Identifying combinatorially symmetric Hidden Markov Models

@article{Burgarth2017IdentifyingCS,
  title={Identifying combinatorially symmetric Hidden Markov Models},
  author={Daniel Burgarth},
  journal={arXiv: Combinatorics},
  year={2017}
}
  • D. Burgarth
  • Published 9 September 2017
  • Mathematics
  • arXiv: Combinatorics
We provide a sufficient criterion for the unique parameter identification of combinatorially symmetric Hidden Markov Models based on the structure of their transition matrix. If the observed states of the chain form a zero forcing set of the graph of the Markov model then it is uniquely identifiable and an explicit reconstruction method is given. 

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References

SHOWING 1-8 OF 8 REFERENCES

Combinatorially symmetric matrices

Indirect Hamiltonian identification through a small gateway

Identifying the many-body Hamiltonian of a large quantum system is essential in understanding many physical phenomena, yet extremely difficult in general. We show that coupling strengths in networks

Zero forcing parameters and minimum rank problems

Inference in Hidden Markov Models

Introduction to Linear Models and Statistical Inference is not meant to compete with these texts—rather, its audience is primarily those taking a statistics course within a mathematics department.

Full control by locally induced relaxation.

A scheme for controlling a large quantum system by acting on a small subsystem only and transferring arbitrary and unknown quantum states from a memory to the large system as well as the inverse ("download access").

Handbook of Linear Algebra

Linear Algebra Linear Algebra Vectors, Matrices, and Systems of Linear Equations Jane Day Linear Independence, Span, and Bases Mark Mills Linear Transformations Francesco Barioli Determinants and

Inverse Problems in Vibration

This article reviews recent literature on inverse problems relating to the reconstruction or estimation of the physical properties of mechanical systems from a knowledge of (some of) their spectral

Hitting Time and Inverse Problems for Markov Chains

Let W n be a simple Markov chain on the integers. Suppose that X n is a simple Markov chain on the integers whose transition probabilities coincide with those of W n off a finite set. We prove that