Markov Population Models are a widespread formalism, with applications in Systems Biology, Performance Evaluation, Ecology, and many other fields. The associated Markov stochastic process in continuous time is often analyzed by simulation, which can be costly for large or stiff systems, particularly when simulations have to be performed in a multi-scale model (e.g. simulating individual cells in a tissue). A strategy to reduce computational load is to abstract the population model, replacing it with a simpler stochastic model, faster to simulate. Here we pursue this idea, building on previous work [3] and constructing an approximate kernel for a Markov process in continuous space and discrete time, capturing the evolution at fixed dt time steps. This kernel is learned automatically from simulations of the original model. Differently from [3], which relies on deep neural networks, we explore here a Bayesian density regression approach based on Dirichlet processes, which provides a principled way to estimate uncertainty.

Bayesian Abstraction of Markov Population Models

Luca Bortolussi
;
Francesca Cairoli
2019

Abstract

Markov Population Models are a widespread formalism, with applications in Systems Biology, Performance Evaluation, Ecology, and many other fields. The associated Markov stochastic process in continuous time is often analyzed by simulation, which can be costly for large or stiff systems, particularly when simulations have to be performed in a multi-scale model (e.g. simulating individual cells in a tissue). A strategy to reduce computational load is to abstract the population model, replacing it with a simpler stochastic model, faster to simulate. Here we pursue this idea, building on previous work [3] and constructing an approximate kernel for a Markov process in continuous space and discrete time, capturing the evolution at fixed dt time steps. This kernel is learned automatically from simulations of the original model. Differently from [3], which relies on deep neural networks, we explore here a Bayesian density regression approach based on Dirichlet processes, which provides a principled way to estimate uncertainty.
978-303030280-1
https://link.springer.com/chapter/10.1007/978-3-030-30281-8_15
File in questo prodotto:
File Dimensione Formato  
paper_26.pdf

embargo fino al 31/07/2020

Descrizione: The final publication is available at Springer via https://link.springer.com/chapter/10.1007/978-3-030-30281-8_15
Tipologia: Bozza finale post-referaggio (post-print)
Licenza: Copyright Editore
Dimensione 799.05 kB
Formato Adobe PDF
799.05 kB Adobe PDF Visualizza/Apri
cover;index;Bortolussi Cairoli.pdf

non disponibili

Tipologia: Documento in Versione Editoriale
Licenza: Copyright Editore
Dimensione 771.03 kB
Formato Adobe PDF
771.03 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11368/2953912
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 2
social impact