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 plot_results(twosample_object,
xlabel="input", ylabel="ouput", title=None,
interval_indices=None, alpha=None, legend=True,
replicate_indices=None, shift=None, *args, **kwargs):
"""
Plot the results given by last prediction.
Two Instance Plots of comparing two groups to each other:
**Parameters:**
twosample_object : :py:class:`gptwosample.twosample`
GPTwoSample object, on which already 'predict' was called.
**Differential Groups:**
.. image:: ../images/plotGPTwoSampleDifferential.pdf
:height: 8cm
**Non-Differential Groups:**
.. image:: ../images/plotGPTwoSampleSame.pdf
:height: 8cm
Returns:
Proper rectangles for use in pylab.legend().
"""
if twosample_object._predicted_mean_variance is None:
print "Not yet predicted"
return
if interval_indices is None:
interval_indices = get_model_structure(
common=SP.array(SP.zeros_like(twosample_object.get_data(common_id)[0]), dtype='bool'),
individual=SP.array(SP.ones_like(twosample_object.get_data(individual_id, 0)[0]), dtype='bool'))
if title is None:
title = r'Prediction result: $\log(p(\mathcal{H}_I)/p(\mathcal{H}_S)) = %.2f $' % (twosample_object.bayes_factor())
# plparams = {'axes.labelsize': 20,
# 'text.fontsize': 20,
# 'legend.fontsize': 18,
# 'title.fontsize': 22,
# 'xtick.labelsize': 20,
# 'ytick.labelsize': 20,
# 'usetex': True }
legend_plots = []
legend_names = []
calc_replicate_indices = replicate_indices is None
alpha_groups = alpha
if alpha is not None:
alpha_groups = 1 - alpha
from matplotlib.cm import jet #@UnresolvedImport
for name, value in twosample_object._predicted_mean_variance.iteritems():
mean = value['mean']
var = SP.sqrt(value['var'])
if len(mean.shape) > 1:
number_of_groups = mean.shape[0]
first = True
for i in range(number_of_groups):
col_num = (i / (2. * number_of_groups))
col = jet(col_num)#(i/number_of_groups,i/number_of_groups,.8)
data = twosample_object.get_data(name, i)
replicate_length = len(SP.unique(data[0]))
number_of_replicates = len(data[0]) / replicate_length
if calc_replicate_indices:
# Assume replicates are appended one after another
replicate_indices = SP.concatenate([SP.repeat(rep, replicate_length) for rep in range(number_of_replicates)])
shifti = deepcopy(shift)
if shifti is not None:
shifti = shift[i * number_of_replicates:(i + 1) * number_of_replicates]
#import pdb;pdb.set_trace()
PLOT.plot_sausage(twosample_object._interpolation_interval_cache[name] - SP.mean(shifti), mean[i], var[i], format_fill={'alpha':0.2, 'facecolor':col}, format_line={'alpha':1, 'color':col, 'lw':3, 'ls':'--'}, alpha=alpha_groups)[0]
else:
PLOT.plot_sausage(twosample_object._interpolation_interval_cache[name],
mean[i], var[i],
format_fill={'alpha':0.2, 'facecolor':col},
format_line={'alpha':1, 'color':col, 'lw':3, 'ls':'--'}, alpha=alpha_groups)[0]
PLOT.plot_training_data(
SP.array(data[0]), SP.array(data[1]),
format_data={'alpha':.8,
'marker':'.',
'linestyle':'--',
'lw':1,
'markersize':6,
'color':col},
replicate_indices=replicate_indices,
shift=shifti, *args, **kwargs)
if(first):
legend_plots.append(PL.Rectangle((0, 0), 1, 1, alpha=.2, fill=True, facecolor=col))
legend_names.append("%s %i" % (name, i + 1))
#first=False
else:
col = jet(1.)
#data = twosample_object.get_data(name, interval_indices=interval_indices)
#PLOT.plot_training_data(
# data[0], data[1],
# format_data={'alpha':.2,
# 'marker':'.',
# 'linestyle':'',
# 'markersize':10,
# 'color':col})
legend_names.append("%s" % (name))
PLOT.plot_sausage(
twosample_object._interpolation_interval_cache[name], mean, var,
format_fill={'alpha':0.2, 'facecolor':col},
format_line={'alpha':1, 'color':col, 'lw':3, 'ls':'--'}, alpha=alpha)[0]
legend_plots.append(PL.Rectangle((0, 0), 1, 1, alpha=.2, fc=col, fill=True))
if legend:
PL.legend(legend_plots, legend_names,
bbox_to_anchor=(0., 0., 1., 0.), loc=3,
ncol=2,
mode="expand",
borderaxespad=0.,
fancybox=False, frameon=False)
PL.xlabel(xlabel)
PL.ylabel(ylabel)
PL.subplots_adjust(top=.88)
PL.title(title, fontsize=22)
return legend_plots
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)
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()
# import copy
# _hyperparams = copy.deepcopy(opt_model_params)
# _logtheta = SP.array([0,0,0,0],dtype='double')
# _logtheta[:2] = _hyperparams['covar'][:2]
# _logtheta[3] = _hyperparams['covar'][2]
# _hyperparams['covar'] = _logtheta
#[opt_model_params,opt_lml]=GPR.optHyper(gpr_BP,hyperparams,priors=priors,gradcheck=True,Ifilter=Ifilter)
import pygp.plot.gpr_plot as gpr_plot
first = True
[M, S] = gpr_opt_hyper.predict(opt_model_params, X)
gpr_plot.plot_sausage(X, M[0], SP.sqrt(S[0]))
gpr_plot.plot_sausage(X, M[1], SP.sqrt(S[1]))
gpr_plot.plot_training_data(x1, C[1], replicate_indices=x1_rep.reshape(-1))
gpr_plot.plot_training_data(x2, T[1], replicate_indices=x2_rep.reshape(-1))
# norm = PL.Normalize()
break_lml = []
plots = SP.int_(SP.sqrt(24) + 1)
PL.figure()
for i, BP in enumerate(x1[0,:]):
#PL.subplot(plots,plots,i+1)
_hyper = copy.deepcopy(opt_model_params)
_logtheta = _hyper['covar']
_logtheta = SP.concatenate((_logtheta, [BP, 10]))#SP.var(y[:,i])]))
_hyper['covar'] = _logtheta
# import copy
# _hyperparams = copy.deepcopy(opt_model_params)
# _logtheta = SP.array([0,0,0,0],dtype='double')
# _logtheta[:2] = _hyperparams['covar'][:2]
# _logtheta[3] = _hyperparams['covar'][2]
# _hyperparams['covar'] = _logtheta
# [opt_model_params,opt_lml]=GPR.optHyper(gpr_BP,hyperparams,priors=priors,gradcheck=True,Ifilter=Ifilter)
import pygp.plot.gpr_plot as gpr_plot
first = True
[M, S] = gpr_opt_hyper.predict(opt_model_params, X)
gpr_plot.plot_sausage(X, M[0], SP.sqrt(S[0]))
gpr_plot.plot_sausage(X, M[1], SP.sqrt(S[1]))
gpr_plot.plot_training_data(x1, C[1], replicate_indices=x1_rep.reshape(-1))
gpr_plot.plot_training_data(x2, T[1], replicate_indices=x2_rep.reshape(-1))
# norm = PL.Normalize()
break_lml = []
plots = SP.int_(SP.sqrt(24) + 1)
PL.figure()
for i, BP in enumerate(x1[0, :]):
# PL.subplot(plots,plots,i+1)
_hyper = copy.deepcopy(opt_model_params)
_logtheta = _hyper["covar"]
_logtheta = SP.concatenate((_logtheta, [BP, 10])) # SP.var(y[:,i])]))
_hyper["covar"] = _logtheta
priors_BP[3] = [lnpriors.lnGauss, [BP, 3]]