Related papers: Differentiable Ranks and Sorting using Optimal Tra…
The sorting operation is one of the most commonly used building blocks in computer programming. In machine learning, it is often used for robust statistics. However, seen as a function, it is piecewise linear and as a result includes many…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…
The top-k operation, i.e., finding the k largest or smallest elements from a collection of scores, is an important model component, which is widely used in information retrieval, machine learning, and data mining. However, if the top-k…
Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal…
Sorting and ranking supervision is a method for training neural networks end-to-end based on ordering constraints. That is, the ground truth order of sets of samples is known, while their absolute values remain unsupervised. For that, we…
Several recent applications of optimal transport (OT) theory to machine learning have relied on regularization, notably entropy and the Sinkhorn algorithm. Because matrix-vector products are pervasive in the Sinkhorn algorithm, several…
Optimal Transport (OT) has established itself as a robust framework for quantifying differences between distributions, with applications that span fields such as machine learning, data science, and computer vision. This paper offers a…
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in its solution. In particular, the OT problem defines a…
In many machine learning applications, it is necessary to meaningfully aggregate, through alignment, different but related datasets. Optimal transport (OT)-based approaches pose alignment as a divergence minimization problem: the aim is to…
Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning. However, computing discrete optimal transport plan for large scale problems with adequate accuracy and efficiency is still highly…
In past work on fairness in machine learning, the focus has been on forcing the prediction of classifiers to have similar statistical properties for people of different demographics. To reduce the violation of these properties, fairness…
Cascade ranking is a widely adopted paradigm in large-scale information retrieval systems for Top-K item selection. However, the Top-K operator is non-differentiable, hindering end-to-end training. Existing methods include Learning-to-Rank…
Optimal transport (OT) aims to find a map $T$ that transports mass from one probability measure to another while minimizing a cost function. Recently, neural OT solvers have gained popularity in high dimensional biological applications such…
Optimal transport (OT) has enjoyed great success in machine learning as a principled way to align datasets via a least-cost correspondence, driven in large part by the runtime efficiency of the Sinkhorn algorithm (Cuturi, 2013). However,…
Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…
The matching principles behind optimal transport (OT) play an increasingly important role in machine learning, a trend which can be observed when OT is used to disambiguate datasets in applications (e.g. single-cell genomics) or used to…
We consider statistical learning problems in which data are observed as a set of probability measures. Optimal transport (OT) is a popular tool to compare and manipulate such objects, but its computational cost becomes prohibitive when the…
Low rank matrix factorization is a fundamental building block in machine learning, used for instance to summarize gene expression profile data or word-document counts. To be robust to outliers and differences in scale across features, a…
Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the…