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Manifold Interpolating Optimal-Transport Flows for Trajectory Inference.

Guillaume Huguet1, D S Magruder2, Alexander Tong1

  • 1Université de Montréal; Mila - Quebec AI Institute.

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|July 3, 2023
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Summary
This summary is machine-generated.

Manifold Interpolating Optimal-Transport Flow (MIOFlow) models continuous population dynamics from static data. This method excels at interpolating between population snapshots, outperforming other generative models.

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Area of Science:

  • Computational Biology
  • Dynamical Systems Modeling
  • Machine Learning

Background:

  • Understanding complex biological systems requires modeling population dynamics over time.
  • Static snapshots of populations at discrete time points limit insights into continuous developmental trajectories.
  • Existing generative models often struggle with accurate interpolation between sparse data samples.

Purpose of the Study:

  • To develop a novel method, Manifold Interpolating Optimal-Transport Flow (MIOFlow), for learning stochastic, continuous population dynamics.
  • To enable accurate interpolation between static population samples using dynamic models and optimal transport.
  • To ensure learned trajectories respect the underlying data manifold geometry.

Main Methods:

  • MIOFlow integrates dynamic models, manifold learning, and optimal transport.
  • Neural Ordinary Differential Equations (Neural ODEs) are trained to interpolate between population snapshots.
  • A geodesic autoencoder (GAE) is employed, regularizing latent space distances with a novel multiscale geodesic distance.
  • Optimal transport with manifold ground distance penalizes deviations from desired trajectories.

Main Results:

  • MIOFlow demonstrates superior performance in interpolating between population snapshots compared to normalizing flows and Schrödinger bridges.
  • The method successfully models complex dynamics, including bifurcations and merges, in simulated data.
  • Application to single-cell RNA sequencing (scRNA-seq) data from embryoid body differentiation and leukemia treatment shows robust performance.

Conclusions:

  • MIOFlow provides a powerful framework for inferring continuous population dynamics from sparse, static data.
  • The integration of optimal transport and manifold learning enables geometrically informed trajectory inference.
  • This approach offers significant advancements for analyzing biological population dynamics, particularly in developmental and disease contexts.