I suppose "multivariate" refers to a function w/ multiple inputs. What function? One that, given an output sequence of a HMM, returns the probability distribution of state switch sequences of the HMM for the output? Something else?
Suppose we've 3 outputs:
Ax. Would a multivariate (bivariate) HMM rather refer to
f(ax, ab) or
d(character, capitalization)? The first would define a probability (distribution) of state switch sequence(s), the second a set of output symbols. Of course, both would be equivalent to monovariant HMMs (e.g. the first to two evaluations of a unary function computing the same state switch probability (distribution) for
ab, the second to a function over an extended character set)