no code implementations • 24 Jan 2019 • Anastasia Podosinnikova, Amelia Perry, Alexander Wein, Francis Bach, Alexandre d'Aspremont, David Sontag
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.
no code implementations • 2 Jul 2018 • Amelia Perry, Alexander S. Wein, Afonso S. Bandeira, Ankur Moitra
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.
no code implementations • 29 Mar 2018 • Afonso S. Bandeira, Amelia Perry, Alexander S. Wein
In these notes we describe heuristics to predict computational-to-statistical gaps in certain statistical problems.
no code implementations • 22 Dec 2016 • Amelia Perry, Alexander S. Wein, Afonso S. Bandeira
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 $d$.
no code implementations • 14 Oct 2016 • Amelia Perry, Alexander S. Wein, Afonso S. Bandeira, Ankur Moitra
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).
no code implementations • 19 Sep 2016 • Amelia Perry, Alexander S. Wein, Afonso S. Bandeira, Ankur Moitra
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.
no code implementations • 20 Jul 2015 • Amelia Perry, Alexander S. Wein
We propose a semidefinite programming (SDP) algorithm for community detection in the stochastic block model, a popular model for networks with latent community structure.