Making transport more robust and interpretable by moving data through a small number of anchor points

• URL: http://arxiv.org/abs/2012.11589v2
• Date: Fri, 12 Feb 2021 00:44:15 GMT
• Title: Making transport more robust and interpretable by moving data through a small number of anchor points
• Authors: Chi-Heng Lin, Mehdi Azabou, Eva L. Dyer
• Abstract summary: We introduce a new form of structured OT that simultaneously learns low-dimensional structure in data while leveraging this structure to solve the alignment task. Compared with OT, the resulting transport plan has better structural interpretability, highlighting the connections between individual data points and local geometry. We show that our method can facilitate alignment in noisy settings and can be used to both correct and interpret domain shift.
• Score: 4.262693522975888
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Optimal transport (OT) is a widely used technique for distribution alignment, with applications throughout the machine learning, graphics, and vision communities. Without any additional structural assumptions on trans-port, however, OT can be fragile to outliers or noise, especially in high dimensions. Here, we introduce a new form of structured OT that simultaneously learns low-dimensional structure in data while leveraging this structure to solve the alignment task. Compared with OT, the resulting transport plan has better structural interpretability, highlighting the connections between individual data points and local geometry, and is more robust to noise and sampling. We apply the method to synthetic as well as real datasets, where we show that our method can facilitate alignment in noisy settings and can be used to both correct and interpret domain shift.

Related papers

• Into the Unknown: Generating Geospatial Descriptions for New Environments [18.736071151303726]
  Rendezvous task requires reasoning over allocentric spatial relationships. Using opensource descriptions paired with coordinates (e.g., Wikipedia) provides training data but suffers from limited spatially-oriented text. We propose a large-scale augmentation method for generating high-quality synthetic data for new environments.
  arXiv  Detail & Related papers  (2024-06-28T14:56:21Z)
• Integrating Efficient Optimal Transport and Functional Maps For Unsupervised Shape Correspondence Learning [43.6925865296259]
  We present an unsupervised shape matching framework that integrates functional map regularizers with a novel OT-based loss derived from SWD. We also introduce an adaptive refinement process utilizing entropy regularized OT, further refining feature alignments for accurate point-to-point correspondences. Our method demonstrates superior performance in non-rigid shape matching, including near-isometric and non-isometric scenarios.
  arXiv  Detail & Related papers  (2024-03-04T07:21:07Z)
• 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)
• Beyond Transfer Learning: Co-finetuning for Action Localisation [64.07196901012153]
  We propose co-finetuning -- simultaneously training a single model on multiple upstream'' and downstream'' tasks. We demonstrate that co-finetuning outperforms traditional transfer learning when using the same total amount of data. We also show how we can easily extend our approach to multiple upstream'' datasets to further improve performance.
  arXiv  Detail & Related papers  (2022-07-08T10:25:47Z)
• Bi-level Alignment for Cross-Domain Crowd Counting [113.78303285148041]
  Current methods rely on external data for training an auxiliary task or apply an expensive coarse-to-fine estimation. We develop a new adversarial learning based method, which is simple and efficient to apply. We evaluate our approach on five real-world crowd counting benchmarks, where we outperform existing approaches by a large margin.
  arXiv  Detail & Related papers  (2022-05-12T02:23:25Z)
• Bending Graphs: Hierarchical Shape Matching using Gated Optimal Transport [80.64516377977183]
  Shape matching has been a long-studied problem for the computer graphics and vision community. We investigate a hierarchical learning design, to which we incorporate local patch-level information and global shape-level structures. We propose a novel optimal transport solver by recurrently updating features on non-confident nodes to learn globally consistent correspondences between the shapes.
  arXiv  Detail & Related papers  (2022-02-03T11:41:46Z)
• Towards a comprehensive visualization of structure in data [0.0]
  We show that a simplified parameter setup with a single control parameter, namely the perplexity, can effectively balance local and global data structure visualization. We also designed a chunk&mix protocol to efficiently parallelize t-SNE and explore data structure across a much wide range of scales.
  arXiv  Detail & Related papers  (2021-11-30T15:43:45Z)
• FLOT: Scene Flow on Point Clouds Guided by Optimal Transport [82.86743909483312]
  We propose and study a method called FLOT that estimates scene flow on point clouds. Inspired by recent works on graph matching, we build a method to find these correspondences by borrowing tools from optimal transport. Our main finding is that FLOT can perform as well as the best existing methods on synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2020-07-22T00:15:30Z)
• A Trainable Optimal Transport Embedding for Feature Aggregation and its Relationship to Attention [96.77554122595578]
  We introduce a parametrized representation of fixed size, which embeds and then aggregates elements from a given input set according to the optimal transport plan between the set and a trainable reference. Our approach scales to large datasets and allows end-to-end training of the reference, while also providing a simple unsupervised learning mechanism with small computational cost.
  arXiv  Detail & Related papers  (2020-06-22T08:35:58Z)
• Geometric Dataset Distances via Optimal Transport [15.153110906331733]
  We propose an alternative notion of distance between datasets that (i) is model-agnostic, (ii) does not involve training, (iii) can compare datasets even if their label sets are completely disjoint and (iv) has solid theoretical footing. This distance relies on optimal transport, which provides it with rich geometry awareness, interpretable correspondences and well-understood properties. Our results show that this novel distance provides meaningful comparison of datasets, and correlates well with transfer learning hardness across various experimental settings and datasets.
  arXiv  Detail & Related papers  (2020-02-07T17:51:26Z)

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.