# Quantifier Elimination for Statistical Problems

arXiv: https://arxiv.org/abs/1301.6698 · HTML: https://mlsanity.com/paper/1301.6698/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2013.

## Built on by (most cited first, 8 of 8)

- [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021)
- [Partial Identification with Noisy Covariates: A Robust Optimization Approach](https://mlsanity.com/paper/2202.10665/) (2022)
- [The Fragility of Fairness: Causal Sensitivity Analysis for Fair Machine Learning](https://mlsanity.com/paper/2410.09600/) (2024)
- [Scalable Computation of Causal Bounds](https://mlsanity.com/paper/2308.02709/) (2023)
- [Entropic Inequality Constraints from e-separation Relations in Directed Acyclic Graphs with Hidden Variables](https://mlsanity.com/paper/2107.07087/) (2021)
- [Restricted Hidden Cardinality Constraints in Causal Models](https://mlsanity.com/paper/2109.05656/) (2021)
- [Testing Causal Models with Hidden Variables in Polynomial Delay via Conditional Independencies](https://mlsanity.com/paper/2409.14593/) (2024)
- [A Counterfactual Analysis of the Dishonest Casino](https://mlsanity.com/paper/2405.15120/) (2024)

## Abstract (arXiv)

Recent improvement on Tarski's procedure for quantifier elimination in the first order theory of real numbers makes it feasible to solve small instances of the following problems completely automatically: 1. listing all equality and inequality constraints implied by a graphical model with hidden variables. 2. Comparing graphyical models with hidden variables (i.e., model equivalence, inclusion, and overlap). 3. Answering questions about the identification of a model or portion of a model, and about bounds on quantities derived from a model. 4. Determing whether a given set of independence assertions. We discuss the foundation of quantifier elimination and demonstrate its application to these problems.