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
real_cov = np.dot(coloring_matrix.T, coloring_matrix)
emp_cov = empirical_covariance(X_train)
loglik_real = -log_likelihood(emp_cov, linalg.inv(real_cov))
###############################################################################
# Plot results
pl.figure(-1)
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',
color='g')
pl.errorbar(n_samples_range,
oa_mse.mean(1),
yerr=oa_mse.std(1),
label='OAS',
color='r')
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
real_cov = np.dot(coloring_matrix.T, coloring_matrix)
emp_cov = empirical_covariance(X_train)
loglik_real = -log_likelihood(emp_cov, linalg.inv(real_cov))
###############################################################################
# Plot results
pl.figure(-1)
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')
pl.ylabel("MSE")
pl.legend(loc="upper right")
pl.title("Comparison of covariance estimators")
pl.xlim(5, 31)
# plot shrinkage coefficient