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• W1914749871 abstract "We study a random graph named the block model in statistics and the partition model in theoretical computer science. In its simplest form, this is a random graph with two equal-sized clusters, with a between-class edge probability of $q$ and a within-class edge probability of $p$. A striking conjecture of Decelle, Krzkala, Moore and Zdeborova based on deep, non-rigorous ideas from statistical physics, gave a precise prediction for the algorithmic threshold of clustering in the sparse planted partition model. In particular, if $p = a/n$ and $q = b/n$, $s=(a-b)/2$ and $p=(a+b)/2$ then Decelle et al. conjectured that it is possible to efficiently cluster in a way correlated with the true partition if $s^2 > p$ and impossible if $s^2 C p ln p$ for some sufficiently large $C$. In a previous work, we proved that indeed it is information theoretically impossible to to cluster if $s^2 p$. A different independent proof of the same result was recently obtained by Laurent Massoulie." @default.
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• W1914749871 date "2013-11-17" @default.
• W1914749871 modified "2023-09-27" @default.
• W1914749871 title "A Proof Of The Block Model Threshold Conjecture" @default.
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