1,218 research outputs found
Community detection and stochastic block models: recent developments
The stochastic block model (SBM) is a random graph model with planted
clusters. It is widely employed as a canonical model to study clustering and
community detection, and provides generally a fertile ground to study the
statistical and computational tradeoffs that arise in network and data
sciences.
This note surveys the recent developments that establish the fundamental
limits for community detection in the SBM, both with respect to
information-theoretic and computational thresholds, and for various recovery
requirements such as exact, partial and weak recovery (a.k.a., detection). The
main results discussed are the phase transitions for exact recovery at the
Chernoff-Hellinger threshold, the phase transition for weak recovery at the
Kesten-Stigum threshold, the optimal distortion-SNR tradeoff for partial
recovery, the learning of the SBM parameters and the gap between
information-theoretic and computational thresholds.
The note also covers some of the algorithms developed in the quest of
achieving the limits, in particular two-round algorithms via graph-splitting,
semi-definite programming, linearized belief propagation, classical and
nonbacktracking spectral methods. A few open problems are also discussed
Will the US Economy Recover in 2010? A Minimal Spanning Tree Study
We calculated the cross correlations between the half-hourly times series of
the ten Dow Jones US economic sectors over the period February 2000 to August
2008, the two-year intervals 2002--2003, 2004--2005, 2008--2009, and also over
11 segments within the present financial crisis, to construct minimal spanning
trees (MSTs) of the US economy at the sector level. In all MSTs, a core-fringe
structure is found, with consumer goods, consumer services, and the industrials
consistently making up the core, and basic materials, oil and gas, healthcare,
telecommunications, and utilities residing predominantly on the fringe. More
importantly, we find that the MSTs can be classified into two distinct,
statistically robust, topologies: (i) star-like, with the industrials at the
center, associated with low-volatility economic growth; and (ii) chain-like,
associated with high-volatility economic crisis. Finally, we present
statistical evidence, based on the emergence of a star-like MST in Sep 2009,
and the MST staying robustly star-like throughout the Greek Debt Crisis, that
the US economy is on track to a recovery.Comment: elsarticle class, includes amsmath.sty, graphicx.sty and url.sty. 68
pages, 16 figures, 8 tables. Abridged version of the manuscript presented at
the Econophysics Colloquim 2010, incorporating reviewer comment
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