Partial Wasserstein Covering

• URL: http://arxiv.org/abs/2106.00886v1
• Date: Wed, 2 Jun 2021 01:48:41 GMT
• Title: Partial Wasserstein Covering
• Authors: Keisuke Kawano, Satoshi Koide, Keisuke Otaki
• Abstract summary: We consider a general task called partial Wasserstein covering with the goal of emulating a large dataset. We model this problem as a discrete optimization problem with partial Wasserstein divergence as an objective function. We show that we can efficiently make two datasets similar in terms of partial Wasserstein divergence, including driving scene datasets.
• Score: 10.52782170493037
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider a general task called partial Wasserstein covering with the goal of emulating a large dataset (e.g., application dataset) using a small dataset (e.g., development dataset) in terms of the empirical distribution by selecting a small subset from a candidate dataset and adding it to the small dataset. We model this task as a discrete optimization problem with partial Wasserstein divergence as an objective function. Although this problem is NP-hard, we prove that it has the submodular property, allowing us to use a greedy algorithm with a 0.63 approximation. However, the greedy algorithm is still inefficient because it requires linear programming for each objective function evaluation. To overcome this difficulty, we propose quasi-greedy algorithms for acceleration, which consist of a series of techniques such as sensitivity analysis based on strong duality and the so-called $C$-transform in the optimal transport field. Experimentally, we demonstrate that we can efficiently make two datasets similar in terms of partial Wasserstein divergence, including driving scene datasets.

Related papers

• Linearized Wasserstein dimensionality reduction with approximation guarantees [65.16758672591365]
  LOT Wassmap is a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. We show that LOT Wassmap attains correct embeddings and that the quality improves with increased sample size. We also show how LOT Wassmap significantly reduces the computational cost when compared to algorithms that depend on pairwise distance computations.
  arXiv  Detail & Related papers  (2023-02-14T22:12:16Z)
• Condensing Graphs via One-Step Gradient Matching [50.07587238142548]
  We propose a one-step gradient matching scheme, which performs gradient matching for only one single step without training the network weights. Our theoretical analysis shows this strategy can generate synthetic graphs that lead to lower classification loss on real graphs. In particular, we are able to reduce the dataset size by 90% while approximating up to 98% of the original performance.
  arXiv  Detail & Related papers  (2022-06-15T18:20:01Z)
• Low Budget Active Learning via Wasserstein Distance: An Integer Programming Approach [81.19737119343438]
  Active learning is the process of training a model with limited labeled data by selecting a core subset of an unlabeled data pool to label. We propose a new integer optimization problem for selecting a core set that minimizes the discrete Wasserstein distance from the unlabeled pool. Our strategy requires high-quality latent features which we obtain by unsupervised learning on the unlabeled pool.
  arXiv  Detail & Related papers  (2021-06-05T21:25:03Z)
• Projection Robust Wasserstein Barycenter [36.97843660480747]
  approximating the Wasserstein barycenter is numerically challenging because of the curse of dimensionality. This paper proposes the projection robust Wasserstein barycenter (PRWB) that mitigates the curse of dimensionality.
  arXiv  Detail & Related papers  (2021-02-05T19:23:35Z)
• Learning High Dimensional Wasserstein Geodesics [55.086626708837635]
  We propose a new formulation and learning strategy for computing the Wasserstein geodesic between two probability distributions in high dimensions. By applying the method of Lagrange multipliers to the dynamic formulation of the optimal transport (OT) problem, we derive a minimax problem whose saddle point is the Wasserstein geodesic. We then parametrize the functions by deep neural networks and design a sample based bidirectional learning algorithm for training.
  arXiv  Detail & Related papers  (2021-02-05T04:25:28Z)
• Sparse PCA via $l_{2,p}$-Norm Regularization for Unsupervised Feature Selection [138.97647716793333]
  We propose a simple and efficient unsupervised feature selection method, by combining reconstruction error with $l_2,p$-norm regularization. We present an efficient optimization algorithm to solve the proposed unsupervised model, and analyse the convergence and computational complexity of the algorithm theoretically.
  arXiv  Detail & Related papers  (2020-12-29T04:08:38Z)
• A Riemannian Block Coordinate Descent Method for Computing the Projection Robust Wasserstein Distance [36.97843660480747]
  The Wasserstein distance has become increasingly important in machine learning and deep learning. A recently proposed approach to alleviate the curse of dimensionality is to project the sampled data onto a lower-dimensional subspace, and then compute the Wasserstein distance between the projected data. However, this approach requires to solve a max-min problem over the Stiefel manifold, which is very challenging in practice. We propose a novel block coordinate descent (RBCD) method to solve this problem, which is based on a novel reformulation of the regularized max-min problem over the Stiefel manifold.
  arXiv  Detail & Related papers  (2020-12-09T17:47:56Z)
• Wasserstein k-means with sparse simplex projection [20.661025590877774]
  This paper presents a proposal of a faster Wasserstein $k$-means algorithm for histogram data. We shrink data samples, centroids, and the ground cost matrix. We harness sparse simplex projection while keeping the degradation of clustering quality lower.
  arXiv  Detail & Related papers  (2020-11-25T06:37:45Z)
• Online Model Selection for Reinforcement Learning with Function Approximation [50.008542459050155]
  We present a meta-algorithm that adapts to the optimal complexity with $tildeO(L5/6 T2/3)$ regret. We also show that the meta-algorithm automatically admits significantly improved instance-dependent regret bounds.
  arXiv  Detail & Related papers  (2020-11-19T10:00:54Z)
• Stochastic Optimization for Regularized Wasserstein Estimators [10.194798773447879]
  We introduce an algorithm to solve a regularized version of the problem of Wasserstein estimators gradient, with a time per step which is sublinear in the natural dimensions. We show that this algorithm can be extended to other tasks, including estimation of Wasserstein barycenters.
  arXiv  Detail & Related papers  (2020-02-20T12:04:05Z)

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.