# Samuel Hopkins

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

### Publications

#### 2018+

**Sum of Squares Meets Program Obfuscation, Revisited.** *Boaz Barak, Samuel B. Hopkins, Aayush Jain, Pravesh Kothari, Amit Sahai.* In submission. eprint

**Mean Estimation with Sub-Gaussian Rates in Polynomial Time.** *Samuel B. Hopkins.* In Submission. arxiv talk 1 (Simons Institute)

**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)

#### 2017

**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

#### 2016

**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)

#### 2015

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

#### 2013

**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