Given a sequence of observations presumed to be produced by an autonomous linear dynamical system, is it possible (and if so how) to determine the likelihood of the sequence without inferring the state space parameters?
My thought was to consider the likelihood of a sequence produced by a transfer function - but I'm not sure if this is possible. I know I can infer the state space parameters and then use a Kalman filter, but ideally I avoid this step.
My particular use case is to learn a encoding/decoding function of observations which in their encoded form could have been produced by an autonomous linear dynamical system. I don't particularly care about the state space parameters while learning the encoding function, and I'm hoping that I can take advantage of this and reduce the computational load during training.