  We present a polyphonic MIDI score-following algorithm capable of following
performances with arbitrary repeats and skips, based on a probabilistic model
of musical performances. It is attractive in practical applications of score
following to handle repeats and skips which may be made arbitrarily during
performances, but the algorithms previously described in the literature cannot
be applied to scores of practical length due to problems with large
computational complexity. We propose a new type of hidden Markov model (HMM) as
a performance model which can describe arbitrary repeats and skips including
performer tendencies on distributed score positions before and after them, and
derive an efficient score-following algorithm that reduces computational
complexity without pruning. A theoretical discussion on how much such
information on performer tendencies improves the score-following results is
given. The proposed score-following algorithm also admits performance mistakes
and is demonstrated to be effective in practical situations by carrying out
evaluations with human performances. The proposed HMM is potentially valuable
for other topics in information processing and we also provide a detailed
description of inference algorithms.
