相关论文: Data Assimilation for Sign-indefinite Priors: A ge…
By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…
\emph{Optimal Transport} (OT) has emerged as an important computational tool in machine learning and computer vision, providing a geometrical framework for studying probability measures. OT unfortunately suffers from the curse of…
The last decade has witnessed an explosion in the development of models, theory and computational algorithms for "big data" analysis. In particular, distributed computing has served as a natural and dominating paradigm for statistical…
We prove that the sequence of marginals obtained from the iterations of the Sinkhorn algorithm or the iterative proportional fitting procedure (IPFP) on joint densities, converges to an absolutely continuous curve on the $2$-Wasserstein…
It is of increasing importance to develop learning methods for ranking. In contrast to many learning objectives, however, the ranking problem presents difficulties due to the fact that the space of permutations is not smooth. In this paper,…
For a broad class of models widely used in practice for choice and ranking data based on Luce's choice axiom, including the Bradley--Terry--Luce and Plackett--Luce models, we show that the associated maximum likelihood estimation problems…
We propose a procedure for estimating the Schr\"odinger bridge between two probability distributions. Unlike existing approaches, our method does not require iteratively simulating forward and backward diffusions or training neural networks…
Despite the success of the popular kernelized support vector machines, they have two major limitations: they are restricted to Positive Semi-Definite (PSD) kernels, and their training complexity scales at least quadratically with the size…
Entropic regularization provides a generalization of the original optimal transport problem. It introduces a penalty term defined by the Kullback-Leibler divergence, making the problem more tractable via the celebrated Sinkhorn algorithm.…
In this work we propose a batch version of the Greenkhorn algorithm for multimarginal regularized optimal transport problems. Our framework is general enough to cover, as particular cases, some existing algorithms like Sinkhorn and…
The Sinkhorn "distance", a variant of the Wasserstein distance with entropic regularization, is an increasingly popular tool in machine learning and statistical inference. However, the time and memory requirements of standard algorithms for…
Sinkhorn's algorithm is a method of choice to solve large-scale optimal transport (OT) problems. In this context, it involves an inverse temperature parameter $\beta$ that determines the speed-accuracy trade-off. To improve this trade-off,…
We consider incremental inference problems from aggregate data for collective dynamics. In particular, we address the problem of estimating the aggregate marginals of a Markov chain from noisy aggregate observations in an incremental…
We introduce a novel discretization scheme for Wasserstein gradient flows that involves successively computing Schr\"{o}dinger bridges with the same marginals. This is different from both the forward/geodesic approximation and the…
Entropy regularized optimal transport and its multi-marginal generalization have attracted increasing attention in various applications, in particular due to efficient Sinkhorn-like algorithms for computing optimal transport plans. However,…
We consider the fundamental problem of sampling the optimal transport coupling between given source and target distributions. In certain cases, the optimal transport plan takes the form of a one-to-one mapping from the source support to the…
We study stability of optimizers and convergence of Sinkhorn's algorithm for the entropic optimal transport problem. In the special case of the quadratic cost, our stability bounds imply that if one of the two entropic potentials is…
We study large random matrices with i.i.d. entries conditioned to have prescribed row and column sums (margins), a problem connected to relative entropy minimization, Schr\"odinger bridges, contingency tables, and random graphs with given…
This paper proposes a general framework of Riemannian adaptive optimization methods. The framework encapsulates several stochastic optimization algorithms on Riemannian manifolds and incorporates the mini-batch strategy that is often used…
A common network inference problem, arising from real-world data constraints, is how to infer a dynamic network from its time-aggregated adjacency matrix and time-varying marginals (i.e., row and column sums). Prior approaches to this…