# Fixed Point Strategies in Data Science

arXiv: https://arxiv.org/abs/2008.02260 · HTML: https://mlsanity.com/paper/2008.02260/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2020.

## Built on by (most cited first, 16 of 16)

- [Robust Implicit Networks via Non-Euclidean Contractions](https://mlsanity.com/paper/2106.03194/) (2021)
- [WaveFit: An Iterative and Non-autoregressive Neural Vocoder based on Fixed-Point Iteration](https://mlsanity.com/paper/2210.01029/) (2022)
- [MURANA: A Generic Framework for Stochastic Variance-Reduced Optimization](https://mlsanity.com/paper/2106.03056/) (2021)
- [Fast Full-frame Video Stabilization with Iterative Optimization](https://mlsanity.com/paper/2307.12774/) (2023)
- [From Noisy Fixed-Point Iterations to Private ADMM for Centralized and Federated Learning](https://mlsanity.com/paper/2302.12559/) (2023)
- [Non-Log-Concave and Nonsmooth Sampling via Langevin Monte Carlo Algorithms](https://mlsanity.com/paper/2305.15988/) (2023)
- [Federated Learning Using Three-Operator ADMM](https://mlsanity.com/paper/2211.04152/) (2022)
- [Learning truly monotone operators with applications to nonlinear inverse problems](https://mlsanity.com/paper/2404.00390/) (2024)
- [A Variational Approach for Joint Image Recovery and Feature Extraction Based on Spatially-Varying Generalised Gaussian Models](https://mlsanity.com/paper/2209.01375/) (2022)
- [Fixed-Point Centrality for Networks](https://mlsanity.com/paper/2209.07070/) (2022)
- [Convex Parameter Estimation of Perturbed Multivariate Generalized Gaussian Distributions](https://mlsanity.com/paper/2312.07479/) (2023)
- [Reciprocal Learning](https://mlsanity.com/paper/2408.06257/) (2024)
- [A block-coordinate descent framework for non-convex composite optimization. Application to sparse precision matrix estimation](https://mlsanity.com/paper/2601.21467/) (2026)
- [WaveNeXt 2: ConvNeXt-Based Fast Neural Vocoders With Residual Denoising and Sub-Modeling for GAN and Diffusion Models](https://mlsanity.com/paper/2605.25506/) (2026)
- [DIFFRACT: Neuralized Utility Maximization for Wireless Networks by Differentiable Programming](https://mlsanity.com/paper/2606.07114/) (2026)
- [1-Lipschitz Neural Networks on Hadamard Manifolds](https://mlsanity.com/paper/2607.19335/) (2026)

## Abstract (arXiv)

The goal of this paper is to promote the use of fixed point strategies in data science by showing that they provide a simplifying and unifying framework to model, analyze, and solve a great variety of problems. They are seen to constitute a natural environment to explain the behavior of advanced convex optimization methods as well as of recent nonlinear methods in data science which are formulated in terms of paradigms that go beyond minimization concepts and involve constructs such as Nash equilibria or monotone inclusions. We review the pertinent tools of fixed point theory and describe the main state-of-the-art algorithms for provably convergent fixed point construction. We also incorporate additional ingredients such as stochasticity, block-implementations, and non-Euclidean metrics, which provide further enhancements. Applications to signal and image processing, machine learning, statistics, neural networks, and inverse problems are discussed.