TY - BOOK

T1 - Strongly reinforced Pólya urns with graph-based competition

AU - Hofstad, van der, R.W.

AU - Holmes, M.P.

AU - Kuznetsov, A.

AU - Ruszel, W.M.

PY - 2014

Y1 - 2014

N2 - 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

AB - 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

M3 - Report

T3 - Report Eurandom

BT - Strongly reinforced Pólya urns with graph-based competition

PB - Eurandom

CY - Eindhoven

ER -