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Adaptive Low-Nonnegative-Rank Approximation for State Aggregation of Markov Chains. (arXiv:1810.06032v1 [math.OC])
来源于:arXiv
This paper develops a low-nonnegative-rank approximation method to identify
the state aggregation structure of a finite-state Markov chain under an
assumption that the state space can be mapped into a handful of meta-states.
The number of meta-states is characterized by the nonnegative rank of the
Markov transition matrix. Motivated by the success of the nuclear norm
relaxation in low rank minimization problems, we propose an atomic regularizer
as a convex surrogate for the nonnegative rank and formulate a convex
optimization problem. Because the atomic regularizer itself is not
computationally tractable, we instead solve a sequence of problems involving a
nonnegative factorization of the Markov transition matrices by using the
proximal alternating linearized minimization method. Two methods for adjusting
the rank of factorization are developed so that local minima are escaped. One
is to append an additional column to the factorized matrices, which can be
interpreted as an approximatio 查看全文>>