# Generate sample data
n_features, n_samples = 30, 20
X_train = np.random.normal(size=(n_samples, n_features))
X_test = np.random.normal(size=(n_samples, n_features))
# Color samples
coloring_matrix = np.random.normal(size=(n_features, n_features))
X_train = np.dot(X_train, coloring_matrix)
X_test = np.dot(X_test, coloring_matrix)
###############################################################################
# Compute Ledoit-Wolf and Covariances on a grid of shrinkages
from scikits.learn.covariance import LedoitWolf, ShrunkCovariance
lw = LedoitWolf()
loglik_lw = lw.fit(X_train).score(X_test)
cov = ShrunkCovariance()
shrinkages = np.logspace(-2, 0, 30)
negative_logliks = [-cov.fit(X_train, shrinkage=s).score(X_test) \
for s in shrinkages]
###############################################################################
# Plot results
pl.loglog(shrinkages, negative_logliks)
pl.xlabel('Shrinkage')
pl.ylabel('Negative log-likelihood')
pl.vlines(lw.shrinkage_,
pl.ylim()[0],
-loglik_lw,
# Generate sample data
n_features, n_samples = 30, 20
X_train = np.random.normal(size=(n_samples, n_features))
X_test = np.random.normal(size=(n_samples, n_features))
# Color samples
coloring_matrix = np.random.normal(size=(n_features, n_features))
X_train = np.dot(X_train, coloring_matrix)
X_test = np.dot(X_test, coloring_matrix)
###############################################################################
# Compute Ledoit-Wolf and Covariances on a grid of shrinkages
from scikits.learn.covariance import LedoitWolf, ShrunkCovariance
lw = LedoitWolf()
loglik_lw = lw.fit(X_train).score(X_test)
cov = ShrunkCovariance()
shrinkages = np.logspace(-2, 0, 30)
negative_logliks = [-cov.fit(X_train, shrinkage=s).score(X_test) \
for s in shrinkages]
###############################################################################
# Plot results
pl.loglog(shrinkages, negative_logliks)
pl.xlabel('Shrinkage')
pl.ylabel('Negative log-likelihood')
pl.vlines(lw.shrinkage_, pl.ylim()[0], -loglik_lw, color='g',
linewidth=3, label='Ledoit-Wolf estimate')
pl.legend()
base_X_train = np.random.normal(size=(n_samples, n_features))
base_X_test = np.random.normal(size=(n_samples, n_features))
# Color samples
coloring_matrix = np.random.normal(size=(n_features, n_features))
X_train = np.dot(base_X_train, coloring_matrix)
X_test = np.dot(base_X_test, coloring_matrix)
###############################################################################
# Compute Ledoit-Wolf and Covariances on a grid of shrinkages
from scikits.learn.covariance import LedoitWolf, OAS, ShrunkCovariance, \
log_likelihood, empirical_covariance
# Ledoit-Wolf optimal shrinkage coefficient estimate
lw = LedoitWolf()
loglik_lw = lw.fit(X_train, assume_centered=True).score(
X_test, assume_centered=True)
# OAS coefficient estimate
oa = OAS()
loglik_oa = oa.fit(X_train, assume_centered=True).score(
X_test, assume_centered=True)
# spanning a range of possible shrinkage coefficient values
shrinkages = np.logspace(-3, 0, 30)
negative_logliks = [-ShrunkCovariance(shrinkage=s).fit(
X_train, assume_centered=True).score(X_test, assume_centered=True) \
for s in shrinkages]
# getting the likelihood under the real model
base_X_train = np.random.normal(size=(n_samples, n_features))
base_X_test = np.random.normal(size=(n_samples, n_features))
# Color samples
coloring_matrix = np.random.normal(size=(n_features, n_features))
X_train = np.dot(base_X_train, coloring_matrix)
X_test = np.dot(base_X_test, coloring_matrix)
###############################################################################
# Compute Ledoit-Wolf and Covariances on a grid of shrinkages
from scikits.learn.covariance import LedoitWolf, OAS, ShrunkCovariance, \
log_likelihood, empirical_covariance
# Ledoit-Wolf optimal shrinkage coefficient estimate
lw = LedoitWolf()
loglik_lw = lw.fit(X_train, assume_centered=True).score(X_test,
assume_centered=True)
# OAS coefficient estimate
oa = OAS()
loglik_oa = oa.fit(X_train, assume_centered=True).score(X_test,
assume_centered=True)
# spanning a range of possible shrinkage coefficient values
shrinkages = np.logspace(-3, 0, 30)
negative_logliks = [-ShrunkCovariance(shrinkage=s).fit(
X_train, assume_centered=True).score(X_test, assume_centered=True) \
for s in shrinkages]
# getting the likelihood under the real model
r = 0.1
real_cov = toeplitz(r**np.arange(n_features))
coloring_matrix = cholesky(real_cov)
n_samples_range = np.arange(6, 31, 1)
repeat = 100
lw_mse = np.zeros((n_samples_range.size, repeat))
oa_mse = np.zeros((n_samples_range.size, repeat))
lw_shrinkage = np.zeros((n_samples_range.size, repeat))
oa_shrinkage = np.zeros((n_samples_range.size, repeat))
for i, n_samples in enumerate(n_samples_range):
for j in range(repeat):
X = np.dot(np.random.normal(size=(n_samples, n_features)),
coloring_matrix.T)
lw = LedoitWolf(store_precision=False)
lw.fit(X, assume_centered=True)
lw_mse[i, j] = lw.error_norm(real_cov, scaling=False)
lw_shrinkage[i, j] = lw.shrinkage_
oa = OAS(store_precision=False)
oa.fit(X, assume_centered=True)
oa_mse[i, j] = oa.error_norm(real_cov, scaling=False)
oa_shrinkage[i, j] = oa.shrinkage_
# plot MSE
pl.subplot(2, 1, 1)
pl.errorbar(n_samples_range,
lw_mse.mean(1),
yerr=lw_mse.std(1),
label='Ledoit-Wolf',
r = 0.1
real_cov = toeplitz(r**np.arange(n_features))
coloring_matrix = cholesky(real_cov)
n_samples_range = np.arange(6, 31, 1)
repeat = 100
lw_mse = np.zeros((n_samples_range.size, repeat))
oa_mse = np.zeros((n_samples_range.size, repeat))
lw_shrinkage = np.zeros((n_samples_range.size, repeat))
oa_shrinkage = np.zeros((n_samples_range.size, repeat))
for i, n_samples in enumerate(n_samples_range):
for j in range(repeat):
X = np.dot(
np.random.normal(size=(n_samples, n_features)), coloring_matrix.T)
lw = LedoitWolf(store_precision=False)
lw.fit(X, assume_centered=True)
lw_mse[i,j] = lw.mse(real_cov)
lw_shrinkage[i,j] = lw.shrinkage_
oa = OAS(store_precision=False)
oa.fit(X, assume_centered=True)
oa_mse[i,j] = oa.mse(real_cov)
oa_shrinkage[i,j] = oa.shrinkage_
# plot MSE
pl.subplot(2,1,1)
pl.errorbar(n_samples_range, lw_mse.mean(1), yerr=lw_mse.std(1),
label='Ledoit-Wolf', color='g')
pl.errorbar(n_samples_range, oa_mse.mean(1), yerr=oa_mse.std(1),
label='OAS', color='r')
r = 0.1
real_cov = toeplitz(r**np.arange(n_features))
coloring_matrix = cholesky(real_cov)
n_samples_range = np.arange(6, 31, 1)
repeat = 100
lw_mse = np.zeros((n_samples_range.size, repeat))
oa_mse = np.zeros((n_samples_range.size, repeat))
lw_shrinkage = np.zeros((n_samples_range.size, repeat))
oa_shrinkage = np.zeros((n_samples_range.size, repeat))
for i, n_samples in enumerate(n_samples_range):
for j in range(repeat):
X = np.dot(np.random.normal(size=(n_samples, n_features)),
coloring_matrix.T)
lw = LedoitWolf(store_precision=False)
lw.fit(X, assume_centered=True)
lw_mse[i, j] = lw.mse(real_cov)
lw_shrinkage[i, j] = lw.shrinkage_
oa = OAS(store_precision=False)
oa.fit(X, assume_centered=True)
oa_mse[i, j] = oa.mse(real_cov)
oa_shrinkage[i, j] = oa.shrinkage_
# plot MSE
pl.subplot(2, 1, 1)
pl.errorbar(n_samples_range,
lw_mse.mean(1),
yerr=lw_mse.std(1),
label='Ledoit-Wolf',
