mlsanityData to 7 Oct 2026

Statistical Learning and Inverse Problems: A Stochastic Gradient Approach

arXiv 2209.14967 ↗First posted 29 Sep 2022stat.ML cs.LGcited by 5

Not on the map. Why?

Abstract (arXiv)

Inverse problems are paramount in Science and Engineering. In this paper, we consider the setup of Statistical Inverse Problem (SIP) and demonstrate how Stochastic Gradient Descent (SGD) algorithms can be used in the linear SIP setting. We provide consistency and finite sample bounds for the excess risk. We also propose a modification for the SGD algorithm where we leverage machine learning methods to smooth the stochastic gradients and improve empirical performance. We exemplify the algorithm in a setting of great interest nowadays: the Functional Linear Regression model. In this case we consider a synthetic data example and examples with a real data classification problem.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 9 of its 34 references that are in the map. First posted on arXiv 29 Sep 2022.

Builds on

9 of 34 references.

References · 9

  1. 2016Deep Convolutional Neural Network for Inverse Problems in Imagingcited by 431
  2. 2020Deep Learning Techniques for Inverse Problems in Imagingcited by 290
  3. 2017Solving ill-posed inverse problems using iterative deep neural networkscited by 145
  4. 2018NETT: Solving Inverse Problems with Deep Neural Networkscited by 89
  5. 2014Functional Regressioncited by 26
  6. 2020Deep Learning Methods for Solving Linear Inverse Problems: Research Directions and Paradigmscited by 16
  7. 2019On the Convergence of Stochastic Gradient Descent for Nonlinear Ill-Posed Problemscited by 4
  8. 2020On the Saturation Phenomenon of Stochastic Gradient Descent for Linear Inverse Problemscited by 3
  9. 2022Functional Classification of Bitcoin Addressescited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 1; 2024: 1; 2025: 2; 2026: 1.

5 papers.

  1. 2024Nonparametric Instrumental Variable Regression through Stochastic Approximate Gradientscited by 6
  2. 2025Controlling the Flow: Stability and Convergence for Stochastic Gradient Descent with Decaying Regularizationcited by 3
  3. 2025Random Gradient-Free Optimization in Infinite Dimensional Spacescited by 1
  4. 2026Functional Gradient Descent with Adaptive Representationscited by 1
  5. 2023Stochastic Gradient Langevin Dynamics Based on Quantization with Increasing Resolutioncited by 0