Convex Regularization

Convex regularization is a technique used to improve the stability and generalization of machine learning models, particularly in solving ill-posed inverse problems like image reconstruction. Current research focuses on developing and analyzing novel convex regularizers, often implemented using neural networks, to enhance model expressiveness and convergence properties, particularly within the context of unsupervised learning and primal-dual optimization algorithms. These advancements are significant because they enable the creation of more robust and reliable algorithms for various applications, including medical imaging and signal processing, while offering improved theoretical guarantees and interpretability compared to purely data-driven approaches.

Papers

August 23, 2024

Controlled Learning of Pointwise Nonlinearities in Neural-Network-Like Architectures
Michael Unser, Alexis Goujon, Stanislas Ducotterd
Regularization Model Nonlinear Model Variational Method Convex Regularization Controllable Network Learning

April 8, 2024

Unsupervised Training of Convex Regularizers using Maximum Likelihood Estimation
Hong Ye Tan, Ziruo Cai, Marcelo Pereyra, Subhadip Mukherjee, Junqi Tang, Carola-Bibiane Schönlieb
Unsupervised Learning Maximum Likelihood Unsupervised Training Convex Regularization Adversarial Regularization Unsupervised Probabilistic Model

February 1, 2024

Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisation
Zakhar Shumaylov, Jeremy Budd, Subhadip Mukherjee, Carola-Bibiane Schönlieb
Inverse Problem Early Stage Convergence Regularization Model Primal Dual Convex Regularization Variational Regularization Convex Neural Network Critical Point Convergent Regularization

November 3, 2023

Sketching for Convex and Nonconvex Regularized Least Squares with Sharp Guarantees
Yingzhen Yang, Ping Li
Least Square General Nonconvex Sparse Signal Convex Regularization Nonconvex Regularization

September 17, 2023

Convex Latent-Optimized Adversarial Regularizers for Imaging Inverse Problems
Huayu Wang, Chen Luo, Taofeng Xie, Qiyu Jin, Guoqing Chen, Zhuo-Xu Cui, Dong Liang
Inverse Problem Regularization Model Convex Regularization Variational Regularization Adversarial Regularization

August 21, 2023

Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms
Alexis Goujon, Sebastian Neumayer, Michael Unser
Global Convergence Convex Regularization

August 2, 2023

Wasserstein Diversity-Enriched Regularizer for Hierarchical Reinforcement Learning
Haorui Li, Jiaqi Liang, Linjing Li, Daniel Zeng
Hierarchical Reinforcement Learning Gradient Regularization Concept Discovery Wasserstein Dictionary Convex Regularization Action Distribution

July 14, 2023

Variance-reduced accelerated methods for decentralized stochastic double-regularized nonconvex strongly-concave minimax problems
Gabriel Mancino-Ball, Yangyang Xu
NCD Method Communication Complexity Convex Regularization Stochastic Nonconvex Nonconvex Regularization Variance Aware Nonsmooth Regularization Decentralized Stochastic Strongly Concave Minimax

April 6, 2023

Classification of Heavy-tailed Features in High Dimensions: a Superstatistical Approach
Urte Adomaityte, Gabriele Sicuro, Pierpaolo Vivo
Classification Code Regularization Model High Dimension Heavy Tailed Gaussian Distribution Convex Regularization General Convex Loss Gaussian Universality Self Fitting Method

November 22, 2022

A Neural-Network-Based Convex Regularizer for Inverse Problems
Alexis Goujon, Sebastian Neumayer, Pakshal Bohra, Stanislas Ducotterd, Michael Unser
Inverse Problem Denoising Process Deep Learning Based Convex Regularization Ridge Function

October 21, 2022

Bridging the Gap Between Target Networks and Functional Regularization
Alexandre Piche, Valentin Thomas, Joseph Marino, Rafael Pardinas, Gian Maria Marconi, Christopher Pal, Mohammad Emtiyaz Khan
Deep Reinforcement Learning Implicit Regularization Convex Regularization Goal Node Functional Regularization

June 18, 2022

Tree-Guided Rare Feature Selection and Logic Aggregation with Electronic Health Records Data
Jianmin Chen, Robert H. Aseltine, Fei Wang, Kun Chen
Electronic Health Record Convex Regularization Binary Feature

June 11, 2022

Learned reconstruction methods with convergence guarantees
Subhadip Mukherjee, Andreas Hauptmann, Ozan Öktem, Marcelo Pereyra, Carola-Bibiane Schönlieb
Image Reconstruction Convergence Guarantee Convex Regularization Incremental Reconstruction Data Driven Reconstruction Reconstruction Technique

May 16, 2022

The Role of Pseudo-labels in Self-training Linear Classifiers on High-dimensional Gaussian Mixture Data
Takashi Takahashi
Strong Generalization Pseudo Label Integral Role Generalization Performance Linear Classifier Convex Regularization Dimensional Gaussian Mixture

April 6, 2022

Random Features Model with General Convex Regularization: A Fine Grained Analysis with Precise Asymptotic Learning Curves
David Bosch, Ashkan Panahi, Ayca Özcelikkale, Devdatt Dubhash
Fine Grained Gaussian Process Learning Rate Random Feature Convex Regularization

March 16, 2022

Non-isotropy Regularization for Proxy-based Deep Metric Learning
Karsten Roth, Oriol Vinyals, Zeynep Akata
Deep Metric Learning Proxy Metric Convex Regularization Proxy Based Deep Metric Learning

Convex Regularization

Papers

Controlled Learning of Pointwise Nonlinearities in Neural-Network-Like Architectures

Unsupervised Training of Convex Regularizers using Maximum Likelihood Estimation

Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisation

Sketching for Convex and Nonconvex Regularized Least Squares with Sharp Guarantees

Convex Latent-Optimized Adversarial Regularizers for Imaging Inverse Problems

Learning Weakly Convex Regularizers for Convergent Image-Reconstruction Algorithms

Wasserstein Diversity-Enriched Regularizer for Hierarchical Reinforcement Learning

Variance-reduced accelerated methods for decentralized stochastic double-regularized nonconvex strongly-concave minimax problems

Classification of Heavy-tailed Features in High Dimensions: a Superstatistical Approach

A Neural-Network-Based Convex Regularizer for Inverse Problems

Bridging the Gap Between Target Networks and Functional Regularization

Tree-Guided Rare Feature Selection and Logic Aggregation with Electronic Health Records Data

Learned reconstruction methods with convergence guarantees

The Role of Pseudo-labels in Self-training Linear Classifiers on High-dimensional Gaussian Mixture Data

Random Features Model with General Convex Regularization: A Fine Grained Analysis with Precise Asymptotic Learning Curves

Non-isotropy Regularization for Proxy-based Deep Metric Learning