# 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.
4 Citations

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## References

SHOWING 1-8 OF 8 REFERENCES

### Indirect Hamiltonian identification through a small gateway

• Physics
• 2009
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

### 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.

• Physics
Physical review letters
• 2007
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

• Mathematics
Journal of Applied Probability
• 2008
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