Controlled and conditioned invariants in linear system theory

Vaněček, Antonín

doi:10.1016/0005-1098(94)90042-6

Cited by 2 publications

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“…The subspace N can be characterized as the largest P -invariant subspace contained in ker C [31], [32]. In the case of HMM the non-observable subspace has another useful property.…”

Section: A Single Time-marginal Problemmentioning

confidence: 99%

Algebraic Reduction of Hidden Markov Models

Grigoletto

Ticozzi

2023

IEEE Trans. Automat. Contr.

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The problem of reducing a Hidden Markov Model (HMM) to one of smaller dimension that exactly reproduces the same marginals is tackled by using a system-theoretic approach. Realization theory tools are extended to HMMs by leveraging suitable algebraic representations of probability spaces. We propose two algorithms that return coarse-grained equivalent HMMs obtained by stochastic projection operators: the first returns models that exactly reproduce the single-time distribution of a given output process, while in the second the full (multitime) distribution is preserved. The reduction method exploits not only the structure of the observed output, but also its initial condition, whenever the latter is known or belongs to a given subclass. Optimal algorithms are derived for a class of HMM, namely observable ones.

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“…The subspace N can be characterized as the largest P -invariant subspace contained in ker C [31], [32]. In the case of HMM the non-observable subspace has another useful property.…”

Section: A Single Time-marginal Problemmentioning

confidence: 99%

Algebraic Reduction of Hidden Markov Models

Grigoletto

Ticozzi

2023

IEEE Trans. Automat. Contr.

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Minimal resources for exact simulation of quantum walks

Grigoletto

Ticozzi

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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A general approach to obtain reduced models for a wide class of discrete-time quantum systems is proposed. The obtained models not only reproduce exactly the output of a given quantum model, but are also guaranteed to satisfy physical constraints, namely complete positivity and preservation of total probability. A fundamental framework for exact model reduction of quantum systems is constructed leveraging on algebraic methods, as well as novel results on quantum conditional expectations in finite-dimensions. The proposed reduction algorithm is illustrated and tested on prototypical examples, including the quantum walk realizing Grover's algorithm.

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Controlled and conditioned invariants in linear system theory

Cited by 2 publications

References 0 publications

Algebraic Reduction of Hidden Markov Models

Algebraic Reduction of Hidden Markov Models

Minimal resources for exact simulation of quantum walks

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