Related papers: Hierarchical Optimal Transport for Document Repres…
We investigate the estimation of an optimal transport map between probability measures on an infinite-dimensional space and reveal its minimax optimal rate. Optimal transport theory defines distances within a space of probability measures,…
Optimal Transport (OT) naturally arises in many machine learning applications, yet the heavy computational burden limits its wide-spread uses. To address the scalability issue, we propose an implicit generative learning-based framework…
Word Mover's Distance (WMD) computes the distance between words and models text similarity with the moving cost between words in two text sequences. Yet, it does not offer good performance in sentence similarity evaluation since it does not…
Recently, finetuning a pretrained language model to capture the similarity between sentence embeddings has shown the state-of-the-art performance on the semantic textual similarity (STS) task. However, the absence of an interpretation…
Textual documents are commonly connected in a hierarchical graph structure where a central document links to others with an exponentially growing connectivity. Though Hyperbolic Graph Neural Networks (HGNNs) excel at capturing such graph…
Transformer architectures are increasingly effective at processing and generating very long chunks of texts, opening new perspectives for document-level machine translation (MT). In this work, we challenge the ability of MT systems to…
Document similarity is the problem of estimating the degree to which a given pair of documents has similar semantic content. An accurate document similarity measure can improve several enterprise relevant tasks such as document clustering,…
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…
Efficient comparison of spherical probability distributions becomes important in fields such as computer vision, geosciences, and medicine. Sliced optimal transport distances, such as spherical and stereographic spherical sliced Wasserstein…
Optimal transport has been an essential tool for reconstructing dynamics from complex data. With the increasingly available multifaceted data, a system can often be characterized across multiple spaces. Therefore, it is crucial to maintain…
Optimal transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it…
We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\mu$ on $\mathcal{X} \subset \mathbb{R}^d$ and a finitely supported measure $\nu$ on $\mathbb{R}^d$ when the transport cost is the…
Measuring the semantic similarity between two sentences is still an important task. The word mover's distance (WMD) computes the similarity via the optimal alignment between the sets of word embeddings. However, WMD does not utilize word…
Medical multi-document summarization (MDS) is a complex task that requires effectively managing cross-document relationships. This paper investigates whether incorporating hierarchical structures in the inputs of MDS can improve a model's…
We present a 2-step optimal transport approach that performs a mapping from a source distribution to a target distribution. Here, the target has the particularity to present new classes not present in the source domain. The first step of…
We present a theoretical framework for a stereo vision method via optimal transport tools. We consider two aligned optical systems and we develop the matching between the two pictures line by line. By considering a regularized version of…
We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal…
We introduce sliced optimal transport dataset distance (s-OTDD), a model-agnostic, embedding-agnostic approach for dataset comparison that requires no training, is robust to variations in the number of classes, and can handle disjoint label…
We consider the problem of learning distributed representations for documents in data streams. The documents are represented as low-dimensional vectors and are jointly learned with distributed vector representations of word tokens using a…
The ability to mimic human notions of semantic distance has widespread applications. Some measures rely only on raw text (distributional measures) and some rely on knowledge sources such as WordNet. Although extensive studies have been…