SEMEstimator

class pgmpy.estimators.SEMEstimator(model)

Bases: object

Base class of SEM estimators. All the estimators inherit this class.

fit(data, method, opt='adam', init_values='random', exit_delta=0.0001, max_iter=1000, **kwargs)

Estimate the parameters of the model from the data.

Parameters:

data: pandas DataFrame or pgmpy.data.Data instance

The data from which to estimate the parameters of the model.

method: str (“ml”|”uls”|”gls”|”2sls”)

The fitting function to use. ML : Maximum Likelihood ULS: Unweighted Least Squares GLS: Generalized Least Squares 2sls: 2-SLS estimator

init_values: str or dict

Options for str: random | std | iv dict: dictionary with keys B and zeta.

**kwargs: dict

Extra parameters required in case of some estimators. GLS:

W: np.array (n x n) where n is the number of observe variables.

2sls:

x: y:

Returns:

pgmpy.model.SEM instance: Instance of the model with estimated parameters

References

[1]

Bollen, K. A. (2010). Structural equations with latent variables. New York: Wiley.

get_init_values(data, method)

Computes the starting values for the optimizer.

gls_loss(params, loss_args)

Method to compute the Weighted Least Squares fitting function. The optimizer calls this method after each iteration with updated params to compute the new loss.

The fitting function for ML is: .. math:: F_{ULS} = tr { [(S - Sigma(theta)) W^{-1}]^2 }

Parameters:

params: dict

params contain all the variables which are updated in each iteration of the optimization.

loss_args: dict

loss_args contain all the variable which are not updated in each iteration but are required to compute the loss.

Returns:

torch.tensor: The loss value for the given params and loss_args

ml_loss(params, loss_args)

Method to compute the Maximum Likelihood loss function. The optimizer calls this method after each iteration with updated params to compute the new loss.

The fitting function for ML is: .. math:: F_{ML} = log |\Sigma(\theta)| + tr(S Sigma^{-1}(theta)) - log S - (p+q)

Parameters:

params: dict

params contain all the variables which are updated in each iteration of the optimization.

loss_args: dict

loss_args contain all the variable which are not updated in each iteration but are required to compute the loss.

Returns:

torch.tensor: The loss value for the given params and loss_args

uls_loss(params, loss_args)

Method to compute the Unweighted Least Squares fitting function. The optimizer calls this method after each iteration with updated params to compute the new loss.

The fitting function for ML is: .. math:: F_{ULS} = tr[(S - Sigma(theta))^2]

Parameters:

params: dict

params contain all the variables which are updated in each iteration of the optimization.

loss_args: dict

loss_args contain all the variable which are not updated in each iteration but are required to compute the loss.

Returns:

torch.tensor: The loss value for the given params and loss_args