Optimal Transport with Adaptive Regularisation

• URL: http://arxiv.org/abs/2310.02925v1
• Date: Wed, 4 Oct 2023 16:05:36 GMT
• Title: Optimal Transport with Adaptive Regularisation
• Authors: Hugues Van Assel, Titouan Vayer, Remi Flamary, Nicolas Courty
• Abstract summary: Regularising the primal formulation of optimal transport (OT) with a strictly convex term leads to enhanced numerical complexity and a denser transport plan. We introduce OT with Adaptive RegularIsation (OTARI), a new formulation of OT that imposes constraints on the mass going in or/and out of each point.
• Score: 14.919246099820548
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 by relying on entropic regularisation. As it is more expensive to diffuse mass for outlier points compared to central ones, this typically results in a significant imbalance in the way mass is spread across the points. This can be detrimental for some applications where a minimum of smoothing is required per point. To remedy this, we introduce OT with Adaptive RegularIsation (OTARI), a new formulation of OT that imposes constraints on the mass going in or/and out of each point. We then showcase the benefits of this approach for domain adaptation.

Related papers

• Expected Sliced Transport Plans [9.33181953215826]
  We propose a "lifting" operation to extend one-dimensional optimal transport plans back to the original space of the measures. We prove that using the EST plan to weight the sum of the individual Euclidean costs for moving from one point to another results in a valid metric between the input discrete probability measures.
  arXiv  Detail & Related papers  (2024-10-16T02:44:36Z)
• SIGMA: Scale-Invariant Global Sparse Shape Matching [50.385414715675076]
  We propose a novel mixed-integer programming (MIP) formulation for generating precise sparse correspondences for non-rigid shapes. We show state-of-the-art results for sparse non-rigid matching on several challenging 3D datasets.
  arXiv  Detail & Related papers  (2023-08-16T14:25:30Z)
• Keypoint-Guided Optimal Transport [85.396726225935]
  We propose a novel KeyPoint-Guided model by ReLation preservation (KPG-RL) that searches for the optimal matching. The proposed KPG-RL model can be solved by Sinkhorn's algorithm and is applicable even when distributions are supported in different spaces. Based on the learned transport plan from dual KPG-RL, we propose a novel manifold barycentric projection to transport source data to the target domain.
  arXiv  Detail & Related papers  (2023-03-23T08:35:56Z)
• Instance-Dependent Generalization Bounds via Optimal Transport [51.71650746285469]
  Existing generalization bounds fail to explain crucial factors that drive the generalization of modern neural networks. We derive instance-dependent generalization bounds that depend on the local Lipschitz regularity of the learned prediction function in the data space. We empirically analyze our generalization bounds for neural networks, showing that the bound values are meaningful and capture the effect of popular regularization methods during training.
  arXiv  Detail & Related papers  (2022-11-02T16:39:42Z)
• InfoOT: Information Maximizing Optimal Transport [58.72713603244467]
  InfoOT is an information-theoretic extension of optimal transport. It maximizes the mutual information between domains while minimizing geometric distances. This formulation yields a new projection method that is robust to outliers and generalizes to unseen samples.
  arXiv  Detail & Related papers  (2022-10-06T18:55:41Z)
• Low-rank Optimal Transport: Approximation, Statistics and Debiasing [51.50788603386766]
  Low-rank optimal transport (LOT) approach advocated in citescetbon 2021lowrank LOT is seen as a legitimate contender to entropic regularization when compared on properties of interest. We target each of these areas in this paper in order to cement the impact of low-rank approaches in computational OT.
  arXiv  Detail & Related papers  (2022-05-24T20:51:37Z)
• Approximating Optimal Transport via Low-rank and Sparse Factorization [19.808887459724893]
  Optimal transport (OT) naturally arises in a wide range of machine learning applications but may often become the computational bottleneck. A novel approximation for OT is proposed, in which the transport plan can be decomposed into the sum of a low-rank matrix and a sparse one.
  arXiv  Detail & Related papers  (2021-11-12T03:10:45Z)
• STORM+: Fully Adaptive SGD with Momentum for Nonconvex Optimization [74.1615979057429]
  We investigate non-batch optimization problems where the objective is an expectation over smooth loss functions. Our work builds on the STORM algorithm, in conjunction with a novel approach to adaptively set the learning rate and momentum parameters.
  arXiv  Detail & Related papers  (2021-11-01T15:43:36Z)
• On the Convergence of Projected Alternating Maximization for Equitable and Optimal Transport [36.97843660480747]
  This paper studies the equitable and optimal transport (EOT) problem, which has many applications. In the discrete distributions case, the EOT problem can be formulated as a linear program (LP) Since this LP is prohibitively large for general solvers, Scetbon etal citescetbonequitable suggests to perturb the problem by adding an entropy regularization. They proposed a projected alternating algorithm (PAM) to solve the dual of the entropy regularized EOT.
  arXiv  Detail & Related papers  (2021-09-29T04:32:06Z)
• Estimation of Stationary Optimal Transport Plans [4.662321040754878]
  We study optimal transport problems in which finite-valued quantities evolve dynamically over time in a stationary fashion. We introduce estimators of both optimal joinings and the optimal joining cost. We extend the consistency and rate analysis to an entropy-penalized version of the optimal joining problem.
  arXiv  Detail & Related papers  (2021-07-25T17:46:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.