def mrd_simulation(optimize=True, plot=True, plot_sim=True, **kw):
D1, D2, D3, N, num_inducing, Q = 150, 200, 400, 500, 3, 7
slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim)
from GPy.models import mrd
from GPy import kern
reload(mrd); reload(kern)
k = kern.linear(Q, [.05] * Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2))
m = mrd.MRD(Ylist, input_dim=Q, num_inducing=num_inducing, kernels=k, initx="", initz='permute', **kw)
for i, Y in enumerate(Ylist):
m['{}_noise'.format(i + 1)] = Y.var() / 100.
# DEBUG
# np.seterr("raise")
if optimize:
print "Optimizing Model:"
m.optimize(messages=1, max_iters=8e3, max_f_eval=8e3, gtol=.1)
if plot:
m.plot_X_1d("MRD Latent Space 1D")
m.plot_scales("MRD Scales")
return m
def bgplvm_simulation(optimize='scg',
plot=True,
max_f_eval=2e4):
# from GPy.core.transformations import logexp_clipped
D1, D2, D3, N, num_inducing, Q = 15, 8, 8, 100, 3, 5
slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot)
from GPy.models import mrd
from GPy import kern
reload(mrd); reload(kern)
Y = Ylist[0]
k = kern.linear(Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2)) # + kern.bias(Q)
m = BayesianGPLVM(Y, Q, init="PCA", num_inducing=num_inducing, kernel=k, _debug=True)
# m.constrain('variance|noise', logexp_clipped())
m['noise'] = Y.var() / 100.
m['linear_variance'] = .01
if optimize:
print "Optimizing model:"
m.optimize(optimize, max_iters=max_f_eval,
max_f_eval=max_f_eval,
messages=True, gtol=.05)
if plot:
m.plot_X_1d("BGPLVM Latent Space 1D")
m.kern.plot_ARD('BGPLVM Simulation ARD Parameters')
return m
def bgplvm_simulation_matlab_compare():
from GPy.util.datasets import simulation_BGPLVM
sim_data = simulation_BGPLVM()
Y = sim_data['Y']
S = sim_data['S']
mu = sim_data['mu']
num_inducing, [_, Q] = 3, mu.shape
from GPy.models import mrd
from GPy import kern
reload(mrd); reload(kern)
k = kern.linear(Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2))
m = BayesianGPLVM(Y, Q, init="PCA", num_inducing=num_inducing, kernel=k,
# X=mu,
# X_variance=S,
_debug=False)
m.auto_scale_factor = True
m['noise'] = Y.var() / 100.
m['linear_variance'] = .01
return m
def bgplvm_simulation(optimize=True, verbose=1,
plot=True, plot_sim=False,
max_iters=2e4,
):
from GPy import kern
from GPy.models import BayesianGPLVM
D1, D2, D3, N, num_inducing, Q = 15, 5, 8, 30, 3, 10
_, _, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim)
Y = Ylist[0]
k = kern.linear(Q, ARD=True) + kern.bias(Q, _np.exp(-2)) + kern.white(Q, _np.exp(-2)) # + kern.bias(Q)
m = BayesianGPLVM(Y, Q, init="PCA", num_inducing=num_inducing, kernel=k)
m['noise'] = Y.var() / 100.
if optimize:
print "Optimizing model:"
m.optimize('scg', messages=verbose, max_iters=max_iters,
gtol=.05)
if plot:
m.plot_X_1d("BGPLVM Latent Space 1D")
m.kern.plot_ARD('BGPLVM Simulation ARD Parameters')
return m
def mrd_simulation(optimize=True, verbose=True, plot=True, plot_sim=True, **kw):
from GPy import kern
from GPy.models import MRD
from GPy.likelihoods import Gaussian
D1, D2, D3, N, num_inducing, Q = 60, 20, 36, 60, 6, 5
_, _, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim)
likelihood_list = [Gaussian(x, normalize=True) for x in Ylist]
k = kern.linear(Q, ARD=True) + kern.bias(Q, _np.exp(-2)) + kern.white(Q, _np.exp(-2))
m = MRD(likelihood_list, input_dim=Q, num_inducing=num_inducing, kernels=k, initx="", initz='permute', **kw)
m.ensure_default_constraints()
for i, bgplvm in enumerate(m.bgplvms):
m['{}_noise'.format(i)] = bgplvm.likelihood.Y.var() / 500.
if optimize:
print "Optimizing Model:"
m.optimize(messages=verbose, max_iters=8e3, gtol=.1)
if plot:
m.plot_X_1d("MRD Latent Space 1D")
m.plot_scales("MRD Scales")
return m
import numpy as np
import pylab as pb
import sys
from GPy import kern
from colvb import MOHGP
np.random.seed(1)
pb.close('all')
#cool structed GP demo
Nclust = 20
Nx = 12
Nobs = [np.random.randint(20,21) for i in range(Nclust)]
X = np.random.rand(Nx,1)*5
X.sort(0)
Kf = kern.rbf(1) + kern.white(1, 1e-6)
S = Kf.K(X)
means = np.vstack([np.tile(np.random.multivariate_normal(np.zeros(Nx),S,1),(N,1)) for N in Nobs]) # GP draws for mean of each cluster
#add GP draw for noise
Ky = kern.rbf(1,0.3,1) + kern.white(1,0.001)
Y = means + np.random.multivariate_normal(np.zeros(Nx),Ky.K(X),means.shape[0])
#construct model
m = MOHGP(X, Kf.copy(), Ky.copy(), Y, K=Nclust)
m.constrain_positive('')
m.optimize()
m.preferred_optimizer='bfgs'
m.systematic_splits()
m.remove_empty_clusters(1e-3)
import numpy as np
import pylab as pb
import sys
from GPy import kern
from colvb import MOHGP
np.random.seed(1)
pb.close('all')
#cool structed GP demo
Nclust = 20
Nx = 12
Nobs = [np.random.randint(20, 21) for i in range(Nclust)]
X = np.random.rand(Nx, 1) * 5
X.sort(0)
Kf = kern.rbf(1) + kern.white(1, 1e-6)
S = Kf.K(X)
means = np.vstack([
np.tile(np.random.multivariate_normal(np.zeros(Nx), S, 1), (N, 1))
for N in Nobs
]) # GP draws for mean of each cluster
#add GP draw for noise
Ky = kern.rbf(1, 0.3, 1) + kern.white(1, 0.001)
Y = means + np.random.multivariate_normal(np.zeros(Nx), Ky.K(X),
means.shape[0])
#construct model
m = MOHGP(X, Kf.copy(), Ky.copy(), Y, K=Nclust)
m.constrain_positive('')
freqs = 2*np.pi + 0.3*(np.random.rand(Nclust)-.5) phases = 2*np.pi*np.random.rand(Nclust) means = np.vstack([np.tile(np.sin(f*X+p).T,(Ni,1)) for f,p,Ni in zip(freqs,phases,Nobs)]) #add a lower freq sin for the noise freqs = .4*np.pi + 0.01*(np.random.rand(means.shape[0])-.5) phases = 2*np.pi*np.random.rand(means.shape[0]) offsets = 0.3*np.vstack([np.sin(f*X+p).T for f,p in zip(freqs,phases)]) Y = means + offsets + np.random.randn(*means.shape)*0.05 #construct full model Kf = kern.rbf(1,0.01,0.001) Ky1 = kern.rbf(1,0.1,0.001) Ky2 = kern.white(1,0.01) Ky = Ky1 + Ky2 m = MOHGP(X,Kf,Ky,Y, K=Nclust, prior_Z = 'DP', alpha=alpha) m.ensure_default_constraints() m.checkgrad(verbose=1) m.randomize() m.optimize() m.systematic_splits() m.systematic_splits() m.plot(1,1,1,0,0,1) #construct model without structure #give it a fighting chance by normalising signals first Y = Y.copy() Y -= Y.mean(1)[:,None]
phases = 2 * np.pi * np.random.rand(Nclust)
means = np.vstack([
np.tile(np.sin(f * X + p).T, (Ni, 1))
for f, p, Ni in zip(freqs, phases, Nobs)
])
#add a lower freq sin for the noise
freqs = .4 * np.pi + 0.01 * (np.random.rand(means.shape[0]) - .5)
phases = 2 * np.pi * np.random.rand(means.shape[0])
offsets = 0.3 * np.vstack([np.sin(f * X + p).T for f, p in zip(freqs, phases)])
Y = means + offsets + np.random.randn(*means.shape) * 0.05
#construct full model
Kf = kern.rbf(1, 0.01, 0.001)
Ky1 = kern.rbf(1, 0.1, 0.001)
Ky2 = kern.white(1, 0.01)
Ky = Ky1 + Ky2
m = MOHGP(X, Kf, Ky, Y, K=Nclust, prior_Z='DP', alpha=alpha)
m.ensure_default_constraints()
m.checkgrad(verbose=1)
m.randomize()
m.optimize()
m.systematic_splits()
m.systematic_splits()
m.plot(1, 1, 1, 0, 0, 1)
#construct model without structure
#give it a fighting chance by normalising signals first
Y = Y.copy()
Y -= Y.mean(1)[:, None]