相关论文: Streaming Sliced Optimal Transport

We investigate the semi-discrete Optimal Transport (OT) problem, where a continuous source measure $\mu$ is transported to a discrete target measure $\nu$, with particular attention to the OT map approximation. In this setting, Stochastic…

Solving large scale Optimal Transport (OT) in machine learning typically relies on sampling measures to obtain a tractable discrete problem. While the discrete solver's accuracy is controllable, the rate of convergence of the discretization…

The problem of learning functions over spaces of probabilities - or distribution regression - is gaining significant interest in the machine learning community. A key challenge behind this problem is to identify a suitable representation…

Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…

Stochastic Gradient Descent (SGD) is one of the most widely used techniques for online optimization in machine learning. In this work, we accelerate SGD by adaptively learning how to sample the most useful training examples at each time…

The Wasserstein distance has been an attractive tool in many fields. But due to its high computational complexity and the phenomenon of the curse of dimensionality in empirical estimation, various extensions of the Wasserstein distance have…

Dataset Distillation (DD) aims to generate a compact synthetic dataset that enables models to achieve performance comparable to training on the full large dataset, significantly reducing computational costs. Drawing from optimal transport…

Wasserstein distance, which measures the discrepancy between distributions, shows efficacy in various types of natural language processing (NLP) and computer vision (CV) applications. One of the challenges in estimating Wasserstein distance…

Existing tensor factorization methods assume that the input tensor follows some specific distribution (i.e. Poisson, Bernoulli, and Gaussian), and solve the factorization by minimizing some empirical loss functions defined based on the…

We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…

The Wasserstein distance, rooted in optimal transport (OT) theory, is a popular discrepancy measure between probability distributions with various applications to statistics and machine learning. Despite their rich structure and…

The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…

We study streaming algorithms for two fundamental geometric problems: computing the cost of a Minimum Spanning Tree (MST) of an $n$-point set $X \subset \{1,2,\dots,\Delta\}^d$, and computing the Earth Mover Distance (EMD) between two…

We introduce the Gaussian transform (GT), an optimal transport inspired iterative method for denoising and enhancing latent structures in datasets. Under the hood, GT generates a new distance function (GT distance) on a given dataset by…

We present a novel inference approach that we call Sample Out-of-Sample (or SOS) inference. The approach can be used widely, ranging from semi-supervised learning to stress testing, and it is fundamental in the application of data-driven…

This paper proposes a data-driven distributionally robust shortest path (DRSP) model where the distribution of the travel time in the transportation network can only be partially observed through a finite number of samples. Specifically, we…

This paper introduces Memory-limited Online Subspace Estimation Scheme (MOSES) for both estimating the principal components of streaming data and reducing its dimension. More specifically, in various applications such as sensor networks,…

Streaming algorithms are generally judged by the quality of their solution, memory footprint, and computational complexity. In this paper, we study the problem of maximizing a monotone submodular function in the streaming setting with a…

Projection robust Wasserstein (PRW) distance, or Wasserstein projection pursuit (WPP), is a robust variant of the Wasserstein distance. Recent work suggests that this quantity is more robust than the standard Wasserstein distance, in…

Efficiently aggregating data from different sources is a challenging problem, particularly when samples from each source are distributed differently. These differences can be inherent to the inference task or present for other reasons:…