dagma.linear.DagmaLinear.minimize¶

dagma.linear.DagmaLinear.minimize(W: numpy.ndarray, mu: float, max_iter: int, s: float, lr: float, tol: float = 1e-06, beta_1: float = 0.99, beta_2: float = 0.999, pbar: tqdm.auto.tqdm | None = None) → tuple[numpy.ndarray, bool]¶

Solves the optimization problem:

\[\arg\min_{W \in \mathbb{W}^s} \mu \cdot Q(W; \mathbf{X}) + h(W),\]

where \(Q\) is the score function. This problem is solved via (sub)gradient descent, where the initial point is W.

Parameters:¶

W : np.ndarray¶

Initial point of (sub)gradient descent.

mu : float¶

Weights the score function.

max_iter : int¶

Maximum number of (sub)gradient iterations.

s : float¶

Number that controls the domain of M-matrices.

lr : float¶

Learning rate.

tol : float, optional¶

Tolerance to admit convergence. Defaults to 1e-6.

beta_1 : float, optional¶

Hyperparamter for Adam. Defaults to 0.99.

beta_2 : float, optional¶

Hyperparamter for Adam. Defaults to 0.999.

pbar : tqdm, optional¶

Controls bar progress. Defaults to tqdm().

Returns:¶

Returns an adjacency matrix until convergence or max_iter is reached. A boolean flag is returned to point success of the optimization. This can be False when at any iteration, the current W point went outside of the domain of M-matrices.

Return type:¶

Tuple[np.ndarray, bool]