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Found 10 papers, 3 papers with code
Wasserstein Mirror Gradient Flow as the limit of the Sinkhorn Algorithm
This limit, which we call the Sinkhorn flow, is an example of a Wasserstein mirror gradient flow, a concept we introduce here inspired by the well-known Euclidean mirror gradient flows.
Manifold Learning with Sparse Regularised Optimal Transport
Manifold learning is a central task in modern statistics and data science.
Trajectory inference for a branching SDE model of cell differentiation
Building on Global Waddington-OT (gWOT), which performs trajectory inference with rigorous theoretical guarantees when birth and death can be neglected, we show how to use lineage trees available with recently developed CRISPR-based measurement technologies to disentangle proliferation and differentiation.
Beyond kNN: Adaptive, Sparse Neighborhood Graphs via Optimal Transport
One of the most common strategies to construct such a graph is based on selecting a fixed number k of nearest neighbours (kNN) for each point.
Trajectory Inference via Mean-field Langevin in Path Space
Trajectory inference aims at recovering the dynamics of a population from snapshots of its temporal marginals.
Towards a mathematical theory of trajectory inference
We devise a theoretical framework and a numerical method to infer trajectories of a stochastic process from samples of its temporal marginals.
Reconstructing probabilistic trees of cellular differentiation from single-cell RNA-seq data
Specifically, we extend the framework of the classical Dirichlet diffusion tree to simultaneously infer branch topology and latent cell states along continuous trajectories over the full tree.
Statistical Optimal Transport via Factored Couplings
We propose a new method to estimate Wasserstein distances and optimal transport plans between two probability distributions from samples in high dimension.
The geometry of kernelized spectral clustering
As a corollary we control the fraction of samples mislabeled by spectral clustering under finite mixtures with nonparametric components.
Sharp Inequalities for $f$-divergences
$f$-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance etc.
