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Notes on Computational Hardness of Hypothesis Testing: Predictions using the Low-Degree Likelihood Ratio
(2019)arXivWorking Paper -
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Subexponential-Time Algorithms for Sparse PCA
(2019)arXivWe study the computational cost of recovering a unit-norm sparse principal component x∈ℝn planted in a random matrix, in either the Wigner or Wishart spiked model (observing either W+λxx⊤ with W drawn from the Gaussian orthogonal ensemble, or N independent samples from (0,In+βxx⊤), respectively). Prior work has shown that when the signal-to-noise ratio (λ or βN/n‾‾‾‾√, respectively) is a small constant and the fraction of nonzero entries ...Working Paper -
A Tight Degree 4 Sum-of-Squares Lower Bound for the Sherrington-Kirkpatrick Hamiltonian
(2019)arXivWorking Paper