'],['kernels.covNoise']]]
hyp.cov = [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(2)]
hyp.cov = hyp.cov + [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(2)]
hyp.cov.append(log(3))
else:
logging.error("The specified kernel function is not supported")
return False
hyp.cov.append(log(uniform(low=0.01, high=0.5)))
## 50% propability to usen the previous best hyper-parameters:
if self.hyp:
random_number = uniform(0.,1.)
if random_number < 0.5:
hyp = self.hyp
try:
vargout = min_wrapper(hyp,gp,'BFGS',self.inffunc,self.meanfunc,self.covfunc,self.likfunc,self.scaled_training_set ,self.adjusted_training_fitness,None,None,True)
hyp = vargout[0]
### we add some sensible checking..
## matern we dont want to overfit
## we know that the function is not just noise hence < -1
## we know for anisotorpic that at least one parameter has to have some meaning
##
press = 0.0
for train_indexes, test_indexes in index_array:
test_set = self.scaled_training_set[test_indexes]
training_set = self.scaled_training_set[train_indexes]
test_fitness = self.adjusted_training_fitness[test_indexes]
training_fitness = self.adjusted_training_fitness[train_indexes]
vargout = gp(hyp, self.inffunc,self.meanfunc,self.covfunc, self.likfunc, training_set, training_fitness, test_set)
predicted_fitness = vargout[2]
press = press + self.calc_press(predicted_fitness, test_fitness)
#if (hyp.cov[-1] < -1.) and not ((conf.corr == "matern3") and hyp.cov[0] < 0.0) and not ((conf.corr == "anisotropic") and all(hyp.cov[:-2] < 0.0)):
logging.info("Press " + str(press) + " " + str(hyp.cov))
if (((not press_best) or (press < press_best))):
best_hyp = hyp
press_best = press
except Exception, e:
logging.debug("Regressor training Failed: " + str(e))
i = i + 1
def train_nlml(self):
## not sure how importatn this crap is..
## SET (hyper)parameters
hyp = hyperParameters()
sn = 0.001; hyp.lik = array([log(sn)])
conf = self.conf
dimensions = len(self.training_set[0])
hyp.mean = [0.5 for d in xrange(dimensions)]
hyp.mean.append(1.0)
hyp.mean = array(hyp.mean)
hyp.mean = array([])
# Scale inputs and particles?
self.input_scaler = preprocessing.StandardScaler().fit(self.training_set)
self.scaled_training_set = self.input_scaler.transform(self.training_set)
# Scale training data
self.output_scaler = preprocessing.StandardScaler(with_std=False).fit(log(self.training_fitness - self.shift_by()))
self.adjusted_training_fitness = self.output_scaler.transform(log(self.training_fitness - self.shift_by()))
## retrain a number of times and pick best likelihood
nlml_best = None
i = 0
while i < conf.random_start:
if conf.corr == "isotropic":
self.covfunc = [['kernels.covSum'], [['kernels.covSEiso'],['kernels.covNoise']]]
hyp.cov = [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(2)]
elif conf.corr == "anisotropic":
self.covfunc = [['kernels.covSum'], [['kernels.covSEard'],['kernels.covNoise']]]
hyp.cov = [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(dimensions+1)]
elif conf.corr == "anirat": ## todo
self.covfunc = [['kernels.covSum'], [['kernels.covRQard'],['kernels.covNoise']]]
hyp.cov = [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(dimensions)]
hyp.cov.append(log(uniform(low=conf.thetaL, high=conf.thetaU)))
hyp.cov.append(log(uniform(low=conf.thetaL, high=conf.thetaU)))
elif conf.corr == "matern3":
self.covfunc = [['kernels.covSum'], [['kernels.covMatern'],['kernels.covNoise']]]
hyp.cov = [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(2)]
hyp.cov.append(log(3))
elif conf.corr == "matern5":
self.covfunc = [['kernels.covSum'], [['kernels.covMatern'],['kernels.covNoise']]]
hyp.cov = [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(2)]
hyp.cov.append(log(5))
elif conf.corr == "rqard":
self.covfunc = [['kernels.covSum'], [['kernels.covRQard'],['kernels.covNoise']]]
hyp.cov = [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(dimensions+2)]
elif conf.corr == "special":
self.covfunc = [['kernels.covSum'], [['kernels.covSEiso'],['kernels.covMatern'],['kernels.covNoise']]]
hyp.cov = [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(2)]
hyp.cov = hyp.cov + [log(uniform(low=conf.thetaL, high=conf.thetaU)) for d in xrange(2)]
hyp.cov.append(log(3))
else:
logging.error("The specified kernel function is not supported")
return False
hyp.cov.append(log(uniform(low=0.1, high=1.0)))
try:
vargout = min_wrapper(hyp,gp,'BFGS',self.inffunc,self.meanfunc,self.covfunc,self.likfunc,self.scaled_training_set ,self.adjusted_training_fitness,None,None,True)
hyp = vargout[0]
vargout = gp(hyp, self.inffunc,self.meanfunc,self.covfunc,self.likfunc,self.scaled_training_set ,self.adjusted_training_fitness, None,None,False)
nlml = vargout[0]
### we add some sensible checking..
## matern we dont want to overfit
## we know that the function is not just noise hence < -1
## we know for anisotorpic that at least one parameter has to have some meaning
##
if (hyp.cov[-1] < -1.) and not ((conf.corr == "matern3") and hyp.cov[0] < 0.0) and not ((conf.corr == "anisotropic") and all(hyp.cov[:-2] < 0.0)):
logging.info(str(nlml) + " " + str(hyp.cov))
if (((not nlml_best) or (nlml < nlml_best))):
self.hyp = hyp
nlml_best = nlml
else:
logging.info("hyper parameter out of spec: " + str(nlml) + " " + str(hyp.cov) + " " + str(hyp.cov[-1]))
i = i - 1
except Exception, e:
logging.debug("Regressor training Failed: " + str(e))
i = i - 1
i = i + 1
#vargout = gp(hyp,inffunc,meanfunc,covfunc,likfunc,x,y,xstar)
#ym = vargout[0]; ys2 = vargout[1]; m = vargout[2]; s2 = vargout[3]
#
#### PLOT results
#if PLOT:
# plotter(xstar,ym,s2,x,y,[-2, 2, -0.9, 3.9])
###----------------------------------------------------------###
### STANDARD GP (example 2) ###
###----------------------------------------------------------###
### USE another covariance function
covfunc = [ ['kernels.covSEiso'] ]
### SET (hyper)parameters
hyp2 = hyperParameters()
hyp2.cov = np.array([-1.0,0.0])
hyp2.mean = np.array([0.5,1.0])
hyp2.lik = np.array([np.log(0.1)])
### PREDICTION
import time
t0 = time.time()
print 'prediction'
vargout = gp(hyp2,inffunc,meanfunc,covfunc,likfunc,x,y,xstar)
ym = vargout[0]; ys2 = vargout[1]; m = vargout[2]; s2 = vargout[3]
print time.time() - t0
### PLOT results
fig = plt.figure()
plt.plot(x1[:, 0], x1[:, 1], 'b+', markersize=12)
plt.plot(x2[:, 0], x2[:, 1], 'r+', markersize=12)
pc = plt.contour(t1, t2,
np.reshape(p2 / (p1 + p2), (t1.shape[0], t1.shape[1])))
fig.colorbar(pc)
plt.grid()
plt.axis([-4, 4, -4, 4])
plt.show()
meanfunc = [['means.meanConst']]
covfunc = [['kernels.covSEard']]
likfunc = [['lik.likErf']]
inffunc = [['inf.infEP']]
hyp = hyperParameters()
hyp.mean = np.array([0.])
hyp.cov = np.array([0.0, 0.0, 0.0])
vargout = min_wrapper(hyp, gp, 'CG', inffunc, meanfunc, covfunc, likfunc,
x, y, None, None, True)
hyp = vargout[0]
#hyp.mean = np.array([-2.842117459073954])
#hyp.cov = np.array([0.051885508906388,0.170633324977413,1.218386482861781])
vargout = gp(hyp, inffunc, meanfunc, covfunc, likfunc, x, y, t,
np.ones((n, 1)))
a = vargout[0]
b = vargout[1]
c = vargout[2]
plt.plot(x,y,'b+',markersize=12)
plt.axis([-1.9,1.9,-0.9,3.9])
plt.grid()
plt.xlabel('input x')
plt.ylabel('output y')
plt.show()
z = np.array([np.linspace(-1.9,1.9,101)]).T # u test points evenly distributed in the interval [-7.5, 7.5]
## DEFINE parameterized covariance function
meanfunc = [ ['means.meanSum'], [ ['means.meanLinear'] , ['means.meanConst'] ] ]
covfunc = [ ['kernels.covMatern'] ]
inffunc = ['inf.infExact']
likfunc = ['lik.likGauss']
## SET (hyper)parameters
hyp = hyperParameters()
hyp.cov = np.array([np.log(0.25),np.log(1.0),np.log(3.0)])
hyp.mean = np.array([0.5,1.0])
sn = 0.1; hyp.lik = np.array([np.log(sn)])
#_________________________________
# STANDARD GP:
## PREDICTION
vargout = gp(hyp,inffunc,meanfunc,covfunc,likfunc,x,y,None,None,False)
print "nlml = ",vargout[0]
vargout = gp(hyp,inffunc,meanfunc,covfunc,likfunc,x,y,z)
ym = vargout[0]; ys2 = vargout[1]
m = vargout[2]; s2 = vargout[3]
## Plot results
plotter(z,ym,ys2,x,y,[-1.9, 1.9, -0.9, 3.9])