  Time-invariant linear dynamical system arises in many real-world
applications,and its usefulness is widely acknowledged. A practical limitation
with this model is that its latent dimension that has a large impact on the
model capability needs to be manually specified. It can be demonstrated that a
lower-order model class could be totally nested into a higher-order class, and
the corresponding likelihood is nondecreasing. Hence, criterion built on the
likelihood is not appropriate for model selection. This paper addresses the
issue and proposes a criterion for linear dynamical system based on the
principle of minimum description length. The latent structure, which is omitted
in previous work, is explicitly considered in this newly proposed criterion.
Our work extends the principle of minimum description length and demonstrates
its effectiveness in the tasks of model training. The experiments on both
univariate and multivariate sequences confirm the good performance of our newly
proposed method.
