# Entropic Trace Estimates for Log Determinants

arXiv: https://arxiv.org/abs/1704.07223 · HTML: https://mlsanity.com/paper/1704.07223/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Apr 2017.

## Built on by (most cited first, 5 of 5)

- [Geometric variational inference](https://mlsanity.com/paper/2105.10470/) (2021)
- [Optimal Query Complexities for Dynamic Trace Estimation](https://mlsanity.com/paper/2209.15219/) (2022)
- [Compute-Optimal LLMs Provably Generalize Better With Scale](https://mlsanity.com/paper/2504.15208/) (2025)
- [Adaptive Cholesky Gaussian Processes](https://mlsanity.com/paper/2202.10769/) (2022)
- [Dynamic estimation of slowly varying sequences](https://mlsanity.com/paper/2606.23655/) (2026)

## Abstract (arXiv)

The scalable calculation of matrix determinants has been a bottleneck to the widespread application of many machine learning methods such as determinantal point processes, Gaussian processes, generalised Markov random fields, graph models and many others. In this work, we estimate log determinants under the framework of maximum entropy, given information in the form of moment constraints from stochastic trace estimation. The estimates demonstrate a significant improvement on state-of-the-art alternative methods, as shown on a wide variety of UFL sparse matrices. By taking the example of a general Markov random field, we also demonstrate how this approach can significantly accelerate inference in large-scale learning methods involving the log determinant.