Add chi-squared confidence level attribute to PyROS EllipsoidalSet
#3434
+169
−16
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
Summary/Motivation:
Motivated by recent user feedback, this PR adds a new PyROS$q^0 \in \mathbb{R}^n$ , positive definite shape matrix $P \in \mathbb{S}_{++}^n$ , and squared semi-axis scale factor $s \geq 0$ is defined by
EllipsoidalSet
attribute and constructor argumentgaussian_conf_lvl
that specifies, as an alternative to the the squared semi-axis scaling factor attribute and constructor argumentscale
, the level of the (ellipsoidal) confidence region of the multivariate Gaussian distribution with meancenter
and covarianceshape_matrix
. Mathematically, the PyROS ellipsoidal set with centerFor confidence level$p \in [0, 1)$ , the $100p$ % multivariate normal confidence region is obtained by setting $s = \chi_{n,p}^2$ , where $\chi_{n,\cdot}^2$ is the (invertible) lower-tail quantile function of the chi-squared distribution with $n$ degrees of freedom. Thus, we ensure that setting $s$ and confidence level $p$ , an update of
gaussian_conf_lvl
triggers, through the invertible mapping between the squared scaling factorscale
, and vice-versa.Changes proposed in this PR:
gaussian_conf_lvl
to PyROSEllipsoidalSet
.Legal Acknowledgement
By contributing to this software project, I have read the contribution guide and agree to the following terms and conditions for my contribution: