Samuel Hopkins

PhD Candidate, Cornell University

algorithms, theoretical machine learning, semidefinite programming, sum of squares optimization, convex hierarchies, hardness of approximation

CV (pdf)
Google Scholar

Supported by a Microsoft PhD Fellowship, an NSF Graduate Research Fellowship, and a Cornell University Fellowship.


Recent and Upcoming Events

Publications and Manuscripts


A Robust Spectral Algorithm for Overcomplete Tensor Decomposition. Samuel B. Hopkins, Tselil Schramm, Jonathan Shi. In submission.

Mixture Models, Robustness, and Sum of Squares Proofs. Samuel B. Hopkins, Jerry Li. STOC 2018. arxiv talk (video)


The power of SoS for detecting hidden structures. Samuel B. Hopkins, Pravesh K. Kothari, Aaron Potechin, Prasad Raghavendra, Tselil Schramm, David Steurer. FOCS 2017. arxiv

Efficient Bayesian estimation from few samples: community detection and related problems. Samuel B. Hopkins, David Steurer. FOCS 2017. arxiv video


A nearly tight sum-of-squares lower bound for the planted clique problem. Boaz Barak, Samuel B. Hopkins, Jonathan Kelner, Pravesh K. Kothari, Ankur Moitra, Aaron Potechin. FOCS 2016, inivted to special issue. arxiv video slides (pdf)

Fast spectral algorithms from sum-of-squares proofs: tensor decomposition and planted sparse vectors. Samuel B. Hopkins, Tselil Schramm, Jonathan Shi, David Steurer. STOC 2016. arxiv slides (pptx)

On the integrality gap of degree-4 sum of squares for planted clique Samuel B. Hopkins, Pravesh K. Kothari, Aaron Potechin, Tselil Schramm, Prasad Raghavendra. SODA 2016, invited to special issue. arxiv 1 (Hopkins-Kothari-Potechin version) and arxiv 2 (Raghavendra-Schramm version)


Tensor principal component analysis via sum-of-squares proofs. Samuel B. Hopkins, Jonathan Shi, David Steurer. COLT 2015, 20 minute presentation. arxiv


Kolmogorov Complexity, Circuits, and the Strength of Formal Theories of Arithmetic Eric Allender, George Davie, Luke Friedman, Samuel B. Hopkins, Iddo Tzameret. Chicago Journal of Theoretical Computer Science. eccc

Other Writing and Talks

Clustering and Sum of Squares Proofs. A series of blog posts on the sum of squares method in unsupervised learning, and in particular on clustering in mixture models. December 2017.
pdf with all the posts
part 1 part 2 part 3 part 4 part 5 part 6

Introduction to Pseudocalibration. Joint talk with Aaron Potechin. Fall 2017. youtube

Lecture Notes on SoS Tensor Decomposition Algorithms. From a guest lecture given in Moses Charikar’s special topics course at Stanford. Spring 2017. pdf


324 Gates Hall
samhop at cs dot cornell dot edu