
Circuit Lower Bounds for the pSpin Optimization Problem
We consider the problem of finding a near ground state of a pspin model...
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Optimal Spectral Recovery of a Planted Vector in a Subspace
Recovering a planted vector v in an ndimensional random subspace of ℝ^N...
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AverageCase Integrality Gap for NonNegative Principal Component Analysis
Montanari and Richard (2015) asked whether a natural semidefinite progra...
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Optimal LowDegree Hardness of Maximum Independent Set
We study the algorithmic task of finding a large independent set in a sp...
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Spectral Planting and the Hardness of Refuting Cuts, Colorability, and Communities in Random Graphs
We study the problem of efficiently refuting the kcolorability of a gra...
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Computational Barriers to Estimation from LowDegree Polynomials
One fundamental goal of highdimensional statistics is to detect or reco...
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Free Energy Wells and Overlap Gap Property in Sparse PCA
We study a variant of the sparse PCA (principal component analysis) prob...
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The AverageCase Time Complexity of Certifying the Restricted Isometry Property
In compressed sensing, the restricted isometry property (RIP) on M × N s...
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Computationally efficient sparse clustering
We study statistical and computational limits of clustering when the mea...
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LowDegree Hardness of Random Optimization Problems
We consider the problem of finding nearly optimal solutions of optimizat...
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Counterexamples to the LowDegree Conjecture
A conjecture of Hopkins (2018) posits that for certain highdimensional ...
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Notes on Computational Hardness of Hypothesis Testing: Predictions using the LowDegree Likelihood Ratio
These notes survey and explore an emerging method, which we call the low...
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SubexponentialTime Algorithms for Sparse PCA
We study the computational cost of recovering a unitnorm sparse princip...
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The Kikuchi Hierarchy and Tensor PCA
For the tensor PCA (principal component analysis) problem, we propose a ...
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Computational Hardness of Certifying Bounds on Constrained PCA Problems
Given a random n × n symmetric matrix W drawn from the Gaussian orthogo...
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Spectral Methods from Tensor Networks
A tensor network is a diagram that specifies a way to "multiply" a colle...
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Optimality and Suboptimality of PCA I: Spiked Random Matrix Models
A central problem of random matrix theory is to understand the eigenvalu...
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Notes on computationaltostatistical gaps: predictions using statistical physics
In these notes we describe heuristics to predict computationaltostatis...
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Estimation under group actions: recovering orbits from invariants
Motivated by geometric problems in signal processing, computer vision, a...
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Statistical limits of spiked tensor models
We study the statistical limits of both detecting and estimating a rank...
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Messagepassing algorithms for synchronization problems over compact groups
Various alignment problems arising in cryoelectron microscopy, communit...
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Optimality and Suboptimality of PCA for Spiked Random Matrices and Synchronization
A central problem of random matrix theory is to understand the eigenvalu...
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How Robust are Reconstruction Thresholds for Community Detection?
The stochastic block model is one of the oldest and most ubiquitous mode...
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Alexander S. Wein
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