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• W3119332546 abstract "We develop a general framework to significantly reduce the degree of sum-of-squares proofs by introducing new variables. To illustrate the power of this framework, we use it to speed up previous algorithms based on sum-of-squares for two important estimation problems, clustering and robust moment estimation. The resulting algorithms offer the same statistical guarantees as the previous best algorithms but have significantly faster running times. Roughly speaking, given a sample of $n$ points in dimension $d$, our algorithms can exploit order-$ell$ moments in time $d^{O(ell)}cdot n^{O(1)}$, whereas a naive implementation requires time $(dcdot n)^{O(ell)}$. Since for the aforementioned applications, the typical sample size is $d^{Theta(ell)}$, our framework improves running times from $d^{O(ell^2)}$ to $d^{O(ell)}$." @default.
• W3119332546 created "2021-01-18" @default.
• W3119332546 creator A5018816569 @default.
• W3119332546 creator A5089128021 @default.
• W3119332546 date "2021-01-05" @default.
• W3119332546 modified "2023-09-27" @default.
• W3119332546 title "SoS Degree Reduction with Applications to Clustering and Robust Moment Estimation" @default.
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• W3119332546 hasPublicationYear "2021" @default.
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