Current state-of-the-art approaches to biological event extraction train models by reconstructing relevant graphs from training sentences, where labeled nodes correspond to tokens that indicate the presence of events and the relations between nodes correspond to the relations between these events and their participants. Since multi-word expressions may also indicate events, these approaches use heuristic rules to define target graphs to reconstruct by mapping various clue words into single tokens. Since training instances define actual problems to solve, the method of deriving graphs must affect the system performance, but there has not been any related study on this aspect, to the best of our knowledge. In this study, we propose an incorporation of an EM algorithm into supervised learning to look for training graphs that are more favorable for model construction. We evaluate our algorithm on the development dataset in the 2009 BioNLP shared task and show that this algorithm makes a statistically meaningful improvement on the performance of trained models over a supervised learning algorithm on a fixed set of training graphs. The models and graphs are available at http://biopathway.org/EventExtraction/.