# Nonlinear Bayesian optimal experimental design using logarithmic Sobolev inequalities

arXiv: https://arxiv.org/abs/2402.15053 · HTML: https://mlsanity.com/paper/2402.15053/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 39 references that are in the map.
- First posted on arXiv 23 Feb 2024.

## Builds on (most cited first, 20 of 20)

- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Rapid Convergence of the Unadjusted Langevin Algorithm: Isoperimetry Suffices](https://mlsanity.com/paper/1903.08568/) (2019)
- [Formal Limitations on the Measurement of Mutual Information](https://mlsanity.com/paper/1811.04251/) (2018)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [A Unified Stochastic Gradient Approach to Designing Bayesian-Optimal Experiments](https://mlsanity.com/paper/1911.00294/) (2019)
- [Guarantees for Greedy Maximization of Non-submodular Functions with Applications](https://mlsanity.com/paper/1703.02100/) (2017)
- [Gradient-based Bayesian Experimental Design for Implicit Models using Mutual Information Lower Bounds](https://mlsanity.com/paper/2105.04379/) (2021)
- [Goal-Oriented Optimal Design of Experiments for Large-Scale Bayesian Linear Inverse Problems](https://mlsanity.com/paper/1802.06517/) (2018)
- [Algorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applications](https://mlsanity.com/paper/1408.2051/) (2014)
- [Curvature and Optimal Algorithms for Learning and Minimizing Submodular Functions](https://mlsanity.com/paper/1311.2110/) (2013)
- [Data-Free Likelihood-Informed Dimension Reduction of Bayesian Inverse Problems](https://mlsanity.com/paper/2102.13245/) (2021)
- [Fast Semidifferential-based Submodular Function Optimization](https://mlsanity.com/paper/1308.1006/) (2013)
- [A Scalable Gradient-Free Method for Bayesian Experimental Design with Implicit Models](https://mlsanity.com/paper/2103.08026/) (2021)
- [Batch greedy maximization of non-submodular functions: Guarantees and applications to experimental design](https://mlsanity.com/paper/2006.04554/) (2020)
- [Submodular Optimization Problems and Greedy Strategies: A Survey](https://mlsanity.com/paper/1905.03308/) (2019)
- [When do wireless network signals appear Poisson?](https://mlsanity.com/paper/1411.3757/) (2014)

## Built on by (most cited first, 2 of 2)

- [Expected information gain estimation via density approximations: Sample allocation and dimension reduction](https://mlsanity.com/paper/2411.08390/) (2024)
- [Sharp detection of low-dimensional structure in probability measures via dimensional logarithmic Sobolev inequalities](https://mlsanity.com/paper/2406.13036/) (2024)

## Abstract (arXiv)

We study the problem of selecting k experiments from a larger candidate pool, where the goal is to maximize mutual information (MI) between the selected subset and the underlying parameters. Finding the exact solution is to this combinatorial optimization problem is computationally costly, not only due to the complexity of the combinatorial search but also the difficulty of evaluating MI in nonlinear/non-Gaussian settings. We propose greedy approaches based on new computationally inexpensive lower bounds for MI, constructed via log-Sobolev inequalities. We demonstrate that our method outperforms random selection strategies, Gaussian approximations, and nested Monte Carlo (NMC) estimators of MI in various settings, including optimal design for nonlinear models with non-additive noise.