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We present an approach to estimate the nature of the Waddington (or epigenetic) landscape that underlies a population of individual cells. Through exploiting high resolution single cell transcription experiments we show that cells can be located on a landscape that reflects their differentiated nature. Our approach makes use of probabilistic non-linear dimensionality reduction that respects the topology of our estimated epigenetic landscape. In simulation studies and analyses of real data wedoi:10.1101/057778 fatcat:wnedwz6wrbajnjqm6uwb5f4f7u