KL_bounds {bnmonitor} | R Documentation |
Bounds for the KL-divergence
Description
Computation of the bounds of the KL-divergence for variations of each parameter of a CI
object.
Usage
KL_bounds(ci, delta)
Arguments
ci |
object of class |
delta |
multiplicative variation coefficient for the entry of the covariance matrix given in |
Details
Let be the covariance matrix of a Gaussian Bayesian network with
vertices.
Let
and
be variation matrices acting additively on
. Let also
be a model-preserving co-variation matrix.
Denote with
and
the original and the perturbed random vectors. Then for a standard sensitivity analysis
whilst for a model-preserving one
where and
are the largest and the smallest eigenvalues, respectively,
and
denotes the Schur or element-wise product.
Value
A dataframe including the KL-divergence bound for each co-variation scheme (model-preserving and standard) and every entry of the covariance matrix. For variations leading to non-positive semidefinite matrix, the dataframe includes a NA
.
References
C. Görgen & M. Leonelli (2020), Model-preserving sensitivity analysis for families of Gaussian distributions. Journal of Machine Learning Research, 21: 1-32.
See Also
Examples
KL_bounds(synthetic_ci,1.05)