  Coarse-grained models are widely used to explain the effective behavior of
partially observable physical systems with hidden degrees of freedom. Reduction
procedures in state space typically disrupt Markovianity and a fluctuation
relation cannot be formulated. A recently developed framework of
transition-based coarse-graining gave rise to a fluctuation relation for a
single current, while all others are hidden. Here, we extend the treatment to
an arbitrary number of observable currents. Crucial for the derivation are the
concepts of mixed currents and their conjugated effective affinities, that can
be inferred from the time series of observable transitions. We also discuss the
connection to generating functions, transient behavior, and how our result
recovers the fluctuation relation for a complete set of currents.
