Statistical inverse learning and 1-regularization

arXiv:2607.07468 · stat.ML, cs.LG, math.ST · Submitted 2026-07-08 · Read on arXiv

Abhishake Rastogi, Tatiana A. Bubba, Tapio Helin, Luca Ratti

stat.ML, cs.LG, math.ST

Submitted: 2026-07-08

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Regularization — 79× in this paper · explained in 3 episodes
• Inverse Problem — 41× in this paper · explained in 2 episodes
• Sparsity — 37× in this paper · explained in 5 episodes
• Hilbert Space — 30× in this paper · explained in 2 episodes
• Consistency — 14× in this paper · explained in 3 episodes
• Lasso — 7× in this paper · explained in 2 episodes
• Minimax Optimality — 7× in this paper · explained in 3 episodes
• Generalization — 4× in this paper · explained in 14 episodes
• Convergence Guarantees — 3× in this paper · explained in 3 episodes
• Verification — 3× in this paper · explained in 2 episodes
• Editor — 2× in this paper · explained in 2 episodes
• Kernel Ridge Regression — 2× in this paper · explained in 2 episodes
• Reconstruction Error — 2× in this paper · explained in 2 episodes
• Sample Complexity — 2× in this paper · explained in 20 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Coherence — 1× in this paper · explained in 2 episodes
• Composition — 1× in this paper · explained in 2 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Feature Selection — 1× in this paper · explained in 4 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Kullback–Leibler Divergence — 1× in this paper · explained in 2 episodes
• Reproducing Kernel Hilbert Space (RKHS) — 1× in this paper · explained in 7 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Uncertainty Quantification — 1× in this paper · explained in 9 episodes
• Universality — 1× in this paper · explained in 2 episodes

Sources

• Compressed sensing for inverse problems II: applications to deconvolution, source recovery, and MRI

Related papers

• Behavior of prediction performance metrics with rare events
• Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs
• A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
• Scalable Posterior Uncertainty for Flexible Density-Based Clustering
• A Transport Geometry of Benign Overfitting
• Efficient quadratic entropy with distance sketches