Samuel Hopkins

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

I am a Miller fellow in the theory group at UC Berkeley, where I am hosted by Prasad Raghavendra and Luca Trevisan. Before that, I got my PhD at Cornell under David Steurer’s watchful eyes.

CV (pdf)




Mean Estimation with Sub-Gaussian Rates in Polynomial Time. Samuel B. Hopkins. In Submission. arxiv

Statistical Inference and Sum of Squares Method. Samuel B. Hopkins. Dissertation. pdf

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

Mixture Models, Robustness, and Sum of Squares Proofs. Samuel B. Hopkins, Jerry Li. STOC 2018. arxiv talk 1 (BIRS) talk 2 (STOC)


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


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

Blog posts I wrote on clustering and learning high-dimensional mixture models using the SoS method (originally appeared on Windows on Theory. pdf

Notes on tensor decomposition using the SoS method (originally notes for a guest lecture at Stanford). pdf


Currently I am supported by the Miller Fellowship at UC Berkeley. In the past, I have received support from by Microsoft PhD Fellowship, an NSF Graduate Research Fellowship, and a Cornell University Fellowship.

I am Samuel B. Hopkins. Maybe you are looking for Samuel Francis Hopkins?


6th Floor, Soda Hall
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