def _preprocess_data(X, y, fit_intercept, epsilon=1.0, range_X=None, range_y=None, copy=True, check_input=True,
**unused_args):
warn_unused_args(unused_args)
if check_input:
X = check_array(X, copy=copy, accept_sparse=False, dtype=FLOAT_DTYPES)
elif copy:
X = X.copy(order='K')
y = np.asarray(y, dtype=X.dtype)
X_scale = np.ones(X.shape[1], dtype=X.dtype)
if fit_intercept:
X_offset = mean(X, axis=0, range=range_X, epsilon=epsilon)
X -= X_offset
y_offset = mean(y, axis=0, range=range_y, epsilon=epsilon)
y = y - y_offset
else:
X_offset = np.zeros(X.shape[1], dtype=X.dtype)
if y.ndim == 1:
y_offset = X.dtype.type(0)
else:
y_offset = np.zeros(y.shape[1], dtype=X.dtype)
return X, y, X_offset, y_offset, X_scale
def _preprocess_data(X,
y,
fit_intercept,
epsilon=1.0,
bounds_X=None,
bounds_y=None,
copy=True,
check_input=True,
**unused_args):
warn_unused_args(unused_args)
if check_input:
X = check_array(X, copy=copy, accept_sparse=False, dtype=FLOAT_DTYPES)
elif copy:
X = X.copy(order='K')
y = np.asarray(y, dtype=X.dtype)
X_scale = np.ones(X.shape[1], dtype=X.dtype)
if fit_intercept:
bounds_X = check_bounds(bounds_X, X.shape[1])
bounds_y = check_bounds(bounds_y, y.shape[1] if y.ndim > 1 else 1)
X = clip_to_bounds(X, bounds_X)
y = clip_to_bounds(y, bounds_y)
X_offset = mean(X,
axis=0,
bounds=bounds_X,
epsilon=epsilon,
accountant=BudgetAccountant())
X -= X_offset
y_offset = mean(y,
axis=0,
bounds=bounds_y,
epsilon=epsilon,
accountant=BudgetAccountant())
y = y - y_offset
else:
X_offset = np.zeros(X.shape[1], dtype=X.dtype)
if y.ndim == 1:
y_offset = X.dtype.type(0)
else:
y_offset = np.zeros(y.shape[1], dtype=X.dtype)
return X, y, X_offset, y_offset, X_scale
def _fit_full(self, X, n_components):
self.accountant.check(self.epsilon, 0)
n_samples, n_features = X.shape
if self.centered:
self.mean_ = np.zeros_like(np.mean(X, axis=0))
else:
if self.bounds is None:
warnings.warn(
"Bounds parameter hasn't been specified, so falling back to determining range from the data.\n"
"This will result in additional privacy leakage. To ensure differential privacy with no "
"additional privacy loss, specify `range` for each valued returned by np.mean().",
PrivacyLeakWarning)
self.bounds = (np.min(X, axis=0), np.max(X, axis=0))
self.bounds = check_bounds(self.bounds, n_features)
self.mean_ = mean(X,
epsilon=self.epsilon / 2,
bounds=self.bounds,
axis=0,
accountant=BudgetAccountant())
X -= self.mean_
if self.data_norm is None:
warnings.warn(
"Data norm has not been specified and will be calculated on the data provided. This will "
"result in additional privacy leakage. To ensure differential privacy and no additional "
"privacy leakage, specify `data_norm` at initialisation.",
PrivacyLeakWarning)
self.data_norm = np.linalg.norm(X, axis=1).max()
X = clip_to_norm(X, self.data_norm)
XtX = np.dot(X.T, X)
mech = Wishart().set_epsilon(self.epsilon if self.centered else self.epsilon / 2).\
set_sensitivity(self.data_norm)
noisy_input = mech.randomise(XtX)
u, s, v = np.linalg.svd(noisy_input)
u, v = svd_flip(u, v)
s = np.sqrt(s)
components_ = v
# Get variance explained by singular values
explained_variance_ = (s**2) / (n_samples - 1)
total_var = explained_variance_.sum()
explained_variance_ratio_ = explained_variance_ / total_var
singular_values_ = s.copy() # Store the singular values.
# Post-process the number of components required
if n_components == 'mle':
try:
n_components = sk_pca._infer_dimension(explained_variance_,
n_samples)
except AttributeError:
n_components = sk_pca._infer_dimension_(
explained_variance_, n_samples, n_features)
elif 0 < n_components < 1.0:
# number of components for which the cumulated explained
# variance percentage is superior to the desired threshold
ratio_cumsum = stable_cumsum(explained_variance_ratio_)
n_components = np.searchsorted(ratio_cumsum, n_components) + 1
# Compute noise covariance using Probabilistic PCA model
# The sigma2 maximum likelihood (cf. eq. 12.46)
if n_components < min(n_features, n_samples):
self.noise_variance_ = explained_variance_[n_components:].mean()
else:
self.noise_variance_ = 0.
self.n_samples_, self.n_features_ = n_samples, n_features
self.components_ = components_[:n_components]
self.n_components_ = n_components
self.explained_variance_ = explained_variance_[:n_components]
self.explained_variance_ratio_ = explained_variance_ratio_[:
n_components]
self.singular_values_ = singular_values_[:n_components]
self.accountant.spend(self.epsilon, 0)
return u, s, v
def _fit_full(self, X, n_components):
self.accountant.check(self.epsilon, 0)
n_samples, n_features = X.shape
if self.centered:
self.mean_ = np.zeros_like(np.mean(X, axis=0))
else:
if self.bounds is None:
warnings.warn(
"Bounds parameter hasn't been specified, so falling back to determining range from the data.\n"
"This will result in additional privacy leakage. To ensure differential privacy with no "
"additional privacy loss, specify `range` for each valued returned by np.mean().",
PrivacyLeakWarning)
self.bounds = (np.min(X, axis=0), np.max(X, axis=0))
self.bounds = self._check_bounds(self.bounds, n_features)
self.mean_ = mean(X, epsilon=self.epsilon / 2, bounds=self.bounds, axis=0, accountant=BudgetAccountant())
X -= self.mean_
if self.data_norm is None:
warnings.warn("Data norm has not been specified and will be calculated on the data provided. This will "
"result in additional privacy leakage. To ensure differential privacy and no additional "
"privacy leakage, specify `data_norm` at initialisation.", PrivacyLeakWarning)
self.data_norm = np.linalg.norm(X, axis=1).max()
X = self._clip_to_norm(X, self.data_norm)
sigma_vec, u_mtx = covariance_eig(X, epsilon=self.epsilon if self.centered else self.epsilon / 2,
norm=self.data_norm,
dims=n_components if isinstance(n_components, Integral) else None)
u_mtx, _ = svd_flip(u_mtx, np.zeros_like(u_mtx).T)
sigma_vec = np.sqrt(sigma_vec)
components_ = u_mtx.T
# Get variance explained by singular values
explained_variance_ = np.sort((sigma_vec ** 2) / (n_samples - 1))[::-1]
total_var = explained_variance_.sum()
explained_variance_ratio_ = explained_variance_ / total_var
singular_values_ = sigma_vec.copy() # Store the singular values.
# Post-process the number of components required
if n_components == 'mle':
n_components = sk_pca._infer_dimension(explained_variance_, n_samples)
elif 0 < n_components < 1.0:
# number of components for which the cumulated explained
# variance percentage is superior to the desired threshold
ratio_cumsum = stable_cumsum(explained_variance_ratio_)
n_components = np.searchsorted(ratio_cumsum, n_components) + 1
# Compute noise covariance using Probabilistic PCA model
# The sigma2 maximum likelihood (cf. eq. 12.46)
if n_components < min(n_features, n_samples):
self.noise_variance_ = explained_variance_[n_components:].mean()
else:
self.noise_variance_ = 0.
self.n_samples_, self.n_features_ = n_samples, n_features
self.components_ = components_[:n_components]
self.n_components_ = n_components
self.explained_variance_ = explained_variance_[:n_components]
self.explained_variance_ratio_ = explained_variance_ratio_[:n_components]
self.singular_values_ = singular_values_[:n_components]
self.accountant.spend(self.epsilon, 0)
return u_mtx, sigma_vec[:n_components], u_mtx.T