# Minimal primes of ideals arising from conditional independence statements

@article{Swanson2011MinimalPO, title={Minimal primes of ideals arising from conditional independence statements}, author={Irena Swanson and Amelia Taylor}, journal={Journal of Algebra}, year={2011}, volume={392}, pages={299-314} }

## 13 Citations

$s$-Hankel hypermatrices and $2\times 2$ determinantal ideals

- Mathematics
- 2016

We introduce the concept of s-Hankel hypermatrix, which generalizes both Hankel matrices and generic hypermatrices. We study two determinantal ideals associated to an s-Hankel hypermatrix: the ideal…

Robustness and Conditional Independence Ideals

- Mathematics
- 2011

We study notions of robustness of Markov kernels and probability distribution of a system that is described by $n$ input random variables and one output random variable. Markov kernels can be…

2 × 2 Permanental Ideals of Hypermatrices

- Mathematics
- 2011

We analyze the structure of ideals generated by some classes of 2 × 2 permanents of hypermatrices, generalizing [9] on 2 × 2 permanental ideals of generic matrices. We compare the obtained structure…

Matroid stratifications of hypergraph varieties, their realization spaces, and discrete conditional independence models

- Mathematics
- 2021

We study conditional independence (CI) models in statistical theory, in the case of discrete random variables, from the point of view of algebraic geometry and matroid theory. Any CI model with…

POSITIVE MARGINS AND PRIMARY DECOMPOSITION

- Mathematics
- 2014

We study random walks on contingency tables with fixed marginals, cor- responding to a (log-linear) hierarchical model. If the set of allowed moves is not a Markov basis, then there exist tables with…

Algebraic Aspects of Conditional Independence and Graphical Models

- MathematicsHandbook of Graphical Models
- 2018

This chapter of the forthcoming Handbook of Graphical Models contains an overview of basic theorems and techniques from algebraic geometry and how they can be applied to the study of conditional…

Robustness, canalyzing functions and systems design

- Mathematics, Computer ScienceTheory in Biosciences
- 2013

It is shown that robust systems can be described in terms of suitable interaction families of Gibbs potentials, which allows us to address the problem of systems design.

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Robustness and Conditional Independence Ideals

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We study notions of robustness of Markov kernels and probability distribution of a system that is described by $n$ input random variables and one output random variable. Markov kernels can be…

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