Strongly reinforced Pólya urns with graph-based competition

R.W. Hofstad, van der, M.P. Holmes, A. Kuznetsov, W.M. Ruszel

Onderzoeksoutput: Boek/rapportRapportAcademic

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Uittreksel

We introduce a class of reinforcement models where, at each time step t, one ¿rst chooses a random subset A_t of colours (independent of the past) from n colours of balls, and then chooses a colour i from this subset with probability proportional to the number of balls of colour i in the urn raised to the power a > 1. We consider stability of equilibria for such models and establish the existence of phase transitions in a number of examples, including when the colours are the edges of a graph, a context which is a toy model for the formation and reinforcement of neural connections. Keywords: reinforcement model, Pólya urn, stochastic approximation algorithm, stable equilibria
Originele taal-2Engels
Plaats van productieEindhoven
UitgeverijEurandom
Aantal pagina's32
StatusGepubliceerd - 2014

Publicatie series

NaamReport Eurandom
Volume2014015
ISSN van geprinte versie1389-2355

Vingerafdruk

Reinforcement
Graph in graph theory
Ball
Choose
Urn model
Subset
Stability of Equilibria
Stochastic Approximation
Stochastic Algorithms
Approximation Algorithms
Phase Transition
Directly proportional
Color
Model

Citeer dit

Hofstad, van der, R. W., Holmes, M. P., Kuznetsov, A., & Ruszel, W. M. (2014). Strongly reinforced Pólya urns with graph-based competition. (Report Eurandom; Vol. 2014015). Eindhoven: Eurandom.
Hofstad, van der, R.W. ; Holmes, M.P. ; Kuznetsov, A. ; Ruszel, W.M. / Strongly reinforced Pólya urns with graph-based competition. Eindhoven : Eurandom, 2014. 32 blz. (Report Eurandom).
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Hofstad, van der, RW, Holmes, MP, Kuznetsov, A & Ruszel, WM 2014, Strongly reinforced Pólya urns with graph-based competition. Report Eurandom, vol. 2014015, Eurandom, Eindhoven.

Strongly reinforced Pólya urns with graph-based competition. / Hofstad, van der, R.W.; Holmes, M.P.; Kuznetsov, A.; Ruszel, W.M.

Eindhoven : Eurandom, 2014. 32 blz. (Report Eurandom; Vol. 2014015).

Onderzoeksoutput: Boek/rapportRapportAcademic

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Hofstad, van der RW, Holmes MP, Kuznetsov A, Ruszel WM. Strongly reinforced Pólya urns with graph-based competition. Eindhoven: Eurandom, 2014. 32 blz. (Report Eurandom).