For a spiked matrix-tensor model with a shared latent vector, sequential matrix-then-tensor recovery reaches the optimal Bayesian weak-recovery thresholds, while joint risk minimization makes even the easy matrix part harder to recover.
Optimal shrinkage of eigenvalues in the spiked covariance model
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Computational Thresholds in Multi-Modal Learning via the Spiked Matrix-Tensor Model
For a spiked matrix-tensor model with a shared latent vector, sequential matrix-then-tensor recovery reaches the optimal Bayesian weak-recovery thresholds, while joint risk minimization makes even the easy matrix part harder to recover.