Proofs, beliefs and algorithms through the lens of Sum of Squares

Excerpt

Boaz Barak and David Steurer


Boaz Barak and David Steurer

work in progress (Fall 2016)

Background (pdf version)

Notation (pdf version)

A random graph with a hidden clique. The sum-of-squares algorithm maintains a set of beliefs about which vertices belong to the hidden clique. Despite learning no new information, as we invest more computation time, the algorithm reduces uncertainty in the beliefs by making them consistent with increasingly powerful proof systems. Initially the beliefs have maximum uncertainty and correspond to the uniform distribution but they eventually converge on the correct hidden clique (red edges).

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