# Finding an ε-close Variation of Parameters in Bayesian Networks

arXiv: https://arxiv.org/abs/2305.10051 · HTML: https://mlsanity.com/paper/2305.10051/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 43 references that are in the map.
- First posted on arXiv 17 May 2023.

## Builds on (most cited first, 10 of 10)

- [The Probabilistic Model Checker Storm](https://mlsanity.com/paper/2002.07080/) (2020)
- [Parameter Synthesis for Markov Models: Faster Than Ever](https://mlsanity.com/paper/1602.05113/) (2016)
- [Synthesis in pMDPs: A Tale of 1001 Parameters](https://mlsanity.com/paper/1803.02884/) (2018)
- [Convex Optimization for Parameter Synthesis in MDPs](https://mlsanity.com/paper/2107.00108/) (2021)
- [Sensitivity analysis beyond linearity](https://mlsanity.com/paper/1901.02062/) (2018)
- [Are Parametric Markov Chains Monotonic?](https://mlsanity.com/paper/1907.08491/) (2019)
- [Gradient-Descent for Randomized Controllers under Partial Observability](https://mlsanity.com/paper/2111.04407/) (2021)
- [You Only Derive Once (YODO): Automatic Differentiation for Efficient Sensitivity Analysis in Bayesian Networks](https://mlsanity.com/paper/2206.08687/) (2022)
- [Bayesian Inference by Symbolic Model Checking](https://mlsanity.com/paper/2007.15071/) (2020)
- [Fine-Tuning the Odds in Bayesian Networks](https://mlsanity.com/paper/2105.14371/) (2021)

## Abstract (arXiv)

This paper addresses the ε-close parameter tuning problem for Bayesian Networks (BNs): find a minimal ε-close amendment of probability entries in a given set of (rows in) conditional probability tables that make a given quantitative constraint on the BN valid. Based on the state-of-the-art "region verification" techniques for parametric Markov chains, we propose an algorithm whose capabilities go beyond any existing techniques. Our experiments show that ε-close tuning of large BN benchmarks with up to 8 parameters is feasible. In particular, by allowing (i) varied parameters in multiple CPTs and (ii) inter-CPT parameter dependencies, we treat subclasses of parametric BNs that have received scant attention so far.