# Bayesian Inference of Log Determinants

arXiv: https://arxiv.org/abs/1704.01445 · HTML: https://mlsanity.com/paper/1704.01445/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2017.

## Built on by (most cited first, 4 of 4)

- [Determinant Estimation under Memory Constraints and Neural Scaling Laws](https://mlsanity.com/paper/2503.04424/) (2025)
- [Adaptive Cholesky Gaussian Processes](https://mlsanity.com/paper/2202.10769/) (2022)
- [Bayesian Quadrature](https://mlsanity.com/paper/2602.16218/) (2026)
- [Batch Active Learning in Gaussian Process Regression using Derivatives](https://mlsanity.com/paper/2408.01861/) (2024)

## Abstract (arXiv)

The log-determinant of a kernel matrix appears in a variety of machine learning problems, ranging from determinantal point processes and generalized Markov random fields, through to the training of Gaussian processes. Exact calculation of this term is often intractable when the size of the kernel matrix exceeds a few thousand. In the spirit of probabilistic numerics, we reinterpret the problem of computing the log-determinant as a Bayesian inference problem. In particular, we combine prior knowledge in the form of bounds from matrix theory and evidence derived from stochastic trace estimation to obtain probabilistic estimates for the log-determinant and its associated uncertainty within a given computational budget. Beyond its novelty and theoretic appeal, the performance of our proposal is competitive with state-of-the-art approaches to approximating the log-determinant, while also quantifying the uncertainty due to budget-constrained evidence.