The RegularizedOptimization submodule#

This submodule implements RegularizedOptimization.R in Python.

It contains functions to learn an cMHN on the full state-space for a given data distribution and implements the L1 regularization.

mhn.full_state_space.RegularizedOptimization.L1(theta: ndarray, eps: float = 1e-05) → float#

Computes the L1 penalty for the given theta matrix.

Parameters:

  • theta (np.ndarray) – The theta matrix representing the cMHN.

  • eps (float, optional) – A small epsilon value, mainly used for the derivative. Default is 1e-05.

Returns:

The L1 penalty for the given theta matrix.

Return type:

float

mhn.full_state_space.RegularizedOptimization.L1_(theta: ndarray, eps: float = 1e-05) → ndarray#

Computes the derivative of the L1 penalty for the given theta matrix.

Parameters:

  • theta (np.ndarray) – The theta matrix representing the cMHN.

  • eps (float, optional) – A small epsilon value to prevent division by zero. Default is 1e-05.

Returns:

The derivative of the L1 penalty.

Return type:

np.ndarray

mhn.full_state_space.RegularizedOptimization.grad_reg(theta: ndarray, pD: ndarray, lam: float, n: int = 0, pth_space: ndarray | None = None) → ndarray#

Computes the gradient with L1 regularization for the given theta matrix.

Parameters:

  • theta (np.ndarray) – The theta matrix representing the cMHN.

  • pD (np.ndarray) – Distribution provided by the training data.

  • lam (float) – Tuning parameter lambda for regularization.

  • n (int, optional) – The number of columns/rows of the theta matrix. Default is 0.

  • pth_space (np.ndarray, optional) – Optional parameter used to avoid recalculating pth, improving performance.

Returns:

The gradient of the L1-regularized score.

Return type:

np.ndarray

mhn.full_state_space.RegularizedOptimization.learn_MHN(pD: ~numpy.ndarray, init: ~numpy.ndarray | None = None, lam: float = 0, maxit: int = 5000, trace: bool = False, reltol: float = 1e-07, round_result: bool = True, callback: ~typing.Callable | None = None, score_func: ~typing.Callable = <function score_reg>, jacobi: ~typing.Callable = <function grad_reg>) → ndarray#

Trains a cMHN to fit a given probability distribution.

Parameters:

  • pD (np.ndarray) – Probability distribution used to train the new model.

  • init (np.ndarray, optional) – Starting point for the training (initial theta). Default is None.

  • lam (float, optional) – Tuning parameter lambda for regularization. Default is 0.

  • maxit (int, optional) – Maximum number of training iterations. Default is 5000.

  • trace (bool, optional) – If True, convergence messages are printed (see scipy.optimize.minimize). Default is False.

  • reltol (float, optional) – Gradient norm must be less than reltol before successful termination. Default is 1e-07.

  • round_result (bool, optional) – If True, the result is rounded to two decimal places. Default is True.

  • callback (Callable, optional) – Function called after each iteration, must take theta as an argument. Default is None.

  • score_func (Callable, optional) – Score function used for training. Default is score_reg.

  • jacobi (Callable, optional) – Gradient function used for training. Default is grad_reg.

Returns:

The trained model (theta matrix).

Return type:

np.ndarray

mhn.full_state_space.RegularizedOptimization.score_reg(theta: ndarray, pD: ndarray, lam: float, n: int | None = None, pth_space: ndarray | None = None) → float#

Computes the score with L1 regularization for the given theta matrix.

Parameters:

  • theta (np.ndarray) – The theta matrix representing the cMHN.

  • pD (np.ndarray) – Distribution provided by the training data.

  • lam (float) – Tuning parameter lambda for regularization.

  • n (int, optional) – The number of columns/rows of the theta matrix. Default is None.

  • pth_space (np.ndarray, optional) – Optional parameter used for communication with the gradient function to improve performance.

Returns:

The score of the current cMHN, penalized with L1 regularization.

Return type:

float