REVIEW 5 cited by
Fundamental limits of low-rank matrix estimation: the non-symmetric case
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
We consider the high-dimensional inference problem where the signal is a low-rank matrix which is corrupted by an additive Gaussian noise. Given a probabilistic model for the low-rank matrix, we compute the limit in the large dimension setting for the mutual information between the signal and the observations, as well as the matrix minimum mean square error, while the rank of the signal remains constant. This allows to locate the information-theoretic threshold for this estimation problem, i.e. the critical value of the signal intensity below which it is impossible to recover the low-rank matrix.
Forward citations
Cited by 5 Pith papers
-
Fundamental Limits of Query-Based Subgraph Detection
For non-adaptive edge-query detection of arbitrary planted subgraphs, the minimum query count is governed by whether the planted graph has dense local witnesses, high-degree hubs, or just many edges.
-
Sharp Spectral Thresholds for Multi-View Spiked Wigner Models
The spectral weak-recovery threshold for linearized AMP in the multi-view spiked Wigner model is SNR(λ,B)=1, where SNR is the largest eigenvalue of Diag(√λ)(B⊙B)Diag(√λ), and this coincides with the information-theore...
-
A solvable high-dimensional model where nonlinear autoencoders learn structure invisible to PCA while test loss misaligns with generalization
In a new spiked-cumulant model, a minimal nonlinear autoencoder provably recovers a PCA-invisible latent factor that linear autoencoders miss, even though its test reconstruction loss is worse.
-
Statistical Limits for Finite-Rank Tensor Estimation
A general q-wise interaction model yields asymptotically exact free energy and MMSE formulas, unifying and extending prior results for heteroskedastic tensors and higher-order assignment problems.
-
Recovery of Planted Subgraphs
Sharp conditions for exact recovery of general planted subgraphs in ER graphs are given by the minimal maximum subgraph density, with matching bounds, a spectral algorithm, and computational hardness results via low-d...
Discussion (0). Continue with ORCID to comment.