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Found 7 papers, 0 papers with code
Overcomplete Independent Component Analysis via SDP
Moreover, we conjecture that the proposed program recovers a mixing component at the rate k < p^2/4 and prove that a mixing component can be recovered with high probability when k < (2 - epsilon) p log p when the original components are sampled uniformly at random on the hyper sphere.
Optimality and Sub-optimality of PCA I: Spiked Random Matrix Models
Our results leverage Le Cam's notion of contiguity, and include: i) For the Gaussian Wigner ensemble, we show that PCA achieves the optimal detection threshold for certain natural priors for the spike.
Notes on computational-to-statistical gaps: predictions using statistical physics
In these notes we describe heuristics to predict computational-to-statistical gaps in certain statistical problems.
Statistical limits of spiked tensor models
Finally, for priors (i) and (ii) we carry out the replica prediction from statistical physics, which is conjectured to give the exact information-theoretic threshold for any fixed $d$.
Message-passing algorithms for synchronization problems over compact groups
Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or SO(3).
Optimality and Sub-optimality of PCA for Spiked Random Matrices and Synchronization
Our results include: I) For the Gaussian Wigner ensemble, we show that PCA achieves the optimal detection threshold for a variety of benign priors for the spike.
A semidefinite program for unbalanced multisection in the stochastic block model
We propose a semidefinite programming (SDP) algorithm for community detection in the stochastic block model, a popular model for networks with latent community structure.
