25 research outputs found
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Inferring spatial and signaling relationships between cells from single cell transcriptomic data.
Single-cell RNA sequencing (scRNA-seq) provides details for individual cells; however, crucial spatial information is often lost. We present SpaOTsc, a method relying on structured optimal transport to recover spatial properties of scRNA-seq data by utilizing spatial measurements of a relatively small number of genes. A spatial metric for individual cells in scRNA-seq data is first established based on a map connecting it with the spatial measurements. The cell-cell communications are then obtained by "optimally transporting" signal senders to target signal receivers in space. Using partial information decomposition, we next compute the intercellular gene-gene information flow to estimate the spatial regulations between genes across cells. Four datasets are employed for cross-validation of spatial gene expression prediction and comparison to known cell-cell communications. SpaOTsc has broader applications, both in integrating non-spatial single-cell measurements with spatial data, and directly in spatial single-cell transcriptomics data to reconstruct spatial cellular dynamics in tissues
Minimax estimation of smooth optimal transport maps
Brenier's theorem is a cornerstone of optimal transport that guarantees the
existence of an optimal transport map between two probability distributions
and over under certain regularity conditions. The main
goal of this work is to establish the minimax estimation rates for such a
transport map from data sampled from and under additional smoothness
assumptions on . To achieve this goal, we develop an estimator based on the
minimization of an empirical version of the semi-dual optimal transport
problem, restricted to truncated wavelet expansions. This estimator is shown to
achieve near minimax optimality using new stability arguments for the semi-dual
and a complementary minimax lower bound. Furthermore, we provide numerical
experiments on synthetic data supporting our theoretical findings and
highlighting the practical benefits of smoothness regularization. These are the
first minimax estimation rates for transport maps in general dimension.Comment: 53 pages, 6 figure
Fully Probabilistic Design for Optimal Transport
The goal of this paper is to introduce a new theoretical framework for
Optimal Transport (OT), using the terminology and techniques of Fully
Probabilistic Design (FPD). Optimal Transport is the canonical method for
comparing probability measures and has been successfully applied in a wide
range of areas (computer vision Rubner et al. [2004], computer graphics Solomon
et al. [2015], natural language processing Kusner et al. [2015], etc.).
However, we argue that the current OT framework suffers from two shortcomings:
first, it is hard to induce generic constraints and probabilistic knowledge in
the OT problem; second, the current formalism does not address the question of
uncertainty in the marginals, lacking therefore the mechanisms to design robust
solutions. By viewing the OT problem as the optimal design of a probability
density function with marginal constraints, we prove that OT is an instance of
the more generic FPD framework. In this new setting, we can furnish the OT
framework with the necessary mechanisms for processing probabilistic
constraints and deriving uncertainty quantifiers, hence establishing a new
extended framework, called FPD-OT. Our main contribution in this paper is to
establish the connection between OT and FPD, providing new theoretical insights
for both. This will lay the foundations for the application of FPD-OT in a
subsequent work, notably in processing more sophisticated knowledge
constraints, as well as in designing robust solutions in the case of uncertain
marginals.Comment: Keywords: Optimal Transport, Fully Probabilistic Design, Convex
optimizatio
Optimal Transport vs Many-to-many assignment for Graph Matching
National audienceGraph matching for shape comparison or network analysis is a challenging issue in machine learning and computer vision. Gener-ally, this problem is formulated as an assignment task, where we seek the optimal matching between the vertices that minimizes the differencebetween the graphs. We compare a standard approach to perform graph matching, to a slightly-adapted version of regularized optimal transport,initially conceived to obtain the Gromov-Wassersein distance between structured objects (e.g. graphs) with probability masses associated to thenodes. We adapt the latter formulation to undirected and unlabeled graphs of different dimensions, by adding dummy vertices to cast the probleminto an assignment framework. The experiments are performed on randomly generated graphs onto which different spatial transformations areapplied. The results are compared with respect to the matching cost and execution time, showcasing the different limitations and/or advantagesof using these techniques for the comparison of graph networks
InfoOT: Information Maximizing Optimal Transport
Optimal transport aligns samples across distributions by minimizing the
transportation cost between them, e.g., the geometric distances. Yet, it
ignores coherence structure in the data such as clusters, does not handle
outliers well, and cannot integrate new data points. To address these
drawbacks, we propose InfoOT, an information-theoretic extension of optimal
transport that maximizes the mutual information between domains while
minimizing geometric distances. The resulting objective can still be formulated
as a (generalized) optimal transport problem, and can be efficiently solved by
projected gradient descent. This formulation yields a new projection method
that is robust to outliers and generalizes to unseen samples. Empirically,
InfoOT improves the quality of alignments across benchmarks in domain
adaptation, cross-domain retrieval, and single-cell alignment