• Publications
  • Influence
Random graphs with a given degree sequence
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it isExpand
  • 259
  • 39
  • PDF
Spectral redemption in clustering sparse networks
TLDR
We propose a way of encoding sparse data using a “nonbacktracking” matrix and show that the corresponding spectral algorithm performs optimally for some popular generative models, including the stochastic block model. Expand
  • 479
  • 38
  • PDF
Reconstruction and estimation in the planted partition model
The planted partition model (also known as the stochastic blockmodel) is a classical cluster-exhibiting random graph model that has been extensively studied in statistics, physics, and computerExpand
  • 257
  • 28
Reconstruction of Markov Random Fields from Samples: Some Observations and Algorithms
TLDR
We analyze a simple algorithm for reconstructing the underlying graph defining a Markov random field on nnodes and maximum degree dgiven observations. Expand
  • 133
  • 24
  • PDF
Computational Transition at the Uniqueness Threshold
  • Allan Sly
  • Mathematics, Computer Science
  • IEEE 51st Annual Symposium on Foundations of…
  • 30 May 2010
TLDR
We prove that at the uniqueness threshold of the hardcore model on the regular tree, approximating the partition function becomes computationally hard on graphs of maximum degree $d$ for fugacity $\lambda_c(d) 0$. Expand
  • 167
  • 19
  • PDF
Stochastic Block Models and Reconstruction
The planted partition model (also known as the stochastic blockmodel) is a classical cluster-exhibiting random graph model that has been extensively studied in statistics, physics, and computerExpand
  • 199
  • 18
  • PDF
Belief propagation, robust reconstruction and optimal recovery of block models
TLDR
We consider the problem of reconstructing sparse symmetric block models with two blocks and connection probabilities a=n and b=n for inter- and intra-block edge probabilities respectively. Expand
  • 135
  • 13
  • PDF
A Proof of the Block Model Threshold Conjecture
TLDR
A striking conjecture of Decelle, Krzkala, Moore and Zdeborová [9], 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. Expand
  • 232
  • 11
  • PDF
The Computational Hardness of Counting in Two-Spin Models on d-Regular Graphs
  • Allan Sly, N. Sun
  • Mathematics, Computer Science
  • IEEE 53rd Annual Symposium on Foundations of…
  • 12 March 2012
TLDR
We show that for both the hard-core (independent set) model and the anti-ferromagnetic Ising model with arbitrary external field, it is NP-hard to approximate the partition function or approximately sample from the model on regular graphs when the model has non-uniqueness on the corresponding regular tree. Expand
  • 112
  • 11
  • PDF
...
1
2
3
4
5
...