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Gaussian mixture model (GMM) classifiers have been shown to give good instrument recognition performance for monophonic music played by a single instrument. However, many applications (such as automatic music transcription) require instrument identification from polyphonic, multi-instrumental recordings. We address this problem by incorporating ideas from missing feature theory into a GMM classifier. Specifically, frequency regions that are dominated by energy from an interfering tone are marked as unreliable and excluded from the classification process. This approach has been evaluated on random two-tone chords and an excerpt from a commercially available compact disc, with promising results.