minor

notears.py

@@ -25,17 +25,17 @@ def _loss(W):
  if loss_type == 'l2':
  R = X - M
  loss = 0.5 / X.shape[0] * (R ** 2).sum()
- D = - 1.0 / X.shape[0] * X.T @ R
+ G_loss = - 1.0 / X.shape[0] * X.T @ R
  elif loss_type == 'logistic':
  loss = 1.0 / X.shape[0] * (np.logaddexp(0, M) - X * M).sum()
- D = 1.0 / X.shape[0] * X.T @ (sigmoid(M) - X)
+ G_loss = 1.0 / X.shape[0] * X.T @ (sigmoid(M) - X)
  elif loss_type == 'poisson':
  S = np.exp(M)
  loss = 1.0 / X.shape[0] * (S - X * M).sum()
- D = 1.0 / X.shape[0] * X.T @ (S - X)
+ G_loss = 1.0 / X.shape[0] * X.T @ (S - X)
  else:
  raise ValueError('unknown loss type')
- return loss, D
+ return loss, G_loss
 
  def _h(W):
  """Evaluate value and gradient of acyclicity constraint."""
@@ -44,7 +44,8 @@ def _h(W):
  M = np.eye(d) + W * W / d # (Yu et al. 2019)
  E = np.linalg.matrix_power(M, d - 1)
  h = (E.T * M).sum() - d
- return h, E
+ G_h = E.T * W * 2
+ return h, G_h
 
  def _adj(w):
  """Convert doubled variables ([2 d^2] array) back to original variables ([d, d] matrix)."""
@@ -53,12 +54,12 @@ def _adj(w):
  def _func(w):
  """Evaluate value and gradient of augmented Lagrangian for doubled variables ([2 d^2] array)."""
  W = _adj(w)
- loss, D = _loss(W)
- h, E = _h(W)
+ loss, G_loss = _loss(W)
+ h, G_h = _h(W)
  obj = loss + 0.5 * rho * h * h + alpha * h + lambda1 * w.sum()
- G = D + (rho * h + alpha) * E.T * W * 2
- grad_cat = np.concatenate((G + lambda1, - G + lambda1), axis=None)
- return obj, grad_cat
+ G_smooth = G_loss + (rho * h + alpha) * G_h
+ g_obj = np.concatenate((G_smooth + lambda1, - G_smooth + lambda1), axis=None)
+ return obj, g_obj
 
  n, d = X.shape
  w_est, rho, alpha, h = np.zeros(2 * d * d), 1.0, 0.0, np.inf # double w_est into (w_pos, w_neg)