Adaptive Aggregation of Markov Chains: Quantitative Analysis of Chemical Reaction Networks
Quantitative analysis of Markov models typically proceeds through numerical methods or simulation-based evaluation. Since the state space of the models can often be large, exact or approximate state aggregation methods (such as lumping or bisimulation reduction) have been proposed to improve the sca...
| Автори: | , , , |
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| Формат: | Conference item |
| Мова: | English |
| Опубліковано: |
2015
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| _version_ | 1826265008329195520 |
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| author | Abate, A Brim, L Ceska, M Kwiatkowska, M |
| author_facet | Abate, A Brim, L Ceska, M Kwiatkowska, M |
| author_sort | Abate, A |
| collection | OXFORD |
| description | Quantitative analysis of Markov models typically proceeds through numerical methods or simulation-based evaluation. Since the state space of the models can often be large, exact or approximate state aggregation methods (such as lumping or bisimulation reduction) have been proposed to improve the scalability of the numerical schemes. However, none of the existing numerical techniques provides general, explicit bounds on the approximation error, a problem particularly relevant when the level of accuracy affects the soundness of verification results. We propose a novel numerical approach that combines the strengths of aggregation techniques (state-space reduction) with those of simulation-based approaches (automatic updates that adapt to the process dynamics). The key advantage of our scheme is that it provides rigorous precision guarantees under different measures. The new approach, which can be used in conjunction with time uniformisation techniques, is evaluated on two models of chemical reaction networks, a signalling pathway and a prokaryotic gene expression network: it demonstrates marked improvement in accuracy without performance degradation, particularly when compared to known state-space truncation techniques. |
| first_indexed | 2024-03-06T20:16:55Z |
| format | Conference item |
| id | oxford-uuid:2c6e85b7-4328-4fb8-a2db-04dd2bafc8bd |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:16:55Z |
| publishDate | 2015 |
| record_format | dspace |
| spelling | oxford-uuid:2c6e85b7-4328-4fb8-a2db-04dd2bafc8bd2022-03-26T12:37:10ZAdaptive Aggregation of Markov Chains: Quantitative Analysis of Chemical Reaction NetworksConference itemhttp://purl.org/coar/resource_type/c_5794uuid:2c6e85b7-4328-4fb8-a2db-04dd2bafc8bdEnglishOxford University Research Archive - Valet2015Abate, ABrim, LCeska, MKwiatkowska, MQuantitative analysis of Markov models typically proceeds through numerical methods or simulation-based evaluation. Since the state space of the models can often be large, exact or approximate state aggregation methods (such as lumping or bisimulation reduction) have been proposed to improve the scalability of the numerical schemes. However, none of the existing numerical techniques provides general, explicit bounds on the approximation error, a problem particularly relevant when the level of accuracy affects the soundness of verification results. We propose a novel numerical approach that combines the strengths of aggregation techniques (state-space reduction) with those of simulation-based approaches (automatic updates that adapt to the process dynamics). The key advantage of our scheme is that it provides rigorous precision guarantees under different measures. The new approach, which can be used in conjunction with time uniformisation techniques, is evaluated on two models of chemical reaction networks, a signalling pathway and a prokaryotic gene expression network: it demonstrates marked improvement in accuracy without performance degradation, particularly when compared to known state-space truncation techniques. |
| spellingShingle | Abate, A Brim, L Ceska, M Kwiatkowska, M Adaptive Aggregation of Markov Chains: Quantitative Analysis of Chemical Reaction Networks |
| title | Adaptive Aggregation of Markov Chains: Quantitative Analysis of Chemical Reaction Networks |
| title_full | Adaptive Aggregation of Markov Chains: Quantitative Analysis of Chemical Reaction Networks |
| title_fullStr | Adaptive Aggregation of Markov Chains: Quantitative Analysis of Chemical Reaction Networks |
| title_full_unstemmed | Adaptive Aggregation of Markov Chains: Quantitative Analysis of Chemical Reaction Networks |
| title_short | Adaptive Aggregation of Markov Chains: Quantitative Analysis of Chemical Reaction Networks |
| title_sort | adaptive aggregation of markov chains quantitative analysis of chemical reaction networks |
| work_keys_str_mv | AT abatea adaptiveaggregationofmarkovchainsquantitativeanalysisofchemicalreactionnetworks AT briml adaptiveaggregationofmarkovchainsquantitativeanalysisofchemicalreactionnetworks AT ceskam adaptiveaggregationofmarkovchainsquantitativeanalysisofchemicalreactionnetworks AT kwiatkowskam adaptiveaggregationofmarkovchainsquantitativeanalysisofchemicalreactionnetworks |