Related papers: Exploring Wasserstein Distance across Concept Embe…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
In recent years, word embeddings have been widely used to measure biases in texts. Even if they have proven to be effective in detecting a wide variety of biases, metrics based on word embeddings lack transparency and interpretability. We…
Although there is an emerging trend towards generating embeddings for primarily unstructured data and, recently, for structured data, no systematic suite for measuring the quality of embeddings has been proposed yet. This deficiency is…
Word embeddings are a popular way to improve downstream performances in contemporary language modeling. However, the underlying geometric structure of the embedding space is not well understood. We present a series of explorations using…
Ontologies form the basic interest in various computer science disciplines such as semantic web, information retrieval, database design, etc. They aim at providing a formal, explicit and shared conceptualization and understanding of common…
In this work several semantic approaches to concept-based query expansion and reranking schemes are studied and compared with different ontology-based expansion methods in web document search and retrieval. In particular, we focus on…
We study a class of quadratic Wasserstein distances on spaces consisting of generalized dynamical systems on a von Neumann algebra. We emphasize how symmetry of such a Wasserstein distance arises, but also study the asymmetric case. This…
The Weisfeiler-Lehman (WL) test is a widely used algorithm in graph machine learning, including graph kernels, graph metrics, and graph neural networks. However, it focuses only on the consistency of the graph, which means that it is unable…
Word embeddings are effective intermediate representations for capturing semantic regularities between words, when learning the representations of text sequences. We propose to view text classification as a label-word joint embedding…
Wasserstein metrics are increasingly being used as similarity scores for images treated as discrete measures on a grid, yet their behavior under noise remains poorly understood. In this work, we consider the sensitivity of the signed…
We consider the problem of finding plausible knowledge that is missing from a given ontology, as a generalisation of the well-studied taxonomy expansion task. One line of work treats this task as a Natural Language Inference (NLI) problem,…
We advocate the use of a notion of entropy that reflects the relative abundances of the symbols in an alphabet, as well as the similarities between them. This concept was originally introduced in theoretical ecology to study the diversity…
In the field of ontology matching, the most systematic evaluation of matching systems is established by the Ontology Alignment Evaluation Initiative (OAEI), which is an annual campaign for evaluating ontology matching systems organized by…
Wasserstein distances provide a metric on a space of probability measures. We consider the space $\Omega$ of all probability measures on the finite set $\chi = \{1, \dots ,n\}$ where $n$ is a positive integer. 1-Wasserstein distance,…
Network embeddings, which learn low-dimensional representations for each vertex in a large-scale network, have received considerable attention in recent years. For a wide range of applications, vertices in a network are typically…
Compositionality in language refers to how much the meaning of some phrase can be decomposed into the meaning of its constituents and the way these constituents are combined. Based on the premise that substitution by synonyms is…
Optimal transport provides a powerful mathematical framework with applications spanning numerous fields. A cornerstone within this domain is the $p$-Wasserstein distance, which serves to quantify the cost of transporting one probability…
The paper proposes a computationally feasible method for measuring context-sensitive semantic distance between words. The distance is computed by adaptive scaling of a semantic space. In the semantic space, each word in the vocabulary V is…
Text-to-pattern distance is a fundamental problem in string matching, where given a pattern of length $m$ and a text of length $n$, over an integer alphabet, we are asked to compute the distance between pattern and the text at every…
The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…