Related papers: Hierarchical Optimal Transport for Document Repres…
A topic model is often formulated as a generative model that explains how each word of a document is generated given a set of topics and document-specific topic proportions. It is focused on capturing the word co-occurrences in a document…
Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground…
Top-K queries are an established heuristic in information retrieval. This paper presents an approach for optimal tiered storage allocation under stream processing workloads using this heuristic: those requiring the analysis of only the…
The number of documents available into Internet moves each day up. For this reason, processing this amount of information effectively and expressibly becomes a major concern for companies and scientists. Methods that represent a textual…
We present a novel neural-networks-based algorithm to compute optimal transport maps and plans for strong and weak transport costs. To justify the usage of neural networks, we prove that they are universal approximators of transport plans…
We compare several approaches to learn an Optimal Map, represented as a neural network, between probability distributions. The approaches fall into two categories: ``Heuristics'' and approaches with a more sound mathematical justification,…
The graph parameters highway dimension and skeleton dimension were introduced to capture the properties of transportation networks. As many important optimization problems like Travelling Salesperson, Steiner Tree or $k$-Center arise in…
Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and…
Machine learning (ML) techniques have recently enabled enormous gains in sensitivity to new phenomena across the sciences. In particle physics, much of this progress has relied on excellent simulations of a wide range of physical processes.…
This work is about the use of regularized optimal-transport distances for convex, histogram-based image segmentation. In the considered framework, fixed exemplar histograms define a prior on the statistical features of the two regions in…
Measuring similarity between texts is an important task for several applications. Available approaches to measure document similarity are inadequate for document pairs that have non-comparable lengths, such as a long document and its…
To remedy the drawbacks of full-mass or fixed-mass constraints in classical optimal transport, we propose adaptive optimal transport which is distinctive from the classical optimal transport in its ability of adaptive-mass preserving. It…
Hypergraphs capture multi-way relationships in data, and they have consequently seen a number of applications in higher-order network analysis, computer vision, geometry processing, and machine learning. In this paper, we develop…
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…
We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…
We develop the relational topic model (RTM), a hierarchical model of both network structure and node attributes. We focus on document networks, where the attributes of each document are its words, that is, discrete observations taken from a…
The optimal transport problem has many applications in machine learning, physics, biology, economics, etc. Although its goal is very clear and mathematically well-defined, finding its optimal solution can be challenging for large datasets…
Optimal Transport is a popular distance metric for measuring similarity between distributions. Exact algorithms for computing Optimal Transport can be slow, which has motivated the development of approximate numerical solvers (e.g. Sinkhorn…
We describe a new method for summarizing similarities and differences in a pair of related documents using a graph representation for text. Concepts denoted by words, phrases, and proper names in the document are represented positionally as…
While the celebrated Word2Vec technique yields semantically rich representations for individual words, there has been relatively less success in extending to generate unsupervised sentences or documents embeddings. Recent work has…