# Posterior Temperature Optimization in Variational Inference for Inverse Problems

arXiv: https://arxiv.org/abs/2106.07533 · HTML: https://mlsanity.com/paper/2106.07533/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 18 references that are in the map.
- First posted on arXiv 11 Jun 2021.

## Builds on (most cited first, 12 of 12)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [A Tutorial on Bayesian Optimization](https://mlsanity.com/paper/1807.02811/) (2018)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Scalable Bayesian Optimization Using Deep Neural Networks](https://mlsanity.com/paper/1502.05700/) (2015)
- [Computed Tomography Reconstruction Using Deep Image Prior and Learned Reconstruction Methods](https://mlsanity.com/paper/2003.04989/) (2020)
- [A statistical theory of cold posteriors in deep neural networks](https://mlsanity.com/paper/2008.05912/) (2020)
- [A Bayesian Perspective on the Deep Image Prior](https://mlsanity.com/paper/1904.07457/) (2019)
- [Well-calibrated Model Uncertainty with Temperature Scaling for Dropout Variational Inference](https://mlsanity.com/paper/1909.13550/) (2019)
- [Uncertainty Estimation in Medical Image Denoising with Bayesian Deep Image Prior](https://mlsanity.com/paper/2008.08837/) (2020)

## Built on by (most cited first, 3 of 3)

- [How Tempering Fixes Data Augmentation in Bayesian Neural Networks](https://mlsanity.com/paper/2205.13900/) (2022)
- [Variational Inference of overparameterized Bayesian Neural Networks: a theoretical and empirical study](https://mlsanity.com/paper/2207.03859/) (2022)
- [Temperature Optimization for Bayesian Deep Learning](https://mlsanity.com/paper/2410.05757/) (2024)

## Abstract (arXiv)

Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice, this often results in a suboptimal posterior temperature and the full potential of the Bayesian approach is not realized. In this paper, we optimize both the parameters of the prior distribution and the posterior temperature using Bayesian optimization. Well-tempered posteriors lead to better predictive performance and improved uncertainty calibration, which we demonstrate for the task of sparse-view CT reconstruction.