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Recent work in supervised learning of term-based retrieval models has shown significantly improved accuracy can often be achieved via better model estimation. In this paper, we show retrieval accuracy with Metzler and Croft's Markov random field (MRF) approach can be similarly improved via supervised learning. While the original MRF method estimates a parameter for each of its three feature classes from data, parameters within each class are set via a uniform weighting scheme adopted from the standard unigram. We conjecture greater MRF retrieval accuracy should be possible by better estimating within-class parameters, particularly for verbose queries employing natural language terms. Retrieval experiments with these queries on three TREC document collections show our improved MRF consistently out-performs both the original MRF and supervised unigram baselines. Additional experiments using blind-feedback and evaluation with optimal weighting demonstrate both the immediate value and further potential of our method.