Related papers: Hierarchical Optimal Transport for Document Repres…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
Hierarchical topic modeling aims to discover latent topics from a corpus and organize them into a hierarchy to understand documents with desirable semantic granularity. However, existing work struggles with producing topic hierarchies of…
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) is a mathematical framework that first emerged in the eighteenth century and has led to a plethora of methods for answering many theoretical and applied questions. The last decade has been a witness to the remarkable…
Cross-domain alignment between image objects and text sequences is key to many visual-language tasks, and it poses a fundamental challenge to both computer vision and natural language processing. This paper investigates a novel approach for…
Semantic matching of natural language sentences or identifying the relationship between two sentences is a core research problem underlying many natural language tasks. Depending on whether training data is available, prior research has…
Traditional multi-view learning methods often rely on two assumptions: ($i$) the samples in different views are well-aligned, and ($ii$) their representations in latent space obey the same distribution. Unfortunately, these two assumptions…
A key principle in assessing textual similarity is measuring the degree of semantic overlap between two texts by considering the word alignment. Such alignment-based approaches are intuitive and interpretable; however, they are empirically…
In many unpaired image domain translation problems, e.g., style transfer or super-resolution, it is important to keep the translated image similar to its respective input image. We propose the extremal transport (ET) which is a mathematical…
As a fundamental problem of natural language processing, it is important to measure the distance between different documents. Among the existing methods, the Word Mover's Distance (WMD) has shown remarkable success in document semantic…
Word embeddings are high dimensional vector representations of words that capture their semantic similarity in the vector space. There exist several algorithms for learning such embeddings both for a single language as well as for several…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
We propose a new approach, Knowledge Distillation using Optimal Transport (KNOT), to distill the natural language semantic knowledge from multiple teacher networks to a student network. KNOT aims to train a (global) student model by…
Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to…
Topic models have evolved from conventional Bayesian probabilistic models to recent Neural Topic Models (NTMs). Although NTMs have shown promising performance when trained and tested on a specific corpus, their generalisation ability across…
Data summarization aims at utilizing a small-scale summary to represent massive datasets as a whole, which is useful for visualization and information sipped generation. However, most existing studies of hierarchical summarization only work…
We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may flow between vectorial entries as well as across space (discrete or continuous). The theory relies on a first step taken to…
To study discrimination in automated decision-making systems, scholars have proposed several definitions of fairness, each expressing a different fair ideal. These definitions require practitioners to make complex decisions regarding which…
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…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…