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Modeling Single-Cell Dynamics Using Unbalanced Parameterized Monge Maps
Luca Eyring · Dominik Klein · Giovanni Palla · Sören Becker · Philipp Weiler · Niki Kilbertus · Fabian Theis

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in Learning Meaningful Representations of Life »
Event URL: https://openreview.net/forum?id=3ZcryDcnoW2 »

Optimal Transport (OT) has proven useful to infer single-cell trajectories of developing biological systems by aligning distributions across time points. Recently, Parameterized Monge Maps (PMM) were introduced to learn the optimal map between two distributions.Here, we apply PMM to model single-cell dynamics and show that PMM fails to account for asymmetric shifts in cell state distributions. To alleviate this limitation, we propose Unbalanced Parameterised Monge Maps (UPMM). We first describe the novel formulation and show on synthetic data how our method extends discrete unbalanced OT to the continuous domain. Then, we demonstrate that UPMM outperforms well-established trajectory inference methods on real-world developmental single-cell data.

Author Information

Luca Eyring (Technical University of Munich)
Dominik Klein (Helmholtz Center Munich)
Giovanni Palla (Technische Universität München)
Sören Becker (Helmholtz Center Munich)
Philipp Weiler (Technische Universität München)
Niki Kilbertus (TUM & Helmholtz AI)
Fabian Theis (Helmholtz Munich)

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