0-1 Phase Transitions in Sparse Spiked Matrix Estimation

By Jean Barbier, Nicolas Macris. 2019

15 citations recorded by the source corpus.

We consider statistical models of estimation of a rank-one matrix (the spike) corrupted by an additive gaussian noise matrix in the sparse limit. In this limit the underlying hidden vector (that constructs the rank-one matrix) has a number of non-zero components that scales sub-linearly with the total dimension of the vector, and the signal strength tends to infinity at an appropriate speed. We prove explicit low-dimensional variational formulas for the asymptotic mutual information between the spike and the observed noisy matrix in suitable sparse limits. For Bernoulli and Bernoulli-Rademacher distributed vectors, and when the sparsity and signal strength satisfy an appropriate scaling relation, these formulas imply sharp 0-1 phase transitions for the asymptotic minimum mean-square-error. A similar phase transition was analyzed recently in the context of sparse high-dimensional linear regression (compressive sensing).

Subfields: Computational Mechanics, Statistics and Probability, Statistical Learning Theory, Signal Processing

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In Computational Mechanics

1. Wei Han
2. Yu Zhang
3. Quoc V. Le

In Statistics and Probability

1. Daniel S. Park
2. Wei Han
3. Yu Zhang
4. Quoc V. Le

In Statistical Learning Theory

1. Daniel S. Park
2. Yu Zhang
3. Quoc V. Le
4. Harald Steck

In Signal Processing

1. Yu Zhang
2. Yonghui Wu
3. Chung-Cheng Chiu
4. Ruoming Pang
5. Wei Han
6. James Qin
7. Jinyu Li
8. Quoc V. Le

Citations in the corpus

• Pushing the Limits of Semi-Supervised Learning for Automatic Speech Recognition (2020, background): “The papers corresponding to each data point have been collected in the bibliography [6, 8, 9, 13–21].”