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Inference is a main task in structured prediction and it is naturally modeledwith a graph. In the context of Markov random fields, noisy observationscorresponding to nodes and edges are usually involved, and the goal of exactinference is to recover the unknown true label for each node precisely. Thefocus of this paper is on the fundamental limits of exact recovery irrespectiveof computational efficiency, assuming the generative process proposed byGloberson et al. (2015). We derive the necessary condition for any algorithmand the sufficient condition for maximum likelihood estimation to achieve exactrecovery with high probability, and reveal that the sufficient and necessaryconditions are tight up to a logarithmic factor for a wide range of graphs.Finally, we show that there exists a gap between the fundamental limits and theperformance of the computationally tractable method of Bello and Honorio(2019), which implies the need for further development of algorithms for exactinference.

On the Fundamental Limits of Exact Inference in Structured Prediction