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We propose polynomial-time algorithms to minimise labelled Markov chains whose transition probabilities are not known exactly, have been perturbed, or can only be obtained by sampling. Our algorithms are based on a new notion of an approximate bisimulation quotient, obtained by lumping together states that are exactly bisimilar in a slightly perturbed system. We present experiments that show that our algorithms are able to recover the structure of the bisimulation quotient of the unperturbed system.doi:10.4230/lipics.fsttcs.2021.28 arXiv:2110.00326v1 fatcat:nsf2hgv2kbatrec2f2kp6mwzgi