# Uncertainty quantification for learned ISTA

arXiv: https://arxiv.org/abs/2309.07982 · HTML: https://mlsanity.com/paper/2309.07982/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 28 references that are in the map.
- First posted on arXiv 14 Sep 2023.

## Builds on (most cited first, 8 of 8)

- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds](https://mlsanity.com/paper/1808.10038/) (2018)
- [Confidence Intervals and Hypothesis Testing for High-Dimensional Regression](https://mlsanity.com/paper/1306.3171/) (2013)
- [Model-Based Deep Learning: On the Intersection of Deep Learning and Optimization](https://mlsanity.com/paper/2205.02640/) (2022)
- [De-biasing the Lasso: Optimal Sample Size for Gaussian Designs](https://mlsanity.com/paper/1508.02757/) (2015)
- [Learning step sizes for unfolded sparse coding](https://mlsanity.com/paper/1905.11071/) (2019)
- [Theoretical Perspectives on Deep Learning Methods in Inverse Problems](https://mlsanity.com/paper/2206.14373/) (2022)
- [Hybrid ISTA: Unfolding ISTA With Convergence Guarantees Using Free-Form Deep Neural Networks](https://mlsanity.com/paper/2204.11640/) (2022)

## Built on by (most cited first, 2 of 2)

- [Non-Asymptotic Uncertainty Quantification in High-Dimensional Learning](https://mlsanity.com/paper/2407.13666/) (2024)
- [With or Without Replacement? Improving Confidence in Fourier Imaging](https://mlsanity.com/paper/2407.13575/) (2024)

## Abstract (arXiv)

Model-based deep learning solutions to inverse problems have attracted increasing attention in recent years as they bridge state-of-the-art numerical performance with interpretability. In addition, the incorporated prior domain knowledge can make the training more efficient as the smaller number of parameters allows the training step to be executed with smaller datasets. Algorithm unrolling schemes stand out among these model-based learning techniques. Despite their rapid advancement and their close connection to traditional high-dimensional statistical methods, they lack certainty estimates and a theory for uncertainty quantification is still elusive. This work provides a step towards closing this gap proposing a rigorous way to obtain confidence intervals for the LISTA estimator.