# Submodular Observation Selection and Information Gathering for Quadratic Models

arXiv: https://arxiv.org/abs/1905.09919 · HTML: https://mlsanity.com/paper/1905.09919/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2019.

## Built on by (most cited first, 9 of 9)

- [Differentiable Learning Under Triage](https://mlsanity.com/paper/2103.08902/) (2021)
- [Training Data Subset Selection for Regression with Controlled Generalization Error](https://mlsanity.com/paper/2106.12491/) (2021)
- [Neural Estimation of Submodular Functions with Applications to Differentiable Subset Selection](https://mlsanity.com/paper/2210.11033/) (2022)
- [Demarcating Endogenous and Exogenous Opinion Dynamics: An Experimental Design Approach](https://mlsanity.com/paper/2102.05954/) (2021)
- [Localized Distributional Robustness in Submodular Multi-Task Subset Selection](https://mlsanity.com/paper/2404.03759/) (2024)
- [Lazy FSCA for Unsupervised Variable Selection](https://mlsanity.com/paper/2103.02687/) (2021)
- [Fast networked data selection via distributed smoothed quantile estimation](https://mlsanity.com/paper/2406.01929/) (2024)
- [Sparse Bayesian Learning for Label Efficiency in Cardiac Real-Time MRI](https://mlsanity.com/paper/2503.21443/) (2025)
- [Probabilistic Multi-Source Data Selection via Learnable Categorical Priors: Variance Reduction and Guaranteed Derandomization](https://mlsanity.com/paper/2610.14942/) (2026)

## Abstract (arXiv)

We study the problem of selecting most informative subset of a large observation set to enable accurate estimation of unknown parameters. This problem arises in a variety of settings in machine learning and signal processing including feature selection, phase retrieval, and target localization. Since for quadratic measurement models the moment matrix of the optimal estimator is generally unknown, majority of prior work resorts to approximation techniques such as linearization of the observation model to optimize the alphabetical optimality criteria of an approximate moment matrix. Conversely, by exploiting a connection to the classical Van Trees' inequality, we derive new alphabetical optimality criteria without distorting the relational structure of the observation model. We further show that under certain conditions on parameters of the problem these optimality criteria are monotone and (weak) submodular set functions. These results enable us to develop an efficient greedy observation selection algorithm uniquely tailored for quadratic models, and provide theoretical bounds on its achievable utility.