# Bayesian Experimental Design via Score Matching

arXiv: https://arxiv.org/abs/2607.08335 · HTML: https://mlsanity.com/paper/2607.08335/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 57 references that are in the map.
- First posted on arXiv 9 Jul 2026.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [Transformer Neural Processes: Uncertainty-Aware Meta Learning Via Sequence Modeling](https://mlsanity.com/paper/2207.04179/) (2022)
- [Modern Bayesian Experimental Design](https://mlsanity.com/paper/2302.14545/) (2023)
- [Variational Bayesian Optimal Experimental Design](https://mlsanity.com/paper/1903.05480/) (2019)
- [Deep Adaptive Design: Amortizing Sequential Bayesian Experimental Design](https://mlsanity.com/paper/2103.02438/) (2021)
- [On Nesting Monte Carlo Estimators](https://mlsanity.com/paper/1709.06181/) (2017)
- [Implicit Deep Adaptive Design: Policy-Based Experimental Design without Likelihoods](https://mlsanity.com/paper/2111.02329/) (2021)
- [Mining gold from implicit models to improve likelihood-free inference](https://mlsanity.com/paper/1805.12244/) (2018)
- [Gradient Estimators for Implicit Models](https://mlsanity.com/paper/1705.07107/) (2017)
- [A Unified Stochastic Gradient Approach to Designing Bayesian-Optimal Experiments](https://mlsanity.com/paper/1911.00294/) (2019)
- [Bayesian Experimental Design for Implicit Models by Mutual Information Neural Estimation](https://mlsanity.com/paper/2002.08129/) (2020)
- [Optimizing Sequential Experimental Design with Deep Reinforcement Learning](https://mlsanity.com/paper/2202.00821/) (2022)
- [A Spectral Approach to Gradient Estimation for Implicit Distributions](https://mlsanity.com/paper/1806.02925/) (2018)
- [Optimal experimental design: Formulations and computations](https://mlsanity.com/paper/2407.16212/) (2024)
- [Efficient Bayesian Experimental Design for Implicit Models](https://mlsanity.com/paper/1810.09912/) (2018)
- [Bayesian Sequential Optimal Experimental Design for Nonlinear Models Using Policy Gradient Reinforcement Learning](https://mlsanity.com/paper/2110.15335/) (2021)
- [Unbiased MLMC stochastic gradient-based optimization of Bayesian experimental designs](https://mlsanity.com/paper/2005.08414/) (2020)
- [AR-DAE: Towards Unbiased Neural Entropy Gradient Estimation](https://mlsanity.com/paper/2006.05164/) (2020)
- [Variational Bayesian Optimal Experimental Design with Normalizing Flows](https://mlsanity.com/paper/2404.13056/) (2024)
- [Nesting Particle Filters for Experimental Design in Dynamical Systems](https://mlsanity.com/paper/2402.07868/) (2024)
- [Step-DAD: Semi-Amortized Policy-Based Bayesian Experimental Design](https://mlsanity.com/paper/2507.14057/) (2025)

## Built on by (most cited first, 1 of 1)

- [Deep adaptive design with an evidential bias criterion](https://mlsanity.com/paper/2608.16466/) (2026)

## Abstract (arXiv)

Policy-based approaches to Bayesian experimental design (BED) allow the learning of deep policy networks that adaptively make intelligent design decisions based on previously collected data. However, the training of such policies is often held back by a fundamental challenge: the double intractability of the expected information gain (EIG). This necessitates expensive or complex approximations that restrict the effort one can invest in optimising the policy itself. To address this, we show that the double intractability of the EIG can be isolated from the policy learning by first solving a score matching problem that is independent of the policy used, then using the learned score approximation to train the policy in a singly intractable manner. This turns the key multiplicative cost into an additive one and reduces the computational burden on the policy training itself, making it far cheaper to train the policy multiple times when needed, e.g. for architecture search, hyperparameter tuning, or avoiding local optima. In our experiments we train multiple competitive policies without inducing a multiplicative cost in likelihood evaluations, which can increase performance by allowing us to select the best policy even without performing hyperparameter or architecture searches.