### abstract ###
Markov random fields are used to model high dimensional distributions in a number of applied areas
Much recent interest has been devoted to the reconstruction of the dependency structure from independent samples from the Markov random fields
We analyze a simple algorithm for reconstructing the underlying graph defining a Markov random field on  SYMBOL  nodes and maximum degree  SYMBOL  given observations
We show that under mild non-degeneracy conditions it reconstructs the generating graph with high probability using  SYMBOL  samples where  SYMBOL  depend on the local interactions
For most local interaction  SYMBOL  are of order  SYMBOL
Our results are optimal as a function of  SYMBOL  up to a multiplicative constant depending on  SYMBOL  and the strength of the local interactions
Our results seem to be the first results for general models that guarantee that  the  generating model is reconstructed
Furthermore, we provide explicit  SYMBOL  running time bound
In cases where the measure on the graph has correlation decay, the running time is  SYMBOL  for all fixed  SYMBOL
We also discuss the effect of observing noisy samples and show that as long as the noise level is low, our algorithm is effective
On the other hand, we construct an example where large noise implies non-identifiability even for generic noise and interactions
Finally, we briefly show that in some simple cases, models with hidden nodes can also be recovered
### introduction ###
In this paper we consider the problem of reconstructing the graph structure of a Markov random field from independent and identically distributed samples
Markov random fields (MRF) provide a very general framework for defining high dimensional distributions and the reconstruction of the MRF from observations has attracted much recent interest, in particular in biology, see eg ~ CITATION  and a list of related references~ CITATION
