# Bayesian experimental design using regularized determinantal point processes

arXiv: https://arxiv.org/abs/1906.04133 · HTML: https://mlsanity.com/paper/1906.04133/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jun 2019.

## Built on by (most cited first, 17 of 17)

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- [Data Curation for Machine Learning Interatomic Potentials by Determinantal Point Processes](https://mlsanity.com/paper/2603.22160/) (2026)
- [Adaptive Sampling for Fast Constrained Maximization of Submodular Function](https://mlsanity.com/paper/2102.06486/) (2021)
- [A Family of Distributions of Random Subsets for Controlling Positive and Negative Dependence](https://mlsanity.com/paper/2408.01022/) (2024)
- [Experimental Design for Any p-Norm](https://mlsanity.com/paper/2305.01942/) (2023)
- [On sampling determinantal and Pfaffian point processes on a quantum computer](https://mlsanity.com/paper/2305.15851/) (2023)
- [Nonparametric estimation of continuous DPPs with kernel methods](https://mlsanity.com/paper/2106.14210/) (2021)
- [Stein Kernelized Molecular Dynamics for Active Learning of Interatomic Potentials](https://mlsanity.com/paper/2606.04100/) (2026)

## Abstract (arXiv)

In experimental design, we are given n vectors in d dimensions, and our goal is to select kll n of them to perform expensive measurements, e.g., to obtain labels/responses, for a linear regression task. Many statistical criteria have been proposed for choosing the optimal design, with popular choices including A- and D-optimality. If prior knowledge is given, typically in the form of a d× d precision matrix mathbf A, then all of the criteria can be extended to incorporate that information via a Bayesian framework. In this paper, we demonstrate a new fundamental connection between Bayesian experimental design and determinantal point processes, the latter being widely used for sampling diverse subsets of data. We use this connection to develop new efficient algorithms for finding (1+ε)-approximations of optimal designs under four optimality criteria: A, C, D and V. Our algorithms can achieve this when the desired subset size k is Omega(fracdmathbf Aε + fraclog 1/εε2), where dmathbf A≤ d is the mathbf A-effective dimension, which can often be much smaller than d. Our results offer direct improvements over a number of prior works, for both Bayesian and classical experimental design, in terms of algorithm efficiency, approximation quality, and range of applicable criteria.