Recursive Bayesian Decoding in State Observation Models: Theory and Application in Quantum-Based Inference
Accurately estimating a sequence of latent variables in state observation models remains a challenging problem, particularly when maintaining coherence among consecutive estimates. While forward filtering and smoothing methods provide coherent marginal distributions, they often fail to maintain cohe...
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2025-06-01
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| author | Branislav Rudić Markus Pichler-Scheder Dmitry Efrosinin |
| author_facet | Branislav Rudić Markus Pichler-Scheder Dmitry Efrosinin |
| author_sort | Branislav Rudić |
| collection | DOAJ |
| description | Accurately estimating a sequence of latent variables in state observation models remains a challenging problem, particularly when maintaining coherence among consecutive estimates. While forward filtering and smoothing methods provide coherent marginal distributions, they often fail to maintain coherence in marginal MAP estimates. Existing methods efficiently handle discrete-state or Gaussian models. However, general models remain challenging. Recently, a recursive Bayesian decoder has been discussed, which effectively infers coherent state estimates in a wide range of models, including Gaussian and Gaussian mixture models. In this work, we analyze the theoretical properties and implications of this method, drawing connections to classical inference frameworks. The versatile applicability of mixture models and the prevailing advantage of the recursive Bayesian decoding method are demonstrated using the double-slit experiment. Rather than inferring the state of a quantum particle itself, we utilize interference patterns from the slit experiments to decode the movement of a non-stationary particle detector. Our findings indicate that, by appropriate modeling and inference, the fundamental uncertainty associated with quantum objects can be leveraged to decrease the induced uncertainty of states associated with classical objects. We thoroughly discuss the interpretability of the simulation results from multiple perspectives. |
| format | Article |
| id | doaj-art-23cedb7b3cf4446bb4dee9b80c541d30 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-23cedb7b3cf4446bb4dee9b80c541d302025-08-20T03:27:24ZengMDPI AGMathematics2227-73902025-06-011312201210.3390/math13122012Recursive Bayesian Decoding in State Observation Models: Theory and Application in Quantum-Based InferenceBranislav Rudić0Markus Pichler-Scheder1Dmitry Efrosinin2Linz Center of Mechatronics GmbH, 4040 Linz, AustriaLinz Center of Mechatronics GmbH, 4040 Linz, AustriaInstitute of Stochastics, Johannes Kepler University, 4040 Linz, AustriaAccurately estimating a sequence of latent variables in state observation models remains a challenging problem, particularly when maintaining coherence among consecutive estimates. While forward filtering and smoothing methods provide coherent marginal distributions, they often fail to maintain coherence in marginal MAP estimates. Existing methods efficiently handle discrete-state or Gaussian models. However, general models remain challenging. Recently, a recursive Bayesian decoder has been discussed, which effectively infers coherent state estimates in a wide range of models, including Gaussian and Gaussian mixture models. In this work, we analyze the theoretical properties and implications of this method, drawing connections to classical inference frameworks. The versatile applicability of mixture models and the prevailing advantage of the recursive Bayesian decoding method are demonstrated using the double-slit experiment. Rather than inferring the state of a quantum particle itself, we utilize interference patterns from the slit experiments to decode the movement of a non-stationary particle detector. Our findings indicate that, by appropriate modeling and inference, the fundamental uncertainty associated with quantum objects can be leveraged to decrease the induced uncertainty of states associated with classical objects. We thoroughly discuss the interpretability of the simulation results from multiple perspectives.https://www.mdpi.com/2227-7390/13/12/2012Bayesian inferencerecursive estimationdecodingstate observation modeldynamic systemsGaussian mixtures |
| spellingShingle | Branislav Rudić Markus Pichler-Scheder Dmitry Efrosinin Recursive Bayesian Decoding in State Observation Models: Theory and Application in Quantum-Based Inference Mathematics Bayesian inference recursive estimation decoding state observation model dynamic systems Gaussian mixtures |
| title | Recursive Bayesian Decoding in State Observation Models: Theory and Application in Quantum-Based Inference |
| title_full | Recursive Bayesian Decoding in State Observation Models: Theory and Application in Quantum-Based Inference |
| title_fullStr | Recursive Bayesian Decoding in State Observation Models: Theory and Application in Quantum-Based Inference |
| title_full_unstemmed | Recursive Bayesian Decoding in State Observation Models: Theory and Application in Quantum-Based Inference |
| title_short | Recursive Bayesian Decoding in State Observation Models: Theory and Application in Quantum-Based Inference |
| title_sort | recursive bayesian decoding in state observation models theory and application in quantum based inference |
| topic | Bayesian inference recursive estimation decoding state observation model dynamic systems Gaussian mixtures |
| url | https://www.mdpi.com/2227-7390/13/12/2012 |
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