相关论文: Low-Rank Optimal Transport through Factor Relaxati…
Regularising the primal formulation of optimal transport (OT) with a strictly convex term leads to enhanced numerical complexity and a denser transport plan. Many formulations impose a global constraint on the transport plan, for instance…
Low-rank model compression is a widely used technique for reducing the computational load when training machine learning models. However, existing methods often rely on relaxing the low-rank constraint of the model weights using a…
Learning to align multiple datasets is an important problem with many applications, and it is especially useful when we need to integrate multiple experiments or correct for confounding. Optimal transport (OT) is a principled approach to…
This paper introduces a framework that utilizes the Safe Screening technique to accelerate the optimization process of the Unbalanced Optimal Transport (UOT) problem by proactively identifying and eliminating zero elements in the sparse…
Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision. The core assumption in the OT problem is the equal total amount of mass in source and target measures, which limits its…
We introduce optimal transport (OT) as a physics-based intermediate event representation for weakly supervised anomaly detection. With only $0.5\%$ injection of resonant signals in the LHC Olympics benchmark datasets, the OT-augmented…
\textbf{Motivation:} Predicting single-cell perturbation responses requires mapping between two unpaired single-cell data distributions. Optimal transport (OT) theory provides a principled framework for constructing such mappings by…
The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…
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…
The nonlinear filtering problem is concerned with finding the conditional probability distribution (posterior) of the state of a stochastic dynamical system, given a history of partial and noisy observations. This paper presents a…
Optimal transport (OT) formalizes the problem of finding an optimal coupling between probability measures given a cost matrix. The inverse problem of inferring the cost given a coupling is Inverse Optimal Transport (IOT). IOT is less well…
Optimal transport (OT) has an important role in transforming data distributions in a manner which engenders fairness. Typically, the OT operators are learnt from the unfair attribute-labelled data, and then used for their repair. Two…
The optimal transport (OT) problem has gained significant traction in modern machine learning for its ability to: (1) provide versatile metrics, such as Wasserstein distances and their variants, and (2) determine optimal couplings between…
Optimal Transport (OT) has proven effective for domain adaptation (DA) by aligning distributions across domains with differing statistical properties. Building on the approach of Courty et al. (2016), who mapped source data to the target…
We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, allowing efficient…
Conditional Optimal Transport (COT) problem aims to find a transport map between conditional source and target distributions while minimizing the transport cost. Recently, these transport maps have been utilized in conditional generative…
It is well known that optimal transport suffers from the curse of dimensionality: when the prescribed marginals are approximated by i.i.d. samples, the convergence of the empirical optimal transport problem to the population counterpart…
Although deep neural networks are well-known for their outstanding performance in tackling complex tasks, their hunger for computational resources remains a significant hurdle, posing energy-consumption issues and restricting their…
Factor graphs are graphical models used to represent a wide variety of problems across robotics, such as Structure from Motion (SfM), Simultaneous Localization and Mapping (SLAM) and calibration. Typically, at their core, they have an…
This paper discusses the efficiency of Hybrid Primal-Dual (HPD) type algorithms to approximate solve discrete Optimal Transport (OT) and Wasserstein Barycenter (WB) problems, with and without entropic regularization. Our first contribution…