Phase Diagram and Approximate Message Passing for Blind Calibration and Dictionary Learning
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Abstract (arXiv)
We consider dictionary learning and blind calibration for signals and matrices created from a random ensemble. We study the mean-squared error in the limit of large signal dimension using the replica method and unveil the appearance of phase transitions delimiting impossible, possible-but-hard and possible inference regions. We also introduce an approximate message passing algorithm that asymptotically matches the theoretical performance, and show through numerical tests that it performs very well, for the calibration problem, for tractable system sizes.
Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). First posted on arXiv 24 Jan 2013.
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Citing papers per year: 2021: 1; 2022: 0; 2023: 1; 2024: 1; 2025: 3.
6 papers.
- 2021Statistical limits of dictionary learning: random matrix theory and the spectral replica methodcited by 10
- 2025Statistical mechanics of extensive-width Bayesian neural networks near interpolationcited by 9
- 2024On the phase diagram of extensive-rank symmetric matrix denoising beyond rotational invariancecited by 4
- 2023Automatic Hyperparameter Tuning in Sparse Matrix Factorizationcited by 1
- 2025Optimal generalisation and learning transition in extensive-width shallow neural networks near interpolationcited by 0
- 2025Statistical physics of deep learning: Optimal learning of a multi-layer perceptron near interpolationcited by 0
- 2025Statistical physics of deep learning: Optimal learning of a multi-layer perceptron near interpolation28 Oct 2025
- 2025Statistical mechanics of extensive-width Bayesian neural networks near interpolation30 May 2025
- 2025Optimal generalisation and learning transition in extensive-width shallow neural networks near interpolation30 Jan 2025
- 2024On the phase diagram of extensive-rank symmetric matrix denoising beyond rotational invariance4 Nov 2024
- 2023Automatic Hyperparameter Tuning in Sparse Matrix Factorization17 May 2023
- 2021Statistical limits of dictionary learning: random matrix theory and the spectral replica method14 Sep 2021