def run_demo():
LG.basicConfig(level=LG.INFO)
random.seed(1)
#1. create toy data
[x,y] = create_toy_data()
n_dimensions = 1
#2. location of unispaced predictions
X = SP.linspace(0,10,100)[:,SP.newaxis]
if 0:
#old interface where the covaraince funciton and likelihood are one thing:
#hyperparamters
covar_parms = SP.log([1,1,1])
hyperparams = {'covar':covar_parms}
#construct covariance function
SECF = se.SqexpCFARD(n_dimensions=n_dimensions)
noiseCF = noise.NoiseCFISO()
covar = combinators.SumCF((SECF,noiseCF))
covar_priors = []
#scale
covar_priors.append([lnpriors.lnGammaExp,[1,2]])
covar_priors.extend([[lnpriors.lnGammaExp,[1,1]] for i in xrange(n_dimensions)])
#noise
covar_priors.append([lnpriors.lnGammaExp,[1,1]])
priors = {'covar':covar_priors}
likelihood = None
if 1:
#new interface with likelihood parametres being decoupled from the covaraince function
likelihood = lik.GaussLikISO()
covar_parms = SP.log([1,1])
hyperparams = {'covar':covar_parms,'lik':SP.log([1])}
#construct covariance function
SECF = se.SqexpCFARD(n_dimensions=n_dimensions)
covar = SECF
covar_priors = []
#scale
covar_priors.append([lnpriors.lnGammaExp,[1,2]])
covar_priors.extend([[lnpriors.lnGammaExp,[1,1]] for i in xrange(n_dimensions)])
lik_priors = []
#noise
lik_priors.append([lnpriors.lnGammaExp,[1,1]])
priors = {'covar':covar_priors,'lik':lik_priors}
gp = GP(covar,likelihood=likelihood,x=x,y=y)
opt_model_params = opt.opt_hyper(gp,hyperparams,priors=priors,gradcheck=False)[0]
#predict
[M,S] = gp.predict(opt_model_params,X)
#create plots
gpr_plot.plot_sausage(X,M,SP.sqrt(S))
gpr_plot.plot_training_data(x,y)
PL.show()
def run_demo():
LG.basicConfig(level=LG.INFO)
random.seed(1)
#1. create toy data
[x, y] = create_toy_data()
n_dimensions = 1
#2. location of unispaced predictions
X = SP.linspace(0, 10, 100)[:, SP.newaxis]
if 0:
#old interface where the covaraince funciton and likelihood are one thing:
#hyperparamters
covar_parms = SP.log([1, 1, 1])
hyperparams = {'covar': covar_parms}
#construct covariance function
SECF = se.SqexpCFARD(n_dimensions=n_dimensions)
noiseCF = noise.NoiseCFISO()
covar = combinators.SumCF((SECF, noiseCF))
covar_priors = []
#scale
covar_priors.append([lnpriors.lnGammaExp, [1, 2]])
covar_priors.extend([[lnpriors.lnGammaExp, [1, 1]]
for i in xrange(n_dimensions)])
#noise
covar_priors.append([lnpriors.lnGammaExp, [1, 1]])
priors = {'covar': covar_priors}
likelihood = None
if 1:
#new interface with likelihood parametres being decoupled from the covaraince function
likelihood = lik.GaussLikISO()
covar_parms = SP.log([1, 1])
hyperparams = {'covar': covar_parms, 'lik': SP.log([1])}
#construct covariance function
SECF = se.SqexpCFARD(n_dimensions=n_dimensions)
covar = SECF
covar_priors = []
#scale
covar_priors.append([lnpriors.lnGammaExp, [1, 2]])
covar_priors.extend([[lnpriors.lnGammaExp, [1, 1]]
for i in xrange(n_dimensions)])
lik_priors = []
#noise
lik_priors.append([lnpriors.lnGammaExp, [1, 1]])
priors = {'covar': covar_priors, 'lik': lik_priors}
gp = GP(covar, likelihood=likelihood, x=x, y=y)
opt_model_params = opt.opt_hyper(gp,
hyperparams,
priors=priors,
gradcheck=False)[0]
#predict
[M, S] = gp.predict(opt_model_params, X)
#create plots
gpr_plot.plot_sausage(X, M, SP.sqrt(S))
gpr_plot.plot_training_data(x, y)
PL.show()
def run_demo():
LG.basicConfig(level=LG.INFO)
PL.figure()
random.seed(1)
#0. generate Toy-Data; just samples from a superposition of a sin + linear trend
n_replicates = 4
xmin = 1
xmax = 2.5 * SP.pi
x1_time_steps = 10
x2_time_steps = 20
x1 = SP.zeros(x1_time_steps * n_replicates)
x2 = SP.zeros(x2_time_steps * n_replicates)
for i in xrange(n_replicates):
x1[i * x1_time_steps:(i + 1) * x1_time_steps] = SP.linspace(
xmin, xmax, x1_time_steps)
x2[i * x2_time_steps:(i + 1) * x2_time_steps] = SP.linspace(
xmin, xmax, x2_time_steps)
C = 2 #offset
#b = 0.5
sigma1 = 0.15
sigma2 = 0.15
n_noises = 1
b = 0
y1 = b * x1 + C + 1 * SP.sin(x1)
# dy1 = b + 1*SP.cos(x1)
y1 += sigma1 * random.randn(y1.shape[0])
y1 -= y1.mean()
y2 = b * x2 + C + 1 * SP.sin(x2)
# dy2 = b + 1*SP.cos(x2)
y2 += sigma2 * random.randn(y2.shape[0])
y2 -= y2.mean()
for i in xrange(n_replicates):
x1[i * x1_time_steps:(i + 1) * x1_time_steps] += .7 + (i / 2.)
x2[i * x2_time_steps:(i + 1) * x2_time_steps] -= .7 + (i / 2.)
x1 = x1[:, SP.newaxis]
x2 = x2[:, SP.newaxis]
x = SP.concatenate((x1, x2), axis=0)
y = SP.concatenate((y1, y2), axis=0)
#predictions:
X = SP.linspace(xmin - n_replicates, xmax + n_replicates,
100 * n_replicates)[:, SP.newaxis]
#hyperparamters
dim = 1
replicate_indices = []
for i, xi in enumerate((x1, x2)):
for rep in SP.arange(i * n_replicates, (i + 1) * n_replicates):
replicate_indices.extend(SP.repeat(rep, len(xi) / n_replicates))
replicate_indices = SP.array(replicate_indices)
n_replicates = len(SP.unique(replicate_indices))
logthetaCOVAR = [1, 1]
logthetaCOVAR.extend(SP.repeat(SP.exp(1), n_replicates))
logthetaCOVAR.extend([sigma1])
logthetaCOVAR = SP.log(logthetaCOVAR) #,sigma2])
hyperparams = {'covar': logthetaCOVAR}
SECF = se.SqexpCFARD(dim)
#noiseCF = noise.NoiseReplicateCF(replicate_indices)
noiseCF = noise.NoiseCFISO()
shiftCF = combinators.ShiftCF(SECF, replicate_indices)
CovFun = combinators.SumCF((shiftCF, noiseCF))
covar_priors = []
#scale
covar_priors.append([lnpriors.lnGammaExp, [1, 2]])
for i in range(dim):
covar_priors.append([lnpriors.lnGammaExp, [1, 1]])
#shift
for i in range(n_replicates):
covar_priors.append([lnpriors.lnGauss, [0, .5]])
#noise
for i in range(n_noises):
covar_priors.append([lnpriors.lnGammaExp, [1, 1]])
covar_priors = SP.array(covar_priors)
priors = {'covar': covar_priors}
Ifilter = {'covar': SP.ones(n_replicates + 3)}
gpr = GP(CovFun, x=x, y=y)
opt_model_params = opt_hyper(gpr,
hyperparams,
priors=priors,
gradcheck=False,
Ifilter=Ifilter)[0]
#predict
[M, S] = gpr.predict(opt_model_params, X)
T = opt_model_params['covar'][2:2 + n_replicates]
PL.subplot(212)
gpr_plot.plot_sausage(X,
M,
SP.sqrt(S),
format_line=dict(alpha=1, color='g', lw=2, ls='-'))
gpr_plot.plot_training_data(x,
y,
shift=T,
replicate_indices=replicate_indices,
draw_arrows=2)
PL.suptitle("Example for GPTimeShift with simulated data", fontsize=23)
PL.title("Regression including time shift")
PL.xlabel("x")
PL.ylabel("y")
ylim = PL.ylim()
gpr = GP(combinators.SumCF((SECF, noiseCF)), x=x, y=y)
priors = {'covar': covar_priors[[0, 1, -1]]}
hyperparams = {'covar': logthetaCOVAR[[0, 1, -1]]}
opt_model_params = opt_hyper(gpr,
hyperparams,
priors=priors,
gradcheck=False)[0]
PL.subplot(211)
#predict
[M, S] = gpr.predict(opt_model_params, X)
gpr_plot.plot_sausage(X,
M,
SP.sqrt(S),
format_line=dict(alpha=1, color='g', lw=2, ls='-'))
gpr_plot.plot_training_data(x, y, replicate_indices=replicate_indices)
PL.title("Regression without time shift")
PL.xlabel("x")
PL.ylabel("y")
PL.ylim(ylim)
PL.subplots_adjust(left=.1,
bottom=.1,
right=.96,
top=.8,
wspace=.4,
hspace=.4)
PL.show()
def run_demo():
LG.basicConfig(level=LG.INFO)
PL.figure()
random.seed(1)
#0. generate Toy-Data; just samples from a superposition of a sin + linear trend
n_replicates = 4
xmin = 1
xmax = 2.5*SP.pi
x1_time_steps = 10
x2_time_steps = 20
x1 = SP.zeros(x1_time_steps*n_replicates)
x2 = SP.zeros(x2_time_steps*n_replicates)
for i in xrange(n_replicates):
x1[i*x1_time_steps:(i+1)*x1_time_steps] = SP.linspace(xmin,xmax,x1_time_steps)
x2[i*x2_time_steps:(i+1)*x2_time_steps] = SP.linspace(xmin,xmax,x2_time_steps)
C = 2 #offset
#b = 0.5
sigma1 = 0.15
sigma2 = 0.15
n_noises = 1
b = 0
y1 = b*x1 + C + 1*SP.sin(x1)
# dy1 = b + 1*SP.cos(x1)
y1 += sigma1*random.randn(y1.shape[0])
y1-= y1.mean()
y2 = b*x2 + C + 1*SP.sin(x2)
# dy2 = b + 1*SP.cos(x2)
y2 += sigma2*random.randn(y2.shape[0])
y2-= y2.mean()
for i in xrange(n_replicates):
x1[i*x1_time_steps:(i+1)*x1_time_steps] += .7 + (i/2.)
x2[i*x2_time_steps:(i+1)*x2_time_steps] -= .7 + (i/2.)
x1 = x1[:,SP.newaxis]
x2 = x2[:,SP.newaxis]
x = SP.concatenate((x1,x2),axis=0)
y = SP.concatenate((y1,y2),axis=0)
#predictions:
X = SP.linspace(xmin-n_replicates,xmax+n_replicates,100*n_replicates)[:,SP.newaxis]
#hyperparamters
dim = 1
replicate_indices = []
for i,xi in enumerate((x1,x2)):
for rep in SP.arange(i*n_replicates, (i+1)*n_replicates):
replicate_indices.extend(SP.repeat(rep,len(xi)/n_replicates))
replicate_indices = SP.array(replicate_indices)
n_replicates = len(SP.unique(replicate_indices))
logthetaCOVAR = [1,1]
logthetaCOVAR.extend(SP.repeat(SP.exp(1),n_replicates))
logthetaCOVAR.extend([sigma1])
logthetaCOVAR = SP.log(logthetaCOVAR)#,sigma2])
hyperparams = {'covar':logthetaCOVAR}
SECF = se.SqexpCFARD(dim)
#noiseCF = noise.NoiseReplicateCF(replicate_indices)
noiseCF = noise.NoiseCFISO()
shiftCF = combinators.ShiftCF(SECF,replicate_indices)
CovFun = combinators.SumCF((shiftCF,noiseCF))
covar_priors = []
#scale
covar_priors.append([lnpriors.lnGammaExp,[1,2]])
for i in range(dim):
covar_priors.append([lnpriors.lnGammaExp,[1,1]])
#shift
for i in range(n_replicates):
covar_priors.append([lnpriors.lnGauss,[0,.5]])
#noise
for i in range(n_noises):
covar_priors.append([lnpriors.lnGammaExp,[1,1]])
covar_priors = SP.array(covar_priors)
priors = {'covar':covar_priors}
Ifilter = {'covar': SP.ones(n_replicates+3)}
gpr = GP(CovFun,x=x,y=y)
opt_model_params = opt_hyper(gpr,hyperparams,priors=priors,gradcheck=False,Ifilter=Ifilter)[0]
#predict
[M,S] = gpr.predict(opt_model_params,X)
T = opt_model_params['covar'][2:2+n_replicates]
PL.subplot(212)
gpr_plot.plot_sausage(X,M,SP.sqrt(S),format_line=dict(alpha=1,color='g',lw=2, ls='-'))
gpr_plot.plot_training_data(x,y,shift=T,replicate_indices=replicate_indices,draw_arrows=2)
PL.suptitle("Example for GPTimeShift with simulated data", fontsize=23)
PL.title("Regression including time shift")
PL.xlabel("x")
PL.ylabel("y")
ylim = PL.ylim()
gpr = GP(combinators.SumCF((SECF,noiseCF)),x=x,y=y)
priors = {'covar':covar_priors[[0,1,-1]]}
hyperparams = {'covar':logthetaCOVAR[[0,1,-1]]}
opt_model_params = opt_hyper(gpr,hyperparams,priors=priors,gradcheck=False)[0]
PL.subplot(211)
#predict
[M,S] = gpr.predict(opt_model_params,X)
gpr_plot.plot_sausage(X,M,SP.sqrt(S),format_line=dict(alpha=1,color='g',lw=2, ls='-'))
gpr_plot.plot_training_data(x,y,replicate_indices=replicate_indices)
PL.title("Regression without time shift")
PL.xlabel("x")
PL.ylabel("y")
PL.ylim(ylim)
PL.subplots_adjust(left=.1, bottom=.1,
right=.96, top=.8,
wspace=.4, hspace=.4)
PL.show()
