psd_check: Check for positive semi-definiteness after a perturbation

In bnmonitor: An Implementation of Sensitivity Analysis in Bayesian Networks

Check for positive semi-definiteness after a perturbation

Description

psd_check returns a boolean to determine if the covariance matrix after a perturbation is positive semi-definite.

Usage

psd_check(x, ...)

## S3 method for class 'GBN'
psd_check(x, entry, delta, ...)

## S3 method for class 'CI'
psd_check(x, type, entry, delta, ...)

Arguments

x	object of class GBN or CI.
...	additional arguments for compatibility.
entry	a vector of length 2 indicating the entry of the covariance matrix to vary.
delta	numeric vector, including the variation parameters that act additively.
type	character string. Type of model-preserving co-variation: either total, partial, row, column or all. If all, the Frobenius norms are computed for every type of co-variation matrix.

Details

The details depend on the class the method psd_check is applied to.

Let \Sigma be the covariance matrix of a Gaussian Bayesian network and let D be a perturbation matrix acting additively. The perturbed covariance matrix \Sigma+D is positive semi-definite if

\rho(D)\leq \lambda_{\min}(\Sigma)

where \lambda_{\min} is the smallest eigenvalue end \rho is the spectral radius.

Value

A dataframe including the variations performed and the check for positive semi-definiteness.

Methods (by class)

• GBN: psd_check for objects GBN

• CI: psd_check for objects CI

References

C. Görgen & M. Leonelli (2020), Model-preserving sensitivity analysis for families of Gaussian distributions. Journal of Machine Learning Research, 21: 1-32.

Examples

psd_check(synthetic_gbn,c(2,4),-3)
psd_check(synthetic_gbn,c(2,3),seq(-1,1,0.1))
psd_check(synthetic_ci,"partial",c(2,4),0.95)
psd_check(synthetic_ci,"all",c(2,3),seq(0.9,1.1,0.01))

bnmonitor documentation built on June 7, 2023, 5:19 p.m.