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278 | import numpy as np
from sklearn.base import BaseEstimator
def _partition(X, idx):
"""
Partition the matrix X into part 1: all but the idx-th row and column,
and part 2: the idx-th row and column
Parameters
----------
X : array-like of shape (n_features, n_features)
idx: the index for partion
Returns
-------
X11: the upper left sub-matrix
X12: the upper right vector
X21: the lower left vector
X22: X[j][j]
"""
n_features = X.shape[0]
indices = np.arange(n_features)
X11 = X[indices != idx, :]
X11 = X11[:, indices != idx]
X22 = X[idx][idx]
X21 = X[idx, indices != idx]
X21 = X21.reshape((1, n_features - 1))
X12 = X[indices != idx, idx]
X12 = X12.reshape((n_features - 1, 1))
return [X11, X12, X21, X22]
def _solve(W, S, Gamma, idx):
W11 = _partition(W, idx)[0]
Gamma12 = _partition(Gamma, idx)[1]
S12 = _partition(S, idx)[1]
zero_indices = np.where(Gamma12 == 0)[0]
S12_new = S12[zero_indices]
W11_new = W11[zero_indices, :]
W11_new = W11_new[:, zero_indices]
beta_ast = np.linalg.inv(W11_new) @ S12_new
beta = np.zeros(Gamma12.shape)
beta[zero_indices] = beta_ast
return beta
def _update(W, idx, beta):
n_features = W.shape[0]
indices = np.arange(n_features)
W11 = _partition(W, idx)[0]
updated_W12 = W11 @ beta
W[indices != idx, idx] = updated_W12.ravel()
W[idx, indices != idx] = updated_W12.ravel()
return
def _update_theta(Theta, Gamma, W, S, idx):
beta = _solve(W, S, Gamma, idx)
S22 = _partition(S, idx)[3]
W12 = _partition(W, idx)[1]
try:
theta22 = 1 / (S22 - W12.T @ beta)
theta12 = (-theta22) * beta
except FloatingPointError as e:
e.args = (e.args[0] + '. Error happened, check for details.')
raise e
Theta[idx, idx] = theta22
n_feature = W.shape[0]
indices = np.arange(n_feature)
Theta[idx, indices != idx] = theta12.ravel()
return
class GraphicalGaussian(BaseEstimator):
def __init__(self, tol=1e-4, max_iter=100, verbose=False):
self.tol = tol
self.max_iter = max_iter
self.verbose = verbose
self.stop_reason = None
self.n_iter = None
self.theta_ = None
self.covariance_ = None
def fit(self, S, Gamma):
# Covariance does not make sense for a single feature
S = self._validate_data(S, ensure_min_features=2,
ensure_min_samples=2,
estimator=self)
# Adjacent matrix does not make sense for a single feature
Gamma = self._validate_data(Gamma, ensure_min_features=2,
ensure_min_samples=2,
estimator=self)
n_feature = S.shape[0]
W = S.copy()
for n_iter in range(self.max_iter):
if self.verbose:
print('executing {}th iteration'.format(n_iter + 1))
W_last = W.copy()
for idx in range(n_feature):
if self.verbose:
print('executing for {}th variable'.format(idx + 1))
beta = _solve(W, S, Gamma, idx)
_update(W, idx, beta)
if np.linalg.norm(W - W_last) < self.tol:
self.stop_reason = 'Covariance estimation converged'
break
if n_iter + 1 == self.max_iter:
self.stop_reason = 'Maximum iteration reached'
# final cycle
Theta = np.zeros(S.shape)
for idx in range(n_feature):
_update_theta(Theta, Gamma, W, S, idx)
self.theta_ = Theta
self.covariance_ = W
self.n_iter = n_iter
return self
# S = np.array([
# [10, 1, 5, 4],
# [1, 10, 2, 6],
# [5, 2, 10, 3],
# [4, 6, 3, 10]
# ], dtype=float)
#
# Gamma = np.array([
# [0, 0, 1, 0],
# [0, 0, 0, 1],
# [1, 0, 0, 0],
# [0, 1, 0, 0]
# ], dtype=float)
#
# model = GraphicalGaussian(verbose=True)
# model.fit(S, Gamma)
#
# print(1)
def _missing_indices(X, i):
return np.argwhere(np.isnan(X[i])).ravel()
def _observed_indices(X, i):
return np.argwhere(~np.isnan(X[i])).ravel()
class GraphicalGaussianEM(BaseEstimator):
def __init__(self,
graph_Gaussian_obj=GraphicalGaussian(),
init_mean=None,
init_cov=None,
tol=1e-4,
max_iter=100,
verbose=False):
self.init_mean = init_mean
self.init_cov = init_cov
self.tol = tol
self.max_iter = max_iter
self.verbose = verbose
self.graph_Gaussian_Obj = graph_Gaussian_obj
self.covariance_ = None
self.mean_ = None
self.imputed_X = None
def _initCov(self, X):
filled_X = X.copy()
inds = np.where(np.isnan(filled_X))
filled_X[inds] = np.take(self.mean_, inds[1])
self.covariance_ = np.cov(filled_X, rowvar=False)
def _init(self, X, init_mean=None, init_cov=None):
if init_mean is None:
self.mean_ = np.nanmean(X, axis=0)
if init_cov is None:
self._initCov(X)
def _e_step(self, X):
n_samples = X.shape[0]
for i in range(n_samples):
if self.verbose:
print('executing {}-th sample'.format(i + 1))
mi, oi = _missing_indices(X, i), _observed_indices(X, i)
if len(mi) == 0:
continue
sigma_mi_oi, sigma_oi_oi = self.covariance_[np.ix_(mi, oi)], self.covariance_[np.ix_(oi, oi)]
sigma_oi_oi_inv = np.linalg.inv(sigma_oi_oi)
imputed = self.mean_[mi] + sigma_mi_oi @ sigma_oi_oi_inv @ (X[i, oi] - self.mean_[oi])
self.imputed_X[i, mi] = imputed.ravel()
def _m_step(self, Gamma):
"""
Use Modified Regression to Estimated Sigma
Parameters
----------
X
Gamma
Returns
-------
"""
self.mean_ = np.nanmean(self.imputed_X, axis=0)
self.covariance_ = self.graph_Gaussian_Obj.fit(self.covariance_, Gamma).covariance_
def _gap(self, mean_old, cov_old):
return np.linalg.norm(self.mean_ - mean_old) + np.linalg.norm(self.covariance_ - cov_old)
def fit(self, X, Gamma):
self._init(X, init_mean=self.init_mean, init_cov=self.init_cov)
self.imputed_X = X.copy()
for n_iter in range(self.max_iter):
if self.verbose:
print('executing {}-th iteration'.format(n_iter + 1))
mean_old = self.mean_.copy()
cov_old = self.covariance_.copy()
self._e_step(X)
self._m_step(Gamma)
if self._gap(mean_old, cov_old) < self.tol:
if self.verbose:
print('stop because convergence criteria met')
break
return self
# S = np.array([
# [10, 1, 5, 4],
# [1, 10, 2, 6],
# [5, 2, 10, 3],
# [4, 6, 3, 10]
# ], dtype=float)
#
# X = np.array([
# [1, np.nan, 3, 4],
# [1, 10, 2, 6],
# [5, 1, np.nan, 3],
# [4, 6, 3, 10]
# ], dtype=float)
#
# Gamma = np.array([
# [0, 0, 1, 0],
# [0, 0, 0, 1],
# [1, 0, 0, 0],
# [0, 1, 0, 0]
# ], dtype=float)
#
# model = GraphicalGaussianEM(verbose=True)
# model.fit(X, Gamma)
#
# print(1)
|