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dim reduction examples Q= > input_dim=

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Max Zwiessele 2013-10-11 16:47:18 +01:00
parent a9b190782d
commit 3132a0362a
1 changed files with 43 additions and 43 deletions
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86
GPy/examples/dimensionality_reduction.py
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@ -14,22 +14,22 @@ default_seed = np.random.seed(123344)
def BGPLVM(seed=default_seed): def BGPLVM(seed=default_seed):
N = 5 N = 5
num_inducing = 4 num_inducing = 4
Q = 3 input_dim = 3
D = 2 D = 2
# generate GPLVM-like data # generate GPLVM-like data
X = np.random.rand(N, Q) X = np.random.rand(N, input_dim)
lengthscales = np.random.rand(Q) lengthscales = np.random.rand(input_dim)
k = (GPy.kern.rbf(Q, .5, lengthscales, ARD=True) k = (GPy.kern.rbf(input_dim, .5, lengthscales, ARD=True)
+ GPy.kern.white(Q, 0.01)) + GPy.kern.white(input_dim, 0.01))
K = k.K(X) K = k.K(X)
Y = np.random.multivariate_normal(np.zeros(N), K, D).T Y = np.random.multivariate_normal(np.zeros(N), K, D).T
lik = Gaussian(Y, normalize=True) lik = Gaussian(Y, normalize=True)
k = GPy.kern.rbf_inv(Q, .5, np.ones(Q) * 2., ARD=True) + GPy.kern.bias(Q) + GPy.kern.white(Q) k = GPy.kern.rbf_inv(input_dim, .5, np.ones(input_dim) * 2., ARD=True) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim)
# k = GPy.kern.rbf(Q) + GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001) # k = GPy.kern.rbf(input_dim) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim, 0.00001)
# k = GPy.kern.rbf(Q, ARD = False) + GPy.kern.white(Q, 0.00001) # k = GPy.kern.rbf(input_dim, ARD = False) + GPy.kern.white(input_dim, 0.00001)
m = GPy.models.BayesianGPLVM(lik, Q, kernel=k, num_inducing=num_inducing) m = GPy.models.BayesianGPLVM(lik, input_dim, kernel=k, num_inducing=num_inducing)
m.lengthscales = lengthscales m.lengthscales = lengthscales
# m.constrain_positive('(rbf|bias|noise|white|S)') # m.constrain_positive('(rbf|bias|noise|white|S)')
# m.constrain_fixed('S', 1) # m.constrain_fixed('S', 1)
@ -64,7 +64,7 @@ def GPLVM_oil_100(optimize=True):
m.plot_latent(labels=m.data_labels) m.plot_latent(labels=m.data_labels)
return m return m
def sparseGPLVM_oil(optimize=True, N=100, Q=6, num_inducing=15, max_iters=50): def sparseGPLVM_oil(optimize=True, N=100, input_dim=6, num_inducing=15, max_iters=50):
np.random.seed(0) np.random.seed(0)
data = GPy.util.datasets.oil() data = GPy.util.datasets.oil()
@ -73,8 +73,8 @@ def sparseGPLVM_oil(optimize=True, N=100, Q=6, num_inducing=15, max_iters=50):
Y /= Y.std(0) Y /= Y.std(0)
# create simple GP model # create simple GP model
kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q) kernel = GPy.kern.rbf(input_dim, ARD=True) + GPy.kern.bias(input_dim)
m = GPy.models.SparseGPLVM(Y, Q, kernel=kernel, num_inducing=num_inducing) m = GPy.models.SparseGPLVM(Y, input_dim, kernel=kernel, num_inducing=num_inducing)
m.data_labels = data['Y'].argmax(axis=1) m.data_labels = data['Y'].argmax(axis=1)
# optimize # optimize
@ -86,7 +86,7 @@ def sparseGPLVM_oil(optimize=True, N=100, Q=6, num_inducing=15, max_iters=50):
# m.plot_latent(labels=m.data_labels) # m.plot_latent(labels=m.data_labels)
return m return m
def swiss_roll(optimize=True, N=1000, num_inducing=15, Q=4, sigma=.2, plot=False): def swiss_roll(optimize=True, N=1000, num_inducing=15, input_dim=4, sigma=.2, plot=False):
from GPy.util.datasets import swiss_roll_generated from GPy.util.datasets import swiss_roll_generated
from GPy.core.transformations import LogexpClipped from GPy.core.transformations import LogexpClipped
@ -102,10 +102,10 @@ def swiss_roll(optimize=True, N=1000, num_inducing=15, Q=4, sigma=.2, plot=False
from sklearn.manifold.isomap import Isomap from sklearn.manifold.isomap import Isomap
iso = Isomap().fit(Y) iso = Isomap().fit(Y)
X = iso.embedding_ X = iso.embedding_
if Q > 2: if input_dim > 2:
X = np.hstack((X, np.random.randn(N, Q - 2))) X = np.hstack((X, np.random.randn(N, input_dim - 2)))
except ImportError: except ImportError:
X = np.random.randn(N, Q) X = np.random.randn(N, input_dim)
if plot: if plot:
from mpl_toolkits import mplot3d from mpl_toolkits import mplot3d
@ -121,14 +121,14 @@ def swiss_roll(optimize=True, N=1000, num_inducing=15, Q=4, sigma=.2, plot=False
var = .5 var = .5
S = (var * np.ones_like(X) + np.clip(np.random.randn(N, Q) * var ** 2, S = (var * np.ones_like(X) + np.clip(np.random.randn(N, input_dim) * var ** 2,
- (1 - var), - (1 - var),
(1 - var))) + .001 (1 - var))) + .001
Z = np.random.permutation(X)[:num_inducing] Z = np.random.permutation(X)[:num_inducing]
kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2)) kernel = GPy.kern.rbf(input_dim, ARD=True) + GPy.kern.bias(input_dim, np.exp(-2)) + GPy.kern.white(input_dim, np.exp(-2))
m = BayesianGPLVM(Y, Q, X=X, X_variance=S, num_inducing=num_inducing, Z=Z, kernel=kernel) m = BayesianGPLVM(Y, input_dim, X=X, X_variance=S, num_inducing=num_inducing, Z=Z, kernel=kernel)
m.data_colors = c m.data_colors = c
m.data_t = t m.data_t = t
@ -140,19 +140,19 @@ def swiss_roll(optimize=True, N=1000, num_inducing=15, Q=4, sigma=.2, plot=False
m.optimize('scg', messages=1) m.optimize('scg', messages=1)
return m return m
def BGPLVM_oil(optimize=True, N=200, Q=7, num_inducing=40, max_iters=1000, plot=False, **k): def BGPLVM_oil(optimize=True, N=200, input_dim=7, num_inducing=40, max_iters=1000, plot=False, **k):
np.random.seed(0) np.random.seed(0)
data = GPy.util.datasets.oil() data = GPy.util.datasets.oil()
# create simple GP model # create simple GP model
kernel = GPy.kern.rbf_inv(Q, 1., [.1] * Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) kernel = GPy.kern.rbf_inv(input_dim, 1., [.1] * input_dim, ARD=True) + GPy.kern.bias(input_dim, np.exp(-2))
Y = data['X'][:N] Y = data['X'][:N]
Yn = Gaussian(Y, normalize=True) Yn = Gaussian(Y, normalize=True)
# Yn = Y - Y.mean(0) # Yn = Y - Y.mean(0)
# Yn /= Yn.std(0) # Yn /= Yn.std(0)
m = GPy.models.BayesianGPLVM(Yn, Q, kernel=kernel, num_inducing=num_inducing, **k) m = GPy.models.BayesianGPLVM(Yn, input_dim, kernel=kernel, num_inducing=num_inducing, **k)
m.data_labels = data['Y'][:N].argmax(axis=1) m.data_labels = data['Y'][:N].argmax(axis=1)
# m.constrain('variance|leng', LogexpClipped()) # m.constrain('variance|leng', LogexpClipped())
@ -193,7 +193,7 @@ def oil_100():
def _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim=False): def _simulate_sincos(D1, D2, D3, N, num_inducing, input_dim, plot_sim=False):
x = np.linspace(0, 4 * np.pi, N)[:, None] x = np.linspace(0, 4 * np.pi, N)[:, None]
s1 = np.vectorize(lambda x: np.sin(x)) s1 = np.vectorize(lambda x: np.sin(x))
s2 = np.vectorize(lambda x: np.cos(x)) s2 = np.vectorize(lambda x: np.cos(x))
@ -253,13 +253,13 @@ def bgplvm_simulation_matlab_compare():
Y = sim_data['Y'] Y = sim_data['Y']
S = sim_data['S'] S = sim_data['S']
mu = sim_data['mu'] mu = sim_data['mu']
num_inducing, [_, Q] = 3, mu.shape num_inducing, [_, input_dim] = 3, mu.shape
from GPy.models import mrd from GPy.models import mrd
from GPy import kern from GPy import kern
reload(mrd); reload(kern) reload(mrd); reload(kern)
k = kern.linear(Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2)) k = kern.linear(input_dim, ARD=True) + kern.bias(input_dim, np.exp(-2)) + kern.white(input_dim, np.exp(-2))
m = BayesianGPLVM(Y, Q, init="PCA", num_inducing=num_inducing, kernel=k, m = BayesianGPLVM(Y, input_dim, init="PCA", num_inducing=num_inducing, kernel=k,
# X=mu, # X=mu,
# X_variance=S, # X_variance=S,
_debug=False) _debug=False)
@ -273,8 +273,8 @@ def bgplvm_simulation(optimize='scg',
max_iters=2e4, max_iters=2e4,
plot_sim=False): plot_sim=False):
# from GPy.core.transformations import LogexpClipped # from GPy.core.transformations import LogexpClipped
D1, D2, D3, N, num_inducing, Q = 15, 5, 8, 30, 3, 10 D1, D2, D3, N, num_inducing, input_dim = 15, 5, 8, 30, 3, 10
slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim) slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, input_dim, plot_sim)
from GPy.models import mrd from GPy.models import mrd
from GPy import kern from GPy import kern
@ -282,8 +282,8 @@ def bgplvm_simulation(optimize='scg',
Y = Ylist[0] Y = Ylist[0]
k = kern.linear(Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2)) # + kern.bias(Q) k = kern.linear(input_dim, ARD=True) + kern.bias(input_dim, np.exp(-2)) + kern.white(input_dim, np.exp(-2)) # + kern.bias(input_dim)
m = BayesianGPLVM(Y, Q, init="PCA", num_inducing=num_inducing, kernel=k) m = BayesianGPLVM(Y, input_dim, init="PCA", num_inducing=num_inducing, kernel=k)
# m.constrain('variance|noise', LogexpClipped()) # m.constrain('variance|noise', LogexpClipped())
m['noise'] = Y.var() / 100. m['noise'] = Y.var() / 100.
@ -298,8 +298,8 @@ def bgplvm_simulation(optimize='scg',
return m return m
def mrd_simulation(optimize=True, plot=True, plot_sim=True, **kw): def mrd_simulation(optimize=True, plot=True, plot_sim=True, **kw):
D1, D2, D3, N, num_inducing, Q = 60, 20, 36, 60, 6, 5 D1, D2, D3, N, num_inducing, input_dim = 60, 20, 36, 60, 6, 5
slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim) slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, input_dim, plot_sim)
likelihood_list = [Gaussian(x, normalize=True) for x in Ylist] likelihood_list = [Gaussian(x, normalize=True) for x in Ylist]
@ -308,8 +308,8 @@ def mrd_simulation(optimize=True, plot=True, plot_sim=True, **kw):
reload(mrd); reload(kern) reload(mrd); reload(kern)
k = kern.linear(Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2)) k = kern.linear(input_dim, ARD=True) + kern.bias(input_dim, np.exp(-2)) + kern.white(input_dim, np.exp(-2))
m = mrd.MRD(likelihood_list, input_dim=Q, num_inducing=num_inducing, kernels=k, initx="", initz='permute', **kw) m = mrd.MRD(likelihood_list, input_dim=input_dim, num_inducing=num_inducing, kernels=k, initx="", initz='permute', **kw)
m.ensure_default_constraints() m.ensure_default_constraints()
for i, bgplvm in enumerate(m.bgplvms): for i, bgplvm in enumerate(m.bgplvms):
@ -330,14 +330,14 @@ def mrd_simulation(optimize=True, plot=True, plot_sim=True, **kw):
def brendan_faces(): def brendan_faces():
from GPy import kern from GPy import kern
data = GPy.util.datasets.brendan_faces() data = GPy.util.datasets.brendan_faces()
Q = 2 input_dim = 2
Y = data['Y'][0:-1:10, :] Y = data['Y'][0:-1:10, :]
# Y = data['Y'] # Y = data['Y']
Yn = Y - Y.mean() Yn = Y - Y.mean()
Yn /= Yn.std() Yn /= Yn.std()
m = GPy.models.GPLVM(Yn, Q) m = GPy.models.GPLVM(Yn, input_dim)
# m = GPy.models.BayesianGPLVM(Yn, Q, num_inducing=100) # m = GPy.models.BayesianGPLVM(Yn, input_dim, num_inducing=100)
# optimize # optimize
m.constrain('rbf|noise|white', GPy.core.transformations.LogexpClipped()) m.constrain('rbf|noise|white', GPy.core.transformations.LogexpClipped())
@ -424,9 +424,9 @@ def robot_wireless():
def stick_bgplvm(model=None): def stick_bgplvm(model=None):
data = GPy.util.datasets.osu_run1() data = GPy.util.datasets.osu_run1()
Q = 6 input_dim = 6
kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2)) kernel = GPy.kern.rbf(input_dim, ARD=True) + GPy.kern.bias(input_dim, np.exp(-2)) + GPy.kern.white(input_dim, np.exp(-2))
m = BayesianGPLVM(data['Y'], Q, init="PCA", num_inducing=20, kernel=kernel) m = BayesianGPLVM(data['Y'], input_dim, init="PCA", num_inducing=20, kernel=kernel)
# optimize # optimize
m.ensure_default_constraints() m.ensure_default_constraints()
m.optimize('scg', messages=1, max_iters=200, xtol=1e-300, ftol=1e-300) m.optimize('scg', messages=1, max_iters=200, xtol=1e-300, ftol=1e-300)
@ -469,11 +469,11 @@ def cmu_mocap(subject='35', motion=['01'], in_place=True):
# X -= X.mean(axis=0) # X -= X.mean(axis=0)
# X /= X.std(axis=0) # X /= X.std(axis=0)
# #
# Q = 10 # input_dim = 10
# num_inducing = 30 # num_inducing = 30
# #
# kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q) + GPy.kern.white(Q) # kernel = GPy.kern.rbf(input_dim, ARD=True) + GPy.kern.bias(input_dim) + GPy.kern.white(input_dim)
# m = GPy.models.BayesianGPLVM(X, Q, kernel=kernel, num_inducing=num_inducing) # m = GPy.models.BayesianGPLVM(X, input_dim, kernel=kernel, num_inducing=num_inducing)
# # m.scale_factor = 100.0 # # m.scale_factor = 100.0
# m.constrain_positive('(white|noise|bias|X_variance|rbf_variance|rbf_length)') # m.constrain_positive('(white|noise|bias|X_variance|rbf_variance|rbf_length)')
# from sklearn import cluster # from sklearn import cluster