The expected minibatch OT plan converges to the true OT plan with quantifiable bias and convergence rates, yielding a regular velocity field for unique flows from source to discrete target in flow matching.
arXiv preprint arXiv:2101.01792 , year=
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OMT reformulates optimal transport for mixture models as a strictly biconvex optimization with a unique global minimizer and stability guarantees, decoupling complexity from sample size.
CellBRIDGE augments feature-based optimal transport with a directed ligand-receptor interaction cost to improve cellular trajectory inference from scRNA-seq population snapshots.
Under smooth unit costs and models, empirical subdifferentials of parameterized transport objectives converge graphically almost surely to the population subdifferential, so subgradient methods approach population critical points.
Observational and counterfactual distributions are linked by identical support and invariant features, enabling a flow-matching estimator with semiparametric efficiency correction to generate debiased counterfactuals from observations.
Formalizes nonlinear M2M regression and introduces transformer architectures as static maps and dynamic velocity fields between probability measures, tested on synthetic, particle, and organoid datasets.
citing papers explorer
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Expected Batch Optimal Transport Plans and Consequences for Flow Matching
The expected minibatch OT plan converges to the true OT plan with quantifiable bias and convergence rates, yielding a regular velocity field for unique flows from source to discrete target in flow matching.
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A Biconvex Formulation for Stable Transport of Mixture Models with a Unique Solution
OMT reformulates optimal transport for mixture models as a strictly biconvex optimization with a unique global minimizer and stability guarantees, decoupling complexity from sample size.
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CellBRIDGE: Learning Cellular Trajectories via Interaction-Aware Alignment
CellBRIDGE augments feature-based optimal transport with a directed ligand-receptor interaction cost to improve cellular trajectory inference from scRNA-seq population snapshots.
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Convergence of empirical subgradients for optimal transport-based objectives
Under smooth unit costs and models, empirical subdifferentials of parameterized transport objectives converge graphically almost surely to the population subdifferential, so subgradient methods approach population critical points.
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Debiased Counterfactual Generation via Flow Matching from Observations
Observational and counterfactual distributions are linked by identical support and invariant features, enabling a flow-matching estimator with semiparametric efficiency correction to generate debiased counterfactuals from observations.
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Measure-to-measure Regression with Transformers
Formalizes nonlinear M2M regression and introduces transformer architectures as static maps and dynamic velocity fields between probability measures, tested on synthetic, particle, and organoid datasets.