Alex Wein

Contact Information

About Me

In Spring 2022 I will be a Postdoctoral Fellow at Georgia Tech, hosted by Santosh Vempala. Previously I was a Simons-Berkeley Research Fellow in the program on Computational Complexity of Statistical Inference at UC Berkeley, and before that, a Courant Instructor (postdoc) at NYU. I am currently on the academic job market.

My research interests include:

• statistical and computational limits of problems arising in machine learning and high-dimensional statistics,
• low-degree polynomials as a restricted model of computation,
• connections between Bayesian inference and statistical physics,
• problems involving group actions (e.g. cryo-EM image processing), including connections to representation theory and invariant theory.

CV (updated 9/24/2021)

Some Recorded Talks [see more]

(10 minutes) A quick intro to the low-degree polynomial method for detection, recovery, and optimization
Bernoulli-IMS One World Symposium, Aug. 2020
[video] [slides]

(50 minutes) The low-degree method for (detection and) recovery
Stanford ISL Colloquium, Oct. 2020
[video] [slides] [paper]

(45 minutes) The low-degree method for random optimization problems
Simons Institute Workshop on Learning and Testing in High Dimensions, Dec. 2020
[video] [slides] [paper1] [paper2]

Surveys

Notes on Computational Hardness of Hypothesis Testing: Predictions using the Low-Degree Likelihood Ratio
Dmitriy Kunisky, Alexander S. Wein, Afonso S. Bandeira
[arXiv]

Notes on Computational-to-Statistical Gaps: Predictions using Statistical Physics
Afonso S. Bandeira, Amelia Perry, Alexander S. Wein
Portugaliae Mathematica, 2018
[arXiv]

Publications/Preprints

Lattice-Based Methods Surpass Sum-of-Squares in Clustering
Ilias Zadik, Min Jae Song, Alexander S. Wein, Joan Bruna
[arXiv]

Circuit Lower Bounds for the p-Spin Optimization Problem
David Gamarnik, Aukosh Jagannath, Alexander S. Wein
[arXiv]

Optimal Spectral Recovery of a Planted Vector in a Subspace
Cheng Mao, Alexander S. Wein
[arXiv] [video]

Average-Case Integrality Gap for Non-Negative Principal Component Analysis
Afonso S. Bandeira, Dmitriy Kunisky, Alexander S. Wein
MSML 2021
[arXiv]

Optimal Low-Degree Hardness of Maximum Independent Set
Alexander S. Wein
Mathematical Statistics and Learning (to appear)
[arXiv] [slides] [video]

Spectral Planting and the Hardness of Refuting Cuts, Colorability, and Communities in Random Graphs
Afonso S. Bandeira, Jess Banks, Dmitriy Kunisky, Cristopher Moore, Alexander S. Wein
COLT 2021
[arXiv] [video1] [video2]

Computational Barriers to Estimation from Low-Degree Polynomials
Tselil Schramm, Alexander S. Wein
[arXiv] [slides] [video]

Free Energy Wells and Overlap Gap Property in Sparse PCA
Gérard Ben Arous, Alexander S. Wein, Ilias Zadik
COLT 2020
[arXiv] [video]

The Average-Case Time Complexity of Certifying the Restricted Isometry Property
Yunzi Ding, Dmitriy Kunisky, Alexander S. Wein, Afonso S. Bandeira
IEEE Transactions on Information Theory, 2021
[arXiv]

Computationally Efficient Sparse Clustering
Matthias Löffler, Alexander S. Wein, Afonso S. Bandeira
[arXiv]

Low-Degree Hardness of Random Optimization Problems
David Gamarnik, Aukosh Jagannath, Alexander S. Wein
FOCS 2020
[arXiv] [slides] [video]

Counterexamples to the Low-Degree Conjecture
Justin Holmgren, Alexander S. Wein
ITCS 2021
[arXiv] [slides] [video]

Subexponential-Time Algorithms for Sparse PCA
Yunzi Ding, Dmitriy Kunisky, Alexander S. Wein, Afonso S. Bandeira
[arXiv] [slides] [video]

The Kikuchi Hierarchy and Tensor PCA
Alexander S. Wein, Ahmed El Alaoui, Cristopher Moore
FOCS 2019
[arXiv] [slides]

Computational Hardness of Certifying Bounds on Constrained PCA Problems
Afonso S. Bandeira, Dmitriy Kunisky, Alexander S. Wein
ITCS 2020
[arXiv] [slides]

Overcomplete Independent Component Analysis via SDP
Anastasia Podosinnikova, Amelia Perry, Alexander S. Wein, Francis Bach, Alexandre d'Aspremont, David Sontag
AISTATS 2019
[arXiv]

Spectral Methods from Tensor Networks
Ankur Moitra, Alexander S. Wein
STOC 2019, invited to SICOMP special issue
[arXiv] [slides]

Estimation Under Group Actions: Recovering Orbits from Invariants
Afonso S. Bandeira, Ben Blum-Smith, Joe Kileel, Amelia Perry, Jonathan Weed, Alexander S. Wein
[arXiv] [slides]

Statistical Limits of Spiked Tensor Models
Amelia Perry, Alexander S. Wein, Afonso S. Bandeira
Annales de l'Institut Henri Poincare (B) Probability and Statistics, 2020
[arXiv]

Message-Passing Algorithms for Synchronization Problems over Compact Groups
Amelia Perry, Alexander S. Wein, Afonso S. Bandeira, Ankur Moitra
Communications on Pure and Applied Mathematics, 2018
[arXiv] [slides]

Optimality and Sub-optimality of PCA I: Spiked Random Matrix Models
Amelia Perry, Alexander S. Wein, Afonso S. Bandeira, Ankur Moitra
Annals of Statistics, 2018
[arXiv] [slides]

Optimality and Sub-optimality of PCA for Spiked Random Matrices and Synchronization
Amelia Perry, Alexander S. Wein, Afonso S. Bandeira, Ankur Moitra
[arXiv]
(Partially subsumed by journal version above)

How Robust are Reconstruction Thresholds for Community Detection?
Ankur Moitra, Amelia Perry, Alexander S. Wein
STOC 2016
[arXiv] [slides]

A Semidefinite Program for Unbalanced Multisection in the Stochastic Block Model
Amelia Perry, Alexander S. Wein
SampTA 2017
[arXiv]

Thesis

Statistical Estimation in the Presence of Group Actions
Ph.D thesis, Massachusetts Institute of Technology, 2018
[PDF] [slides]