210,054 research outputs found
Recommended from our members
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
Regularized Optimal Transport Layers for Generalized Global Pooling Operations
Global pooling is one of the most significant operations in many machine
learning models and tasks, which works for information fusion and structured
data (like sets and graphs) representation. However, without solid mathematical
fundamentals, its practical implementations often depend on empirical
mechanisms and thus lead to sub-optimal, even unsatisfactory performance. In
this work, we develop a novel and generalized global pooling framework through
the lens of optimal transport. The proposed framework is interpretable from the
perspective of expectation-maximization. Essentially, it aims at learning an
optimal transport across sample indices and feature dimensions, making the
corresponding pooling operation maximize the conditional expectation of input
data. We demonstrate that most existing pooling methods are equivalent to
solving a regularized optimal transport (ROT) problem with different
specializations, and more sophisticated pooling operations can be implemented
by hierarchically solving multiple ROT problems. Making the parameters of the
ROT problem learnable, we develop a family of regularized optimal transport
pooling (ROTP) layers. We implement the ROTP layers as a new kind of deep
implicit layer. Their model architectures correspond to different optimization
algorithms. We test our ROTP layers in several representative set-level machine
learning scenarios, including multi-instance learning (MIL), graph
classification, graph set representation, and image classification.
Experimental results show that applying our ROTP layers can reduce the
difficulty of the design and selection of global pooling -- our ROTP layers may
either imitate some existing global pooling methods or lead to some new pooling
layers fitting data better. The code is available at
\url{https://github.com/SDS-Lab/ROT-Pooling}
Structured ambiguity sets for distributionally robust optimization
Distributionally robust optimization (DRO) incorporates robustness against
uncertainty in the specification of probabilistic models. This paper focuses on
mitigating the curse of dimensionality in data-driven DRO problems with optimal
transport ambiguity sets. By exploiting independence across lower-dimensional
components of the uncertainty, we construct structured ambiguity sets that
exhibit a faster shrinkage as the number of collected samples increases. This
narrows down the plausible models of the data-generating distribution and
mitigates the conservativeness that the decisions of DRO problems over such
ambiguity sets may face. We establish statistical guarantees for these
structured ambiguity sets and provide dual reformulations of their associated
DRO problems for a wide range of objective functions. The benefits of the
approach are demonstrated in a numerical example
- …