Related papers: Learning Embeddings into Entropic Wasserstein Spac…

While word embeddings have been shown to implicitly encode various forms of attributional knowledge, the extent to which they capture relational information is far more limited. In previous work, this limitation has been addressed by…

Distributional semantic models capture word-level meaning that is useful in many natural language processing tasks and have even been shown to capture cognitive aspects of word meaning. The majority of these models are purely text based,…

Word embeddings represent a transformative technology for analyzing text data in social work research, offering sophisticated tools for understanding case notes, policy documents, research literature, and other text-based materials. This…

The practical applications of Wasserstein distances (WDs) are constrained by their sample and computational complexities. Sliced-Wasserstein distances (SWDs) provide a workaround by projecting distributions onto one-dimensional subspaces,…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

In this paper we study supervised learning tasks on the space of probability measures. We approach this problem by embedding the space of probability measures into $L^2$ spaces using the optimal transport framework. In the embedding spaces,…

Empirical data can often be considered as samples from a set of probability distributions. Kernel methods have emerged as a natural approach for learning to classify these distributions. Although numerous kernels between distributions have…

Most existing word embedding approaches do not distinguish the same words in different contexts, therefore ignoring their contextual meanings. As a result, the learned embeddings of these words are usually a mixture of multiple meanings. In…

Machine learning, deep learning, and NLP methods on knowledge graphs are present in different fields and have important roles in various domains from self-driving cars to friend recommendations on social media platforms. However, to apply…

Probabilistic embeddings have several advantages over deterministic embeddings as they map each data point to a distribution, which better describes the uncertainty and complexity of data. Many works focus on adjusting the distribution…

Datasets with non-trivial large scale topology can be hard to embed in low-dimensional Euclidean space with existing dimensionality reduction algorithms. We propose to model topologically complex datasets using vector bundles, in such a way…

Representation learning is a fundamental building block for analyzing entities in a database. While the existing embedding learning methods are effective in various data mining problems, their applicability is often limited because these…

Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified…

Traditional neural embeddings represent concepts as points, excelling at similarity but struggling with higher-level reasoning and asymmetric relationships. We introduce a novel paradigm: embedding concepts as linear subspaces. This…

Relational representation learning transforms relational data into continuous and low-dimensional vector representations. However, vector-based representations fall short in capturing crucial properties of relational data that are complex…

We introduce principal curves in Wasserstein space, and in general compact metric spaces. Our motivation for the Wasserstein case comes from optimal-transport-based trajectory inference, where a developing population of cells traces out a…

Word embeddings improve the performance of NLP systems by revealing the hidden structural relationships between words. Despite their success in many applications, word embeddings have seen very little use in computational social science NLP…

In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global nonlinear dimensionality reduction algorithms in imaging…

We present an unsupervised approach for discovering semantic representations of mathematical equations. Equations are challenging to analyze because each is unique, or nearly unique. Our method, which we call equation embeddings, finds good…

We present a new technique called "DSNE" which learns the velocity embeddings of low dimensional map points when given the high-dimensional data points with its velocities. The technique is a variation of Stochastic Neighbor Embedding,…