bnmonitor {bnmonitor}

bnmonitor: A package for sensitivity analysis and robustness in Bayesian networks

Description

Sensitivity and robustness analysis for Bayesian networks.

Details

bnmonitor provides functions to perform sensitivity analysis for both discrete Bayesian networks (DBNs) and Gaussian Bayesian networks (GBNs). The following types of sensitivity investigations are available:

• Parametric sensitivity analysis: Investigate the effect of changes in some of the parameter values in a Bayesian network and quantify the difference between the original and perturbed Bayesian networks using dissimilarity measures (both for DBNs and GBNs).

• Robustness to data: Verify how well a Bayesian network fits a specific dataset that was used either for learning or for testing (only for DBNs).

• Node influence: Quantify how much the nodes of a Bayesian network influence an output node of interest (only for DBNs).

• Edge strength: Assess the strength of the edges of a Bayesian network (only for DBNs).

• Other investigations: Including the diameter of the conditional probability tables, measures of asymmetric independence, and level amalgamation.

DBNs - Robustness to data

The available functions for robustness are:

• Node monitors (node_monitor): contribution of each vertex to the overall log-likelihood of the model.

• Observation's influence (influential_obs): difference in the log-likelihood of a model learnt with the full dataset and with all but one observation.

• Final node monitors (node_monitor): marginal and conditional node monitors to assess the fit of a vertex distribution to the full dataset.

• Sequential node monitors (seq_node_monitor): marginal and conditional node monitors for a specific vertex only using sequentially subsets of the dataset.

• Sequential parent-child monitor (seq_pa_ch_monitor): parent-child node monitor for a specific vertex and a specific configuration of its parents using sequentially subsets of the dataset.

DBNs - Co-variation schemes

The available co-variation schemes are:

• Uniform co-variation scheme (uniform_covar): distributes the probability mass to be co-varied uniformly among the co-varying parameters.

• Proportional co-variation scheme (proportional_covar): distributes the probability mass to be co-varied in the same proportion as in the original Bayesian network.

• Order-preserving co-variation scheme (orderp_covar):distributes the to be co-varied probability mass among the co-varying parameters so that the original order of parameters is preserved.

DBNs - Dissimilarity measures

The dissimilarity measures quantify the difference between a Bayesian network and its update after parameter variation.
The available dissimilarity measures are:

• Chan-Darwiche distance (CD)

• Kullback-Leibler divergence (KL)

DBNs - Sensitivity functions

The available functions for sensitivity analysis are:

• Sensitivity function (sensitivity): returns a certain probability of interest given a parameter change. Evidence can be considered.

• Sensitivity query (sensquery): returns the parameter changes needed to get a certain probability of interest. Evidence can be considered.

DBNs - Node influence

The available functions for node influence are:

• Mutual information (mutual_info): returns the mutual information between a node and all other nodes of a DBN.

• Distance-weighted influence (dwi): returns the distance-weighted influence between a node and all other nodes of a DBN.

• Edge-weighted influence (ewi): returns the edge-weighted influence between a node and all other nodes of a DBN.

DBNs - Edge strength

The available functions for edge strength are:

• Measure of edge strength (edge_strength): returns the edge strength measure for all edges of a DBN.

DBNs - Other sensitivity measures

Other sensitivity measures available are:

• Diameter (diameter): returns the diameter of the conditional probability tables of all non-root nodes of a DBN.

• Level amalgamation (amalgamation): returns the diameter of all children conditional probability tables of a node in DBN when every pair of levels are merged.

• Measures of asymmetric independence (asy_measure): returns the indexes of context-specific and partial conditional independence for all variables of a DBN.

GBNs - Model-Preserving matrices

The available functions to construct model-preserving co-variation matrices are:

• Total co-variation matrix (total_covar_matrix).

• Partial co-variation matrix (partial_covar_matrix).

• Row-based co-variation matrix (row_covar_matrix).

• Column-based co-variation matrix (col_covar_matrix).

GBNs - Mean and Covariance variations

The available functions to perturb the distribution of a GBN are:

• Mean variations (mean_var).

• Standard covariance variations (covariance_var).

• Model-preserving covariance variations (model_pres_cov).

GBNs - Dissimilarity measures

The available dissimilarity measures are:

• Frobenius norm (Fro).

• Jeffrey's distance (Jeffreys).

• Kullback-Leibler divergence (KL).

• Upper bound to the KL divergence (KL_bounds).