  Classical probability distributions on sets of sequences can be modeled using
quantum states. Here, we do so with a quantum state that is pure and entangled.
Because it is entangled, the reduced densities that describe subsystems also
carry information about the complementary subsystem. This is in contrast to the
classical marginal distributions on a subsystem in which information about the
complementary system has been integrated out and lost. A training algorithm
based on the density matrix renormalization group (DMRG) procedure uses the
extra information contained in the reduced densities and organizes it into a
tensor network model. An understanding of the extra information contained in
the reduced densities allow us to examine the mechanics of this DMRG algorithm
and study the generalization error of the resulting model. As an illustration,
we work with the even-parity dataset and produce an estimate for the
generalization error as a function of the fraction of the dataset used in
training.
